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  <front>
    <title abbrev="MLS">The Messaging Layer Security (MLS) Protocol</title>
    <seriesInfo name="Internet-Draft" value="draft-ietf-mls-protocol-17"/>
    <author initials="R." surname="Barnes" fullname="Richard Barnes">
      <organization>Cisco</organization>
      <address>
        <email>rlb@ipv.sx</email>
      </address>
    </author>
    <author initials="B." surname="Beurdouche" fullname="Benjamin Beurdouche">
      <organization>Inria &amp; Mozilla</organization>
      <address>
        <email>ietf@beurdouche.com</email>
      </address>
    </author>
    <author initials="R." surname="Robert" fullname="Raphael Robert">
      <organization>Phoenix R&amp;D</organization>
      <address>
        <email>ietf@raphaelrobert.com</email>
      </address>
    </author>
    <author initials="J." surname="Millican" fullname="Jon Millican">
      <organization>Meta Platforms</organization>
      <address>
        <email>jmillican@meta.com</email>
      </address>
    </author>
    <author initials="E." surname="Omara" fullname="Emad Omara">
      <organization>Google</organization>
      <address>
        <email>emadomara@google.com</email>
      </address>
    </author>
    <author initials="K." surname="Cohn-Gordon" fullname="Katriel Cohn-Gordon">
      <organization>University of Oxford</organization>
      <address>
        <email>me@katriel.co.uk</email>
      </address>
    </author>
    <date year="2022" month="December" day="19"/>
    <area>Security</area>
    <keyword>Internet-Draft</keyword>
    <abstract>
      <t>Messaging applications are increasingly making use of end-to-end
security mechanisms to ensure that messages are only accessible to
the communicating endpoints, and not to any servers involved in delivering
messages.  Establishing keys to provide such protections is
challenging for group chat settings, in which more than two
clients need to agree on a key but may not be online at the same
time.  In this document, we specify a key establishment
protocol that provides efficient asynchronous group key establishment
with forward secrecy and post-compromise security for groups
in size ranging from two to thousands.</t>
    </abstract>
    <note removeInRFC="true">
      <name>Discussion Venues</name>
      <t>Source for this draft and an issue tracker can be found at
  <eref target="https://github.com/mlswg/mls-protocol">https://github.com/mlswg/mls-protocol</eref>.</t>
    </note>
  </front>
  <middle>
    <section anchor="introduction">
      <name>Introduction</name>
      <t>RFC EDITOR: PLEASE REMOVE THE FOLLOWING PARAGRAPH The source for
this draft is maintained in GitHub. Suggested changes should be
submitted as pull requests at https://github.com/mlswg/mls-protocol.
Instructions are on that page as well. Editorial changes can be
managed in GitHub, but any substantive change should be discussed on
the MLS mailing list.</t>
      <t>A group of users who want to send each other encrypted messages needs
a way to derive shared symmetric encryption keys. For two parties,
this problem has been studied thoroughly, with the Double Ratchet
emerging as a common solution <xref target="DoubleRatchet"/> <xref target="Signal"/>.
Channels implementing the Double Ratchet enjoy fine-grained forward secrecy
as well as post-compromise security, but are nonetheless efficient
enough for heavy use over low-bandwidth networks.</t>
      <t>For a group of size greater than two, a common strategy is to
unilaterally broadcast symmetric "sender" keys over existing shared
symmetric channels, and then for each member to send messages to the
group encrypted with their own sender key. On the one hand, using sender keys
improves efficiency relative to pairwise broadcast of individual messages, and
it provides forward secrecy (with the addition of a hash ratchet).
On the other hand, it is difficult to achieve post-compromise security with
sender keys, requiring a number of key update messages that scales as the square
of the group size.
An adversary who learns a sender key can often indefinitely and
passively eavesdrop on that member's messages.  Generating and
distributing a new sender key provides a form of post-compromise
security with regard to that sender.  However, it requires
computation and communications resources that scale linearly with
the size of the group.</t>
      <t>In this document, we describe a protocol based on tree structures
that enable asynchronous group keying with forward secrecy and
post-compromise security.  Based on earlier work on "asynchronous
ratcheting trees" <xref target="ART"/>, the protocol presented here uses an
asynchronous key-encapsulation mechanism for tree structures.
This mechanism allows the members of the group to derive and update
shared keys with costs that scale as the log of the group size.</t>
      <section anchor="operating-context">
        <name>Operating Context</name>
        <t>MLS is designed to operate in the context described in
<xref target="I-D.ietf-mls-architecture"/>.  In particular, we assume that the following
services are provided:</t>
        <ul spacing="normal">
          <li>
            <t>A Delivery Service (DS) that routes MLS messages among the participants in the
protocol.  The following types of delivery are typically required:  </t>
            <ul spacing="normal">
              <li>Pre-publication of KeyPackage objects for clients</li>
              <li>Broadcast delivery of Proposal and Commit messages to members of a group</li>
              <li>Unicast delivery of Welcome messages to new members of a group</li>
              <li>Sequencing of Commit messages (see <xref target="sequencing"/>)</li>
            </ul>
          </li>
          <li>An Authentication Service (AS) that enables group members to authenticate the
credentials presented by other group members.</li>
        </ul>
        <t>The DS and AS may also apply additional policies to MLS operations to obtain
additional security properties.  For example, MLS enables any participant to add
or remove members of a group; a DS could enforce a policy that only certain
members are allowed to perform these operations.  MLS authenticates all members
of a group; a DS could help ensure that only clients with certain types of
credential are admitted. MLS provides no inherent protection against denial of
service; A DS could also enforce rate limits in order to mitigate these risks.</t>
      </section>
      <section anchor="change-log">
        <name>Change Log</name>
        <t>RFC EDITOR PLEASE DELETE THIS SECTION.</t>
        <t>draft-15</t>
        <ul spacing="normal">
          <li>Include ciphersuite in group context (*)</li>
          <li>Add new new_proposal_member SenderType (*)</li>
          <li>Always use a full tree (*)</li>
          <li>Change KeyPackage identifier extension to be LeafNode identifier (*)</li>
          <li>Use new tree for context in path secret encryption (*)</li>
          <li>Use a hash function for hash identifiers (*)</li>
          <li>Add a marker byte to tree hash input structs (*)</li>
          <li>Recommend that group ids are generated randomly (*)</li>
          <li>Update external senders extension to have SignaturePublicKey and Credential (*)</li>
          <li>Replace LeafNodeRef with leaf index (*)</li>
          <li>Remove AppAck proposal (*)</li>
          <li>Make padding arbitrary-size and all-zero (*)</li>
          <li>Require that unmerged_leaves be ordered</li>
          <li>Derive the commit secret from the end of the UpdatePath, not the root</li>
          <li>Specify the precise points in the protocol where credential validation must be done</li>
          <li>Make PSK provisions more uniform, e.g., always generating a fresh random nonce</li>
          <li>Improve parent hash guarantees with stricter checks on tree correctness</li>
          <li>Streamline some structs, e.g., folding GroupContext into GroupInfo</li>
          <li>Provide clearer rules for validating and applying commits</li>
          <li>Clarify tree hash and parent hash, and correct examples</li>
          <li>Clean up struct names and references to outdated structs</li>
          <li>Cite AEAD limits draft</li>
        </ul>
        <t>draft-14</t>
        <ul spacing="normal">
          <li>Ensure that a signature public key is always intelligible (*)</li>
          <li>Clean up terminology of derived secrets/keys</li>
          <li>Fix parent hash (*)</li>
          <li>Specify compatibility behavior around new credentials</li>
          <li>Add Path Required to Proposal Type template</li>
          <li>Sub-group branching requires fresh key packages for each member</li>
          <li>Use <tt>aasvg</tt> and typed code blocks</li>
          <li>Require init key and leaf key to be different</li>
          <li>Preconfigured senders extension and removal of signature key indirection</li>
        </ul>
        <t>draft-13</t>
        <ul spacing="normal">
          <li>TLS syntax updates (including variable-header-length vectors) (*)</li>
          <li>Stop generating redundant PKE key pairs. (*)</li>
          <li>Move validation of identity change to the AS</li>
          <li>Add message/mls MIME type registration</li>
          <li>Split LeafNode from KeyPackage (*)</li>
          <li>Remove endpoint_id (*)</li>
          <li>Reorganize to make section layout more sane</li>
          <li>Forbid proposals by reference in external commits (*)</li>
          <li>Domain separation for KeyPackage and Proposal references (*)</li>
          <li>Downgrade MUST to SHOULD for commit senders including all valid commits</li>
          <li>Stronger parent hashes for authenticated identities (*)</li>
          <li>Move wire_format to a separate tagged-union structure MLSMessage</li>
          <li>Generalize tree extend/truncate algorithms</li>
          <li>Add algorithms for link-based trees</li>
          <li>Forbid self-Update entirely (*)</li>
          <li>Consolidate resumption PSK cases (*)</li>
          <li>384 Ciphersuite Addition</li>
          <li>Remove explicit version pin on HPKE (*)</li>
          <li>Remove the requirement for Add in external commit (*)</li>
          <li>Use smaller, fixed-size hash-based identifiers (*)</li>
          <li>Be explicit that Credentials can attest to multiple identities (*)</li>
        </ul>
        <t>draft-12</t>
        <ul spacing="normal">
          <li>Use the GroupContext to derive the joiner_secret (*)</li>
          <li>Make PreSharedKeys non optional in GroupSecrets (*)</li>
          <li>Update name for this particular key (*)</li>
          <li>Truncate tree size on removal (*)</li>
          <li>Use HPKE draft-08 (*)</li>
          <li>Clarify requirements around identity in MLS groups (*)</li>
          <li>Signal the intended wire format for MLS messages (*)</li>
          <li>Inject GroupContext as HPKE info instead of AAD (*)</li>
          <li>Clarify extension handling and make extension updatable (*)</li>
          <li>Improve extensibility of Proposals (*)</li>
          <li>Constrain proposal in External Commit (*)</li>
          <li>Remove the notion of a 'leaf index' (*)</li>
          <li>Add group_context_extensions proposal ID (*)</li>
          <li>Add RequiredCapabilities extension (*)</li>
          <li>Use cascaded KDF instead of concatenation to consolidate PSKs (*)</li>
          <li>Use key package hash to index clients in message structs (*)</li>
          <li>Don't require PublicGroupState for external init (*)</li>
          <li>Make ratchet tree section clearer.</li>
          <li>Handle non-member sender cases in MLSPlaintextTBS</li>
          <li>Clarify encoding of signatures with NIST curves</li>
          <li>Remove OPEN ISSUEs and TODOs</li>
          <li>Normalize the description of the zero vector</li>
        </ul>
        <t>draft-11</t>
        <ul spacing="normal">
          <li>Include subtree keys in parent hash (*)</li>
          <li>Pin HPKE to draft-07 (*)</li>
          <li>Move joiner secret to the end of the first key schedule epoch (*)</li>
          <li>Add an AppAck proposal</li>
          <li>Make initializations of transcript hashes consistent</li>
        </ul>
        <t>draft-10</t>
        <ul spacing="normal">
          <li>Allow new members to join via an external Commit (*)</li>
          <li>Enable proposals to be sent inline in a Commit (*)</li>
          <li>Re-enable constant-time Add (*)</li>
          <li>Change expiration extension to lifetime extension (*)</li>
          <li>Make the tree in the Welcome optional (*)</li>
          <li>PSK injection, re-init, sub-group branching (*)</li>
          <li>Require the initial init_secret to be a random value (*)</li>
          <li>Remove explicit sender data nonce (*)</li>
          <li>Do not encrypt to joiners in UpdatePath generation (*)</li>
          <li>Move MLSPlaintext signature under the confirmation tag (*)</li>
          <li>Explicitly authenticate group membership with MLSPLaintext (*)</li>
          <li>Clarify X509Credential structure (*)</li>
          <li>Remove unneeded interim transcript hash from GroupInfo (*)</li>
          <li>IANA considerations</li>
          <li>Derive an authentication secret</li>
          <li>Use Extract/Expand from HPKE KDF</li>
          <li>Clarify that application messages MUST be encrypted</li>
        </ul>
        <t>draft-09</t>
        <ul spacing="normal">
          <li>Remove blanking of nodes on Add (*)</li>
          <li>Change epoch numbers to uint64 (*)</li>
          <li>Add PSK inputs (*)</li>
          <li>Add key schedule exporter (*)</li>
          <li>Sign the updated direct path on Commit, using "parent hashes" and one
signature per leaf (*)</li>
          <li>Use structured types for external senders (*)</li>
          <li>Redesign Welcome to include confirmation and use derived keys (*)</li>
          <li>Remove ignored proposals (*)</li>
          <li>Always include an Update with a Commit (*)</li>
          <li>Add per-message entropy to guard against nonce reuse (*)</li>
          <li>Use the same hash ratchet construct for both application and handshake keys (*)</li>
          <li>Add more ciphersuites</li>
          <li>Use HKDF to derive key pairs (*)</li>
          <li>Mandate expiration of ClientInitKeys (*)</li>
          <li>Add extensions to GroupContext and flesh out the extensibility story (*)</li>
          <li>Rename ClientInitKey to KeyPackage</li>
        </ul>
        <t>draft-08</t>
        <ul spacing="normal">
          <li>Change ClientInitKeys so that they only refer to one ciphersuite (*)</li>
          <li>Decompose group operations into Proposals and Commits (*)</li>
          <li>Enable Add and Remove proposals from outside the group (*)</li>
          <li>Replace Init messages with multi-recipient Welcome message (*)</li>
          <li>Add extensions to ClientInitKeys for expiration and downgrade resistance (*)</li>
          <li>Allow multiple Proposals and a single Commit in one MLSPlaintext (*)</li>
        </ul>
        <t>draft-07</t>
        <ul spacing="normal">
          <li>Initial version of the Tree based Application Key Schedule (*)</li>
          <li>Initial definition of the Init message for group creation (*)</li>
          <li>Fix issue with the transcript used for newcomers (*)</li>
          <li>Clarifications on message framing and HPKE contexts (*)</li>
        </ul>
        <t>draft-06</t>
        <ul spacing="normal">
          <li>Reorder blanking and update in the Remove operation (*)</li>
          <li>Rename the GroupState structure to GroupContext (*)</li>
          <li>Rename UserInitKey to ClientInitKey</li>
          <li>Resolve the circular dependency that draft-05 introduced in the
confirmation MAC calculation (*)</li>
          <li>Cover the entire MLSPlaintext in the transcript hash (*)</li>
        </ul>
        <t>draft-05</t>
        <ul spacing="normal">
          <li>Common framing for handshake and application messages (*)</li>
          <li>Handshake message encryption (*)</li>
          <li>Convert from literal state to a commitment via the "tree hash" (*)</li>
          <li>Add credentials to the tree and remove the "roster" concept (*)</li>
          <li>Remove the secret field from tree node values</li>
        </ul>
        <t>draft-04</t>
        <ul spacing="normal">
          <li>Updating the language to be similar to the Architecture document</li>
          <li>ECIES is now renamed in favor of HPKE (*)</li>
          <li>Using a KDF instead of a Hash in TreeKEM (*)</li>
        </ul>
        <t>draft-03</t>
        <ul spacing="normal">
          <li>Added ciphersuites and signature schemes (*)</li>
          <li>Re-ordered fields in UserInitKey to make parsing easier (*)</li>
          <li>Fixed inconsistencies between Welcome and GroupState (*)</li>
          <li>Added encryption of the Welcome message (*)</li>
        </ul>
        <t>draft-02</t>
        <ul spacing="normal">
          <li>Removed ART (*)</li>
          <li>Allowed partial trees to avoid double-joins (*)</li>
          <li>Added explicit key confirmation (*)</li>
        </ul>
        <t>draft-01</t>
        <ul spacing="normal">
          <li>Initial description of the Message Protection mechanism. (*)</li>
          <li>Initial specification proposal for the Application Key Schedule
using the per-participant chaining of the Application Secret design. (*)</li>
          <li>Initial specification proposal for an encryption mechanism to protect
Application Messages using an AEAD scheme. (*)</li>
          <li>Initial specification proposal for an authentication mechanism
of Application Messages using signatures. (*)</li>
          <li>Initial specification proposal for a padding mechanism to improving
protection of Application Messages against traffic analysis. (*)</li>
          <li>Inversion of the Group Init Add and Application Secret derivations
in the Handshake Key Schedule to be ease chaining in case we switch
design. (*)</li>
          <li>Removal of the UserAdd construct and split of GroupAdd into Add
and Welcome messages (*)</li>
          <li>Initial proposal for authenticating handshake messages by signing
over group state and including group state in the key schedule (*)</li>
          <li>Added an appendix with example code for tree math</li>
          <li>Changed the ECIES mechanism used by TreeKEM so that it uses nonces
generated from the shared secret</li>
        </ul>
        <t>draft-00</t>
        <ul spacing="normal">
          <li>Initial adoption of draft-barnes-mls-protocol-01 as a WG item.</li>
        </ul>
      </section>
    </section>
    <section anchor="terminology">
      <name>Terminology</name>
      <t>The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in
BCP 14 <xref target="RFC2119"/> <xref target="RFC8174"/> when, and only when, they appear in all
capitals, as shown here.</t>
      <dl>
        <dt>Client:</dt>
        <dd>
          <t>An agent that uses this protocol to establish shared cryptographic
state with other clients.  A client is defined by the
cryptographic keys it holds.</t>
        </dd>
        <dt>Group:</dt>
        <dd>
          <t>A group represents a logical collection of clients that share a common
secret value at any given time.  Its state is represented as a linear
sequence of epochs in which each epoch depends on its predecessor.</t>
        </dd>
        <dt>Epoch:</dt>
        <dd>
          <t>A state of a group in which a specific set of authenticated clients hold
shared cryptographic state.</t>
        </dd>
        <dt>Member:</dt>
        <dd>
          <t>A client that is included in the shared state of a group, hence
has access to the group's secrets.</t>
        </dd>
        <dt>Key Package:</dt>
        <dd>
          <t>A signed object describing a client's identity and capabilities, and including
a hybrid public-key encryption (HPKE <xref target="RFC9180"/>) public key that
can be used to encrypt to that client, and which other clients can use to
introduce the client to a new group.</t>
        </dd>
        <dt>Group Context:</dt>
        <dd>
          <t>An object that summarizes the state of the group. The group context is signed
to bind a message to a particular group, and also provided to new members to
help them join a group.</t>
        </dd>
        <dt>Signature Key:</dt>
        <dd>
          <t>A signing key pair used to authenticate the sender of a message.</t>
        </dd>
        <dt>Handshake Message:</dt>
        <dd>
          <t>A PublicMessage or PrivateMessage carrying an MLS Proposal or Commit
object, as opposed to application data.</t>
        </dd>
        <dt>Application Message:</dt>
        <dd>
          <t>A PrivateMessage carrying application data.</t>
        </dd>
      </dl>
      <t>Terminology specific to tree computations is described in
<xref target="ratchet-tree-terminology"/>.</t>
      <t>In general, symmetric values are referred to as "keys" or "secrets"
interchangeably.  Either term denotes a value that MUST be kept confidential to
a Client.  When labeling individual values, we typically use "secret" to refer
to a value that is used derive further secret values, and "key" to refer to a
value that is used with an algorithm such as HMAC or an AEAD algorithm.</t>
      <t>The PublicMessage and PrivateMessage formats are defined in <xref target="message-framing"/>;
they represent integrity-protected and confidentiality-protected messages,
respectively.  Security notions such as forward secrecy and post-compromise
security are defined in <xref target="security-considerations"/>.</t>
      <section anchor="presentation-language">
        <name>Presentation Language</name>
        <t>We use the TLS presentation language <xref target="RFC8446"/> to describe the structure of
protocol messages.  In addition to the base syntax, we add two additional
features, the ability for fields to be optional and the ability for vectors to
have variable-size length headers.</t>
        <section anchor="optional-value">
          <name>Optional Value</name>
          <t>An optional value is encoded with a presence-signaling octet, followed by the
value itself if present.  When decoding, a presence octet with a value other
than 0 or 1 MUST be rejected as malformed.</t>
          <sourcecode type="tls"><![CDATA[
struct {
    uint8 present;
    select (present) {
        case 0: struct{};
        case 1: T value;
    };
} optional<T>;
]]></sourcecode>
        </section>
        <section anchor="variable-size-vector-length-headers">
          <name>Variable-size Vector Length Headers</name>
          <t>In the TLS presentation language, vectors are encoded as a sequence of encoded
elements prefixed with a length.  The length field has a fixed size set by
specifying the minimum and maximum lengths of the encoded sequence of elements.</t>
          <t>In MLS, there are several vectors whose sizes vary over significant ranges.  So
instead of using a fixed-size length field, we use a variable-size length using
a variable-length integer encoding based on the one in Section 16 of
<xref target="RFC9000"/>. They differ only in that the one here requires a minimum-size
encoding. Instead of presenting min and max values, the vector description
simply includes a <tt>V</tt>. For example:</t>
          <sourcecode type="tls"><![CDATA[
struct {
    uint32 fixed<0..255>;
    opaque variable<V>;
} StructWithVectors;
]]></sourcecode>
          <t>Such a vector can represent values with length from 0 bytes to 2^30 bytes.
The variable-length integer encoding reserves the two most significant bits
of the first byte to encode the base 2 logarithm of the integer encoding length
in bytes.  The integer value is encoded on the remaining bits, in network byte
order.  The encoded value MUST use the smallest number of bits required to
represent the value.  When decoding, values using more bits than necessary MUST
be treated as malformed.</t>
          <t>This means that integers are encoded on 1, 2, or 4 bytes and can encode 6-,
14-, or 30-bit values respectively.</t>
          <table anchor="integer-summary">
            <name>Summary of Integer Encodings</name>
            <thead>
              <tr>
                <th align="left">Prefix</th>
                <th align="left">Length</th>
                <th align="left">Usable Bits</th>
                <th align="left">Min</th>
                <th align="left">Max</th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td align="left">00</td>
                <td align="left">1</td>
                <td align="left">6</td>
                <td align="left">0</td>
                <td align="left">63</td>
              </tr>
              <tr>
                <td align="left">01</td>
                <td align="left">2</td>
                <td align="left">14</td>
                <td align="left">64</td>
                <td align="left">16383</td>
              </tr>
              <tr>
                <td align="left">10</td>
                <td align="left">4</td>
                <td align="left">30</td>
                <td align="left">16384</td>
                <td align="left">1073741823</td>
              </tr>
              <tr>
                <td align="left">11</td>
                <td align="left">invalid</td>
                <td align="left">-</td>
                <td align="left">-</td>
                <td align="left">-</td>
              </tr>
            </tbody>
          </table>
          <t>Vectors that start with "11" prefix are invalid and MUST be rejected.</t>
          <t>For example:</t>
          <ul spacing="normal">
            <li>The four byte length value 0x9d7f3e7d decodes to 494878333.</li>
            <li>The two byte length value 0x7bbd decodes to 15293.</li>
            <li>The single byte length value 0x25 decodes to 37.</li>
          </ul>
          <t>The following figure adapts the pseudocode provided in <xref target="RFC9000"/> to add a
check for minimum-length encoding:</t>
          <sourcecode type="pseudocode"><![CDATA[
ReadVarint(data):
  // The length of variable-length integers is encoded in the
  // first two bits of the first byte.
  v = data.next_byte()
  prefix = v >> 6
  if prefix == 3:
    raise Exception('invalid variable length integer prefix')

  length = 1 << prefix

  // Once the length is known, remove these bits and read any
  // remaining bytes.
  v = v & 0x3f
  repeat length-1 times:
    v = (v << 8) + data.next_byte()

  // Check that the encoder used the minimum bits required
  if prefix >= 1 && v < (1 << (8*(1 << (prefix-1))-2)):
    raise Exception('minimum encoding was not used')

  return v
]]></sourcecode>
          <t>The use of variable-size integers for vector lengths allows vectors to grow
very large, up to 2^30 bytes.  Implementations should take care not to allow
vectors to overflow available storage.  To facilitate debugging of potential
interoperability problems, implementations SHOULD provide a clear error when
such an overflow condition occurs.</t>
        </section>
      </section>
    </section>
    <section anchor="protocol-overview">
      <name>Protocol Overview</name>
      <t>The core functionality of MLS is continuous group authenticated key exchange
(AKE).  As with other authenticated key exchange protocols (such as TLS), the
participants in the protocol agree on a common secret value, and each
participant can verify the identity of the other participants.  MLS provides
group AKE in the sense that there can be more than two participants in the
protocol, and continuous group AKE in the sense that the set of participants in
the protocol can change over time.</t>
      <t>The core organizing principles of MLS are <em>groups</em> and <em>epochs</em>.  A group
represents a logical collection of clients that share a common secret value at
any given time.  The history of a group is divided into a linear sequence of
epochs.  In each epoch, a set of authenticated <em>members</em> agree on an <em>epoch
secret</em> that is known only to the members of the group in that epoch.  The set
of members involved in the group can change from one epoch to the next, and MLS
ensures that only the members in the current epoch have access to the epoch
secret.  From the epoch secret, members derive further shared secrets for
message encryption, group membership authentication, and so on.</t>
      <t>The creator of an MLS group creates the group's first epoch unilaterally, with
no protocol interactions.  Thereafter, the members of the group advance their
shared cryptographic state from one epoch to another by exchanging MLS messages:</t>
      <ul spacing="normal">
        <li>A <em>KeyPackage</em> object describes a client's capabilities and provides keys that
can be used to add the client to a group.</li>
        <li>A <em>Proposal</em> message proposes a change to be made in the next epoch, such as
adding or removing a member</li>
        <li>A <em>Commit</em> message initiates a new epoch by instructing members of the group
to implement a collection of proposals</li>
        <li>A <em>Welcome</em> message provides a new member to the group with the information to
initialize their state for the epoch in which they were added or in which they
want to add themselves to the group</li>
      </ul>
      <t>KeyPackage and Welcome messages are used to initiate a group or introduce new
members, so they are exchanged between group members and clients not yet in the
group.</t>
      <t>Proposal and Commit messages are sent from one member of a group to the others.
MLS provides a common framing layer for sending messages within a group:
A <em>PublicMessage</em> provides sender authentication for unencrypted Proposal and Commit
messages.  A <em>PrivateMessage</em> provides encryption and authentication for
both Proposal/Commit messages as well as any application data.</t>
      <section anchor="cryptographic-state-and-evolution">
        <name>Cryptographic State and Evolution</name>
        <t>The cryptographic state at the core of MLS is divided into three areas of responsibility:</t>
        <figure>
          <name>Overview of MLS group evolution</name>
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                  <text x="272" y="36">...</text>
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                  <text x="276" y="116">epoch_secret</text>
                  <text x="56" y="148">Ratchet</text>
                  <text x="532" y="148">Secret</text>
                  <text x="52" y="164">Tree</text>
                  <text x="532" y="164">Tree</text>
                  <text x="136" y="212">commit_secret</text>
                  <text x="276" y="212">epoch_secret</text>
                  <text x="432" y="212">encryption_secret</text>
                  <text x="276" y="308">epoch_secret</text>
                  <text x="272" y="388">...</text>
                </g>
              </svg>
            </artwork>
            <artwork type="ascii-art"><![CDATA[
                          .-    ...    -.
                         |               |
                         |       |       |
                         |       |       | Key Schedule
                         |       V       |
                         |  epoch_secret |
.                        |       |       |                             .
|\ Ratchet               |       |       |                     Secret /|
| \ Tree                 |       |       |                      Tree / |
|  \                     |       |       |                          /  |
|   \                    |       V       |                         /   |
|    +--> commit_secret --> epoch_secret --> encryption_secret -->+    |
|   /                    |       |       |                         \   |
|  /                     |       |       |                          \  |
| /                      |       |       |                           \ |
|/                       |       |       |                            \|
'                        |       V       |                             '
                         |  epoch_secret |
                         |       |       |
                         |       |       |
                         |       V       |
                         |               |
                          '-    ...    -'
]]></artwork>
          </artset>
        </figure>
        <ul spacing="normal">
          <li>A <em>ratchet tree</em> that represents the membership of the group, providing group
members a way to authenticate each other and efficiently encrypt messages to
subsets of the group.  Each epoch has a distinct ratchet tree. It seeds the
<em>key schedule</em>.</li>
          <li>
            <t>A <em>key schedule</em> that describes the chain of key derivations used to progress from
epoch to epoch (mainly using the <em>init_secret</em> and <em>epoch_secret</em>), as well as the derivation of
a variety of other secrets (see <xref target="epoch-derived-secrets"/>), for example:
            </t>
            <ul spacing="normal">
              <li>An <em>encryption secret</em> that is used to initialize the secret tree for the
epoch.</li>
              <li>An <em>exporter secret</em> that allows other protocols to leverage MLS as a
generic authenticated group key exchange.</li>
              <li>A <em>resumption secret</em> that members can use to prove their membership in the
group, e.g., in the case of branching a subgroup.</li>
            </ul>
          </li>
          <li>A <em>secret tree</em> derived from the key schedule that represents shared secrets
used by the members of the group for encrypting and authenticating messages.
Each epoch has a distinct secret tree.</li>
        </ul>
        <t>Each member of the group maintains a partial view of these components of the group's
state.  MLS messages are used to initialize these views and keep them in sync as
the group transitions between epochs.</t>
        <t>Each new epoch is initiated with a Commit message.  The Commit instructs
existing members of the group to update their views of the ratchet tree by applying
a set of Proposals, and uses the updated ratchet tree to distribute fresh
entropy to the group.  This fresh entropy is provided only to members in the new
epoch and not to members who have been removed. Commits thus maintain the property that the
the epoch secret is confidential to the members in the current epoch.</t>
        <t>For each Commit that adds one or more members to the group, there is a single corresponding
Welcome message.  The Welcome message provides all the new members with the information
they need to initialize their views of the key schedule and ratchet tree, so
that these views align with the views held by other members of the group
in this epoch.</t>
      </section>
      <section anchor="example-protocol-execution">
        <name>Example Protocol Execution</name>
        <t>There are three major operations in the lifecycle of a group:</t>
        <ul spacing="normal">
          <li>Adding a member, initiated by a current member;</li>
          <li>Updating the leaf secret of a member;</li>
          <li>Removing a member.</li>
        </ul>
        <t>Each of these operations is "proposed" by sending a message of the corresponding
type (Add / Update / Remove).  The state of the group is not changed, however,
until a Commit message is sent to provide the group with fresh entropy.  In this
section, we show each proposal being committed immediately, but in more advanced
deployment cases an application might gather several proposals before
committing them all at once.  In the illustrations below, we show the Proposal
and Commit messages directly, while in reality they would be sent encapsulated in
PublicMessage or PrivateMessage objects.</t>
        <t>Before the initialization of a group, clients publish KeyPackages to a directory
provided by the Service Provider (see <xref target="prepublish-flow"/>).</t>
        <figure anchor="prepublish-flow">
          <name>Clients A, B, and C publish KeyPackages to the directory</name>
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            <artwork type="ascii-art"><![CDATA[
                                                               Group
A                B                C            Directory       Channel
|                |                |                |              |
| KeyPackageA    |                |                |              |
+------------------------------------------------->|              |
|                |                |                |              |
|                | KeyPackageB    |                |              |
|                +-------------------------------->|              |
|                |                |                |              |
|                |                | KeyPackageC    |              |
|                |                +--------------->|              |
|                |                |                |              |
]]></artwork>
          </artset>
        </figure>
        <t><xref target="create-flow"/> shows how these prepublished KeyPackages are used to create a group.
When a client A wants to establish a group with B and C, it first initializes a
group state containing only itself and downloads KeyPackages for B and C. For
each member, A generates an Add and Commit message adding that member, and
broadcasts them to the group. It also generates a Welcome message and sends this
directly to the new member (there's no need to send it to the group). Only after
A has received its Commit message back from the Delivery Service does it update its
state to reflect the new member's addition.</t>
        <t>Once A has updated its state, the new member has processed the Welcome, and any
other group members have processed the Commit, they will all have consistent
representations of the group state, including a group secret that is known only
to the members the group. The new member will be able to read and send new
messages to the group, but messages sent before they were added to the group
will not be accessible.</t>
        <figure anchor="create-flow">
          <name>Client A creates a group with clients B and C</name>
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            <artwork type="ascii-art"><![CDATA[
                                                               Group
A              B              C          Directory            Channel
|              |              |              |                   |
|         KeyPackageB, KeyPackageC           |                   |
|<-------------------------------------------+                   |
|              |              |              |                   |
|              |              |              | Add(A->AB)        |
|              |              |              | Commit(Add)       |
+--------------------------------------------------------------->|
|              |              |              |                   |
|  Welcome(B)  |              |              |                   |
+------------->|              |              |                   |
|              |              |              |                   |
|              |              |              | Add(A->AB)        |
|              |              |              | Commit(Add)       |
|<---------------------------------------------------------------+
|              |              |              |                   |
|              |              |              |                   |
|              |              |              | Add(AB->ABC)      |
|              |              |              | Commit(Add)       |
+--------------------------------------------------------------->|
|              |              |              |                   |
|              |  Welcome(C)  |              |                   |
+---------------------------->|              |                   |
|              |              |              |                   |
|              |              |              | Add(AB->ABC)      |
|              |              |              | Commit(Add)       |
|<---------------------------------------------------------------+
|              |<------------------------------------------------+
|              |              |              |                   |
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        </figure>
        <t>Subsequent additions of group members proceed in the same way.  Any
member of the group can download a KeyPackage for a new client
and broadcast Add and Commit messages that the current group will use to update
their state, and a Welcome message that the new client can use to
initialize its state and join the group.</t>
        <t>To enforce the forward secrecy and post-compromise security of messages, each
member periodically updates the keys that represent them to the group.  A member
does this by sending a Commit (possibly with no proposals), or by sending an
Update message that is committed by another member (see <xref target="update-flow"/>).
Once the other members of
the group have processed these messages, the group's secrets will be unknown to
an attacker that had compromised the sender's prior leaf secret.</t>
        <t>Update messages SHOULD be sent at regular intervals of time as long as the group
is active, and members that don't update SHOULD eventually be removed from the
group. It's left to the application to determine an appropriate amount of time
between Updates.  In general, however, applications should take care that they
do not send MLS messages at a rate that overwhelms the transport over which
messages are being sent.</t>
        <figure anchor="update-flow">
          <name>Client B proposes to update its key, and client A commits the proposal.  As a result, the keys for both B and A updated, so the group has post-compromise security with respect to both of them.</name>
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                                                          Group
A              B     ...      Z          Directory        Channel
|              |              |              |              |
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|              +------------------------------------------->|
|              |              |              | Update(B)    |
|<----------------------------------------------------------+
|              |<-------------------------------------------+
|              |              |<----------------------------+
|              |              |              |              |
| Commit(Upd)  |              |              |              |
+---------------------------------------------------------->|
|              |              |              | Commit(Upd)  |
|<----------------------------------------------------------+
|              |<-------------------------------------------+
|              |              |<----------------------------+
|              |              |              |              |
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        </figure>
        <t>Members are removed from the group in a similar way, as shown in <xref target="remove-flow"/>.
Any member of the group can send a Remove proposal followed by a
Commit message.  The Commit message provides new entropy to all members of the
group except the removed member.  This new entropy is added to the epoch secret
for the new epoch so that it is not known to the removed member.
Note that this does not necessarily imply that any member
is actually allowed to evict other members; groups can
enforce access control policies on top of these
basic mechanism.</t>
        <figure anchor="remove-flow">
          <name>Client Z removes client B from the group</name>
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                <path d="M 128,64 L 128,168" fill="none" stroke="black"/>
                <path d="M 128,184 L 128,224" fill="none" stroke="black"/>
                <path d="M 248,64 L 248,168" fill="none" stroke="black"/>
                <path d="M 248,200 L 248,224" fill="none" stroke="black"/>
                <path d="M 368,64 L 368,104" fill="none" stroke="black"/>
                <path d="M 368,120 L 368,168" fill="none" stroke="black"/>
                <path d="M 488,64 L 488,224" fill="none" stroke="black"/>
                <path d="M 248,112 L 480,112" fill="none" stroke="black"/>
                <path d="M 16,176 L 488,176" fill="none" stroke="black"/>
                <path d="M 136,192 L 488,192" fill="none" stroke="black"/>
                <path d="M 256,208 L 488,208" fill="none" stroke="black"/>
                <polygon class="arrowhead" points="488,112 476,106.4 476,117.6" fill="black" transform="rotate(0,480,112)"/>
                <polygon class="arrowhead" points="264,208 252,202.4 252,213.6" fill="black" transform="rotate(180,256,208)"/>
                <polygon class="arrowhead" points="144,192 132,186.4 132,197.6" fill="black" transform="rotate(180,136,192)"/>
                <polygon class="arrowhead" points="24,176 12,170.4 12,181.6" fill="black" transform="rotate(180,16,176)"/>
                <g class="text">
                  <text x="488" y="36">Group</text>
                  <text x="8" y="52">A</text>
                  <text x="128" y="52">B</text>
                  <text x="184" y="52">...</text>
                  <text x="248" y="52">Z</text>
                  <text x="368" y="52">Directory</text>
                  <text x="488" y="52">Channel</text>
                  <text x="296" y="84">Remove(B)</text>
                  <text x="304" y="100">Commit(Rem)</text>
                  <text x="416" y="148">Remove(B)</text>
                  <text x="424" y="164">Commit(Rem)</text>
                  <text x="368" y="228">|</text>
                </g>
              </svg>
            </artwork>
            <artwork type="ascii-art"><![CDATA[
                                                          Group
A              B     ...      Z          Directory       Channel
|              |              |              |              |
|              |              | Remove(B)    |              |
|              |              | Commit(Rem)  |              |
|              |              +---------------------------->|
|              |              |              |              |
|              |              |              | Remove(B)    |
|              |              |              | Commit(Rem)  |
|<----------------------------------------------------------+
|              |<-------------------------------------------+
|              |              |<----------------------------+
|              |              |              |              |
]]></artwork>
          </artset>
        </figure>
      </section>
      <section anchor="relationships-between-epochs">
        <name>Relationships Between Epochs</name>
        <t>A group has a single linear sequence of epochs. Groups and epochs are generally
independent of one another. However, it can sometimes be useful to link epochs
cryptographically, either within a group or across groups. MLS derives a
resumption pre-shared key (PSK) from each epoch to allow entropy extracted from
one epoch to be injected into a future epoch. This link guarantees that members
entering the new epoch agree on a key if and only if they were members of the group
during the epoch from which the resumption key was extracted.</t>
        <t>MLS supports two ways to tie a new group to an existing group. Reinitialization
closes one group and creates a new group comprising the same members with
different parameters. Branching starts a new group with a subset of the original
group's participants (with no effect on the original group).  In both cases,
the new group is linked to the old group via a resumption PSK.</t>
        <figure>
          <name>Reinitializing a group</name>
          <artset>
            <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="240" width="272" viewBox="0 0 272 240" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
                <path d="M 48,40 L 48,112" fill="none" stroke="black"/>
                <path d="M 224,136 L 224,208" fill="none" stroke="black"/>
                <path d="M 56,80 L 72,80" fill="none" stroke="black"/>
                <polygon class="arrowhead" points="232,208 220,202.4 220,213.6" fill="black" transform="rotate(90,224,208)"/>
                <polygon class="arrowhead" points="64,80 52,74.4 52,85.6" fill="black" transform="rotate(180,56,80)"/>
                <polygon class="arrowhead" points="56,112 44,106.4 44,117.6" fill="black" transform="rotate(90,48,112)"/>
                <g class="text">
                  <text x="56" y="36">epoch_A_[n-1]</text>
                  <text x="108" y="84">ReInit</text>
                  <text x="48" y="132">epoch_A_[n]</text>
                  <text x="224" y="132">epoch_B_[0]</text>
                  <text x="48" y="148">.</text>
                  <text x="48" y="164">.</text>
                  <text x="136" y="164">PSK(usage=reinit)</text>
                  <text x="132" y="180">.....................&gt;</text>
                  <text x="224" y="228">epoch_B_[1]</text>
                </g>
              </svg>
            </artwork>
            <artwork type="ascii-art"><![CDATA[
epoch_A_[n-1]
     |
     |
     |<-- ReInit
     |
     V
epoch_A_[n]           epoch_B_[0]
     .                     |
     .  PSK(usage=reinit)  |
     .....................>|
                           |
                           V
                      epoch_B_[1]
]]></artwork>
          </artset>
        </figure>
        <figure>
          <name>Branching a group</name>
          <artset>
            <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="144" width="272" viewBox="0 0 272 144" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
                <path d="M 48,40 L 48,112" fill="none" stroke="black"/>
                <path d="M 224,40 L 224,112" fill="none" stroke="black"/>
                <polygon class="arrowhead" points="232,112 220,106.4 220,117.6" fill="black" transform="rotate(90,224,112)"/>
                <polygon class="arrowhead" points="56,112 44,106.4 44,117.6" fill="black" transform="rotate(90,48,112)"/>
                <g class="text">
                  <text x="48" y="36">epoch_A_[n]</text>
                  <text x="224" y="36">epoch_B_[0]</text>
                  <text x="136" y="68">PSK(usage=branch)</text>
                  <text x="136" y="84">....................&gt;</text>
                  <text x="56" y="132">epoch_A_[n+1]</text>
                  <text x="224" y="132">epoch_B_[1]</text>
                </g>
              </svg>
            </artwork>
            <artwork type="ascii-art"><![CDATA[
epoch_A_[n]           epoch_B_[0]
     |                     |
     |  PSK(usage=branch)  |
     |....................>|
     |                     |
     V                     V
epoch_A_[n+1]         epoch_B_[1]
]]></artwork>
          </artset>
        </figure>
        <t>Applications may also choose to use resumption PSKs to link epochs in other
ways.  For example, the following figure shows a case where a resumption PSK
from epoch <tt>n</tt> is injected into epoch <tt>n+k</tt>.  This demonstrates that the members
of the group at epoch <tt>n+k</tt> were also members at epoch <tt>n</tt>, irrespective of any
changes to these members' keys due to Updates or Commits.</t>
        <figure>
          <name>Reinjecting entropy from an earlier epoch</name>
          <artset>
            <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="304" width="248" viewBox="0 0 248 304" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
                <path d="M 48,40 L 48,176" fill="none" stroke="black"/>
                <path d="M 48,200 L 48,272" fill="none" stroke="black"/>
                <polygon class="arrowhead" points="56,272 44,266.4 44,277.6" fill="black" transform="rotate(90,48,272)"/>
                <polygon class="arrowhead" points="56,176 44,170.4 44,181.6" fill="black" transform="rotate(90,48,176)"/>
                <g class="text">
                  <text x="48" y="36">epoch_A_[n]</text>
                  <text x="156" y="68">PSK(usage=application)</text>
                  <text x="136" y="84">.....................</text>
                  <text x="216" y="100">.</text>
                  <text x="216" y="116">.</text>
                  <text x="40" y="132">.</text>
                  <text x="56" y="132">.</text>
                  <text x="216" y="132">...</text>
                  <text x="216" y="148">.</text>
                  <text x="216" y="164">.</text>
                  <text x="216" y="180">.</text>
                  <text x="64" y="196">epoch_A_[n+k-1]</text>
                  <text x="216" y="196">.</text>
                  <text x="216" y="212">.</text>
                  <text x="216" y="228">.</text>
                  <text x="136" y="244">&lt;....................</text>
                  <text x="56" y="292">epoch_A_[n+k]</text>
                </g>
              </svg>
            </artwork>
            <artwork type="ascii-art"><![CDATA[
epoch_A_[n]
     |
     |  PSK(usage=application)
     |.....................
     |                    .
     |                    .
    ...                  ...
     |                    .
     |                    .
     V                    .
epoch_A_[n+k-1]           .
     |                    .
     |                    .
     |<....................
     |
     V
epoch_A_[n+k]
]]></artwork>
          </artset>
        </figure>
      </section>
    </section>
    <section anchor="ratchet-tree-concepts">
      <name>Ratchet Tree Concepts</name>
      <t>The protocol uses "ratchet trees" for deriving shared secrets among a group of
clients.  A ratchet tree is an arrangement of secrets and key pairs among the
members of a group in a way that allows for secrets to be efficiently updated to
reflect changes in the group.</t>
      <t>Ratchet trees allow a group to efficiently remove any member by encrypting new
entropy to a subset of the group.  A ratchet tree assigns shared keys to
subgroups of the overall group, so that, for example, encrypting to all but one
member of the group requires only log(N) encryptions, instead of the N-1
encryptions that would be needed to encrypt to each participant individually
(where N is the number of members in the group).</t>
      <t>This remove operation allows MLS to efficiently achieve
post-compromise security.  In an Update proposal or a full Commit message, an old (possibly
compromised) representation of a member is efficiently removed from the group and
replaced with a freshly generated instance.</t>
      <section anchor="ratchet-tree-terminology">
        <name>Ratchet Tree Terminology</name>
        <t>Trees consist of <em>nodes</em>. A node is a
<em>leaf</em> if it has no children, and a <em>parent</em> otherwise; note that all
parents in our trees have precisely
two children, a <em>left</em> child and a <em>right</em> child. A node is the <em>root</em>
of a tree if it has no parents, and <em>intermediate</em> if it has both
children and parents. The <em>descendants</em> of a node are that node's
children, and the descendants of its children, and we say a tree
<em>contains</em> a node if that node is a descendant of the root of the tree,
or if the node itself is the root of the tree. Nodes are <em>siblings</em> if they share the same parent.</t>
        <t>A <em>subtree</em> of a tree is the tree given by any node (the <em>head</em> of the
subtree) and its descendants. The <em>size</em> of a tree or subtree is the
number of leaf nodes it contains.  For a given parent node, its <em>left
subtree</em> is the subtree with its left child as head (respectively
<em>right subtree</em>).</t>
        <t>Every tree used in this protocol is a perfect binary tree, that is, a complete
balanced binary tree with <tt>2^d</tt> leaves all at the same depth <tt>d</tt>.  This
structure is unique for a given depth <tt>d</tt>.</t>
        <t>There are multiple ways that an implementation might represent a ratchet tree in
memory.  A convenient property of left-balanced binary trees (including the
complete trees used here) is that they can be represented as an array of nodes,
with node relationships computed based on the nodes' indices in the array.  A
more traditional representation based on linked node objects may also be used.
<xref target="array-based-trees"/> and <xref target="link-based-trees"/> provide some details on how to
implement the tree operations required for MLS in these representations.  MLS
places no requirements on implementations' internal representations of ratchet
trees.  An implementation may use any tree representation and associated
algorithms, as long as they produce correct protocol messages.</t>
        <section anchor="ratchet-tree-nodes">
          <name>Ratchet Tree Nodes</name>
          <t>Each leaf node in a ratchet tree is given an <em>index</em> (or <em>leaf index</em>), starting
at <tt>0</tt> from the left to <tt>2^d - 1</tt> at the right (for a tree with <tt>2^d</tt> leaves). A tree
with <tt>2^d</tt> leaves has <tt>2^(d+1) - 1</tt> nodes, including parent nodes.</t>
          <t>Each node in a ratchet tree is either <em>blank</em> (containing no value) or it holds
an asymmetric key pair with some associated data:</t>
          <ul spacing="normal">
            <li>A public key (for the HPKE scheme in use, see <xref target="ciphersuites"/>)</li>
            <li>A private key (only within the member's direct path, see <xref target="views"/>)</li>
            <li>A credential (only for leaf nodes)</li>
            <li>An ordered list of "unmerged" leaves (see <xref target="views"/>)</li>
            <li>A hash of certain information about the node's parent, as of the last time the
node was changed (see <xref target="parent-hashes"/>).</li>
          </ul>
          <t>Every node, regardless of whether the node is blank or populated, has
a corresponding <em>hash</em> that summarizes the contents of the subtree
below that node.  The rules for computing these hashes are described
in <xref target="tree-hashes"/>.</t>
          <t>The <em>resolution</em> of a node is an ordered list of non-blank nodes
that collectively cover all non-blank descendants of the node.  The resolution
of a node is effectively a depth-first, left-first enumeration of the nearest
non-blank nodes below the node:</t>
          <ul spacing="normal">
            <li>The resolution of a non-blank node comprises the node itself,
followed by its list of unmerged leaves, if any</li>
            <li>The resolution of a blank leaf node is the empty list</li>
            <li>The resolution of a blank intermediate node is the result of
concatenating the resolution of its left child with the resolution
of its right child, in that order</li>
          </ul>
          <t>For example, consider the following subtree, where the <tt>_</tt> character
represents a blank node and unmerged leaves are indicated in square
brackets:</t>
          <figure anchor="resolution-tree">
            <name>A tree with blanks and unmerged leaves</name>
            <artwork type="ascii-art"><![CDATA[
               ...
               /
              _
        ______|______
       /             \
      X[B]            _
    __|__           __|__
   /     \         /     \
  _       _       Y       _
 / \     / \     / \     / \
A   B   _   D   E   F   _   H

0   1   2   3   4   5   6   7
]]></artwork>
          </figure>
          <t>In this tree, we can see all of the above rules in play:</t>
          <ul spacing="normal">
            <li>The resolution of node X is the list [X, B]</li>
            <li>The resolution of leaf 2 or leaf 6 is the empty list []</li>
            <li>The resolution of top node is the list [X, B, Y, H]</li>
          </ul>
        </section>
        <section anchor="paths-through-a-ratchet-tree">
          <name>Paths through a Ratchet Tree</name>
          <t>The <em>direct path</em> of a root is the empty list, and of any other node
is the concatenation of that node's parent along with the parent's direct path.</t>
          <t>The <em>copath</em> of a node is the node's sibling concatenated with the list of
siblings of all the nodes in its direct path, excluding the root.</t>
          <t>The <em>filtered direct path</em> of a leaf node L is the node's direct path, with any
node removed whose child on the copath of L has an empty resolution (keeping in
mind that any unmerged leaves of the copath child count toward its resolution).
The removed nodes do not need their own key pairs because encrypting to the
node's key pair would be equivalent to encrypting to its non-copath child.</t>
          <t>For example, consider the following tree (where blank nodes are indicated with
<tt>_</tt>, but also assigned a label for reference):</t>
          <figure anchor="full-tree">
            <name>A complete tree with five members, with labels for blank parent nodes</name>
            <artset>
              <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="240" width="256" viewBox="0 0 256 240" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
                  <path d="M 56,104 L 56,128" fill="none" stroke="black"/>
                  <path d="M 120,48 L 120,64" fill="none" stroke="black"/>
                  <path d="M 184,112 L 184,128" fill="none" stroke="black"/>
                  <path d="M 72,64 L 168,64" fill="none" stroke="black"/>
                  <path d="M 40,128 L 72,128" fill="none" stroke="black"/>
                  <path d="M 168,128 L 200,128" fill="none" stroke="black"/>
                  <path d="M 72,128 L 80,144" fill="none" stroke="black"/>
                  <path d="M 92,168 L 96,176" fill="none" stroke="black"/>
                  <path d="M 168,64 L 176,80" fill="none" stroke="black"/>
                  <path d="M 200,128 L 208,144" fill="none" stroke="black"/>
                  <path d="M 220,168 L 224,176" fill="none" stroke="black"/>
                  <path d="M 32,144 L 40,128" fill="none" stroke="black"/>
                  <path d="M 64,80 L 72,64" fill="none" stroke="black"/>
                  <path d="M 80,176 L 84,168" fill="none" stroke="black"/>
                  <path d="M 160,144 L 168,128" fill="none" stroke="black"/>
                  <path d="M 208,176 L 212,168" fill="none" stroke="black"/>
                  <g class="text">
                    <text x="120" y="36">W</text>
                    <text x="136" y="36">=</text>
                    <text x="164" y="36">root</text>
                    <text x="64" y="100">_=U</text>
                    <text x="184" y="100">Y</text>
                    <text x="24" y="164">T</text>
                    <text x="96" y="164">_=V</text>
                    <text x="152" y="164">X</text>
                    <text x="224" y="164">_=Z</text>
                    <text x="16" y="180">/</text>
                    <text x="32" y="180">\</text>
                    <text x="144" y="180">/</text>
                    <text x="160" y="180">\</text>
                    <text x="8" y="196">A</text>
                    <text x="40" y="196">B</text>
                    <text x="72" y="196">_</text>
                    <text x="104" y="196">_</text>
                    <text x="136" y="196">E</text>
                    <text x="168" y="196">F</text>
                    <text x="200" y="196">G</text>
                    <text x="240" y="196">_=H</text>
                    <text x="8" y="228">0</text>
                    <text x="40" y="228">1</text>
                    <text x="72" y="228">2</text>
                    <text x="104" y="228">3</text>
                    <text x="136" y="228">4</text>
                    <text x="168" y="228">5</text>
                    <text x="200" y="228">6</text>
                    <text x="232" y="228">7</text>
                  </g>
                </svg>
              </artwork>
              <artwork type="ascii-art"><![CDATA[
              W = root
              |
        .-----+-----.
       /             \
      _=U             Y
      |               |
    .-+-.           .-+-.
   /     \         /     \
  T       _=V     X       _=Z
 / \     / \     / \     / \
A   B   _   _   E   F   G   _=H

0   1   2   3   4   5   6   7
]]></artwork>
            </artset>
          </figure>
          <t>In this tree, the direct paths, copaths, and filtered direct paths for the leaf
nodes are as follows:</t>
          <table>
            <thead>
              <tr>
                <th align="left">Node</th>
                <th align="left">Direct path</th>
                <th align="left">Copath</th>
                <th align="left">Filtered Direct Path</th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td align="left">A</td>
                <td align="left">T, U, W</td>
                <td align="left">B, V, Y</td>
                <td align="left">T, W</td>
              </tr>
              <tr>
                <td align="left">B</td>
                <td align="left">T, U, W</td>
                <td align="left">A, V, Y</td>
                <td align="left">T, W</td>
              </tr>
              <tr>
                <td align="left">E</td>
                <td align="left">X, Y, W</td>
                <td align="left">F, Z, U</td>
                <td align="left">X, Y, W</td>
              </tr>
              <tr>
                <td align="left">F</td>
                <td align="left">X, Y, W</td>
                <td align="left">E, Z, U</td>
                <td align="left">X, Y, W</td>
              </tr>
              <tr>
                <td align="left">G</td>
                <td align="left">Z, Y, W</td>
                <td align="left">H, X, U</td>
                <td align="left">Y, W</td>
              </tr>
            </tbody>
          </table>
        </section>
      </section>
      <section anchor="views">
        <name>Views of a Ratchet Tree</name>
        <t>We generally assume that each participant maintains a complete and
up-to-date view of the public state of the group's ratchet tree,
including the public keys for all nodes and the credentials
associated with the leaf nodes.</t>
        <t>No participant in an MLS group knows the private key associated with
every node in the tree. Instead, each member is assigned to a leaf of the tree,
which determines the subset of private keys it knows. The
credential stored at that leaf is one provided by the member.</t>
        <t>In particular, MLS maintains the members' views of the tree in such
a way as to maintain the <em>tree invariant</em>:</t>
        <artwork><![CDATA[
The private key for a node in the tree is known to a member of
the group only if the node's subtree contains that member's leaf.
]]></artwork>
        <t>In other words, if a node is not blank, then it holds a public key.
The corresponding private key is known only to members occupying
leaves below that node.</t>
        <t>The reverse implication is not true: A member may not know the private keys of
all the intermediate nodes they're below.  Such a member has an <em>unmerged</em> leaf.
Encrypting to an intermediate node requires encrypting to the node's public key,
as well as the public keys of all the unmerged leaves below it.  A leaf is
unmerged when it is first added, because the process of adding the leaf does not
give it access to all of the nodes above it in the tree.  Leaves are "merged" as
they receive the private keys for nodes, as described in
<xref target="ratchet-tree-evolution"/>.</t>
        <t>For example, consider a four-member group (A, B, C, D) where the node above the
right two members is blank.  (This is what it would look like if A created a
group with B, C, and D.)  Then the public state of the tree and the views of the
private keys of the tree held by each participant would be as follows, where <tt>_</tt>
represents a blank node, <tt>?</tt> represents an unknown private key, and <tt>pk(X)</tt>
represents the public key corresponding to the private key <tt>X</tt>:</t>
        <artwork type="ascii-art"><![CDATA[
         Public Tree
============================
            pk(ABCD)
          /          \
    pk(AB)            _
     / \             / \
pk(A)   pk(B)   pk(C)   pk(D)


 Private @ A       Private @ B       Private @ C       Private @ D
=============     =============     =============     =============
     ABCD              ABCD              ABCD              ABCD
    /   \             /   \             /   \             /   \
  AB      _         AB      _         ?       _         ?       _
 / \     / \       / \     / \       / \     / \       / \     / \
A   ?   ?   ?     ?   B   ?   ?     ?   ?   C   ?     ?   ?   ?   D
]]></artwork>
        <t>Note how the tree invariant applies: Each member knows only their own leaf, and
the private key AB is known only to A and B.</t>
      </section>
    </section>
    <section anchor="cryptographic-objects">
      <name>Cryptographic Objects</name>
      <section anchor="ciphersuites">
        <name>Ciphersuites</name>
        <t>Each MLS session uses a single ciphersuite that specifies the
following primitives to be used in group key computations:</t>
        <ul spacing="normal">
          <li>
            <t>HPKE parameters:
            </t>
            <ul spacing="normal">
              <li>A Key Encapsulation Mechanism (KEM)</li>
              <li>A Key Derivation Function (KDF)</li>
              <li>An Authenticated Encryption with Associated Data (AEAD) encryption algorithm</li>
            </ul>
          </li>
          <li>A hash algorithm</li>
          <li>A MAC algorithm</li>
          <li>A signature algorithm</li>
        </ul>
        <t>MLS uses HPKE for public-key encryption <xref target="RFC9180"/>.  The
<tt>DeriveKeyPair</tt> function associated to the KEM for the ciphersuite maps octet
strings to HPKE key pairs.  As in HPKE, MLS assumes that an AEAD algorithm
produces a single ciphertext output from AEAD encryption (aligning with
<xref target="RFC5116"/>), as opposed to a separate ciphertext and tag.</t>
        <t>Ciphersuites are represented with the CipherSuite type. The ciphersuites are
defined in <xref target="mls-ciphersuites"/>.</t>
        <section anchor="public-keys">
          <name>Public Keys</name>
          <t>HPKE public keys are opaque values in a format defined by the underlying
protocol (see the Cryptographic Dependencies section of the HPKE specification
for more information).</t>
          <sourcecode type="tls"><![CDATA[
opaque HPKEPublicKey<V>;
]]></sourcecode>
          <t>Signature public keys are likewise represented as opaque values in a format
defined by the ciphersuite's signature scheme.</t>
          <sourcecode type="tls"><![CDATA[
opaque SignaturePublicKey<V>;
]]></sourcecode>
          <t>For ciphersuites using Ed25519 or Ed448 signature schemes, the public key is in
the format specified in <xref target="RFC8032"/>.  For ciphersuites using ECDSA with the
NIST curves (P-256, P-384, or P-521), the public key is represented as an
encoded UncompressedPointRepresentation struct, as defined in <xref target="RFC8446"/>.</t>
        </section>
        <section anchor="signing">
          <name>Signing</name>
          <t>The signature algorithm specified in the ciphersuite is the mandatory algorithm
to be used for signatures in FramedContentAuthData and the tree signatures.  It
MUST be the same as the signature algorithm specified in the credentials in the
leaves of the tree (including the leaf node information in KeyPackages used to
add new members).</t>
          <t>The signatures used in this document are encoded as specified in <xref target="RFC8446"/>.
In particular, ECDSA signatures are DER-encoded and EdDSA signatures are defined
as the concatenation of <tt>r</tt> and <tt>s</tt> as specified in <xref target="RFC8032"/>.</t>
          <t>To disambiguate different signatures used in MLS, each signed value is prefixed
by a label as shown below:</t>
          <sourcecode type="pseudocode"><![CDATA[
SignWithLabel(SignatureKey, Label, Content) =
    Signature.Sign(SignatureKey, SignContent)

VerifyWithLabel(VerificationKey, Label, Content, SignatureValue) =
    Signature.Verify(VerificationKey, SignContent, SignatureValue)
]]></sourcecode>
          <t>Where SignContent is specified as:</t>
          <sourcecode type="tls"><![CDATA[
struct {
    opaque label<V>;
    opaque content<V>;
} SignContent;
]]></sourcecode>
          <t>And its fields set to:</t>
          <sourcecode type="pseudocode"><![CDATA[
label = "MLS 1.0 " + Label;
content = Content;
]]></sourcecode>
          <t>Here, the functions <tt>Signature.Sign</tt> and <tt>Signature.Verify</tt> are defined by the
signature algorithm.  If MLS extensions require signatures by group members,
they should re-use the SignWithLabel construction, using a distinct label.  To
avoid collisions in these labels, an IANA registry is defined in
<xref target="mls-signature-labels"/>.</t>
        </section>
        <section anchor="public-key-encryption">
          <name>Public-Key Encryption</name>
          <t>As with signing, MLS includes a label and context in encryption operations to
avoid confusion between ciphertexts produced for different purposes.  Encryption
and decryption including this label and context are done as follows:</t>
          <sourcecode type="pseudocode"><![CDATA[
EncryptWithLabel(PublicKey, Label, Context, Plaintext) =
  SealBase(PublicKey, EncryptContext, "", Plaintext)

DecryptWithLabel(PrivateKey, Label, Context, KEMOutput, Ciphertext) =
  OpenBase(KEMOutput, PrivateKey, EncryptContext, "", Ciphertext)
]]></sourcecode>
          <t>Where EncryptContext is specified as:</t>
          <sourcecode type="tls"><![CDATA[
struct {
  opaque label<V>;
  opaque context<V>;
} EncryptContext;
]]></sourcecode>
          <t>And its fields set to:</t>
          <artwork><![CDATA[
label = "MLS 1.0 " + Label;
context = Context;
]]></artwork>
          <t>Here, the functions <tt>SealBase</tt> and <tt>OpenBase</tt> are defined <xref target="RFC9180"/>, using the
HPKE algorithms specified by the group's ciphersuite.  If MLS extensions
require HPKE encryption operations, they should re-use the EncryptWithLabel
construction, using a distinct label.  To avoid collisions in these labels, an
IANA registry is defined in <xref target="mls-public-key-encryption-labels"/>.</t>
        </section>
      </section>
      <section anchor="hash-based-identifiers">
        <name>Hash-Based Identifiers</name>
        <t>Some MLS messages refer to other MLS objects by hash.  For example, Welcome
messages refer to KeyPackages for the members being welcomed, and Commits refer
to Proposals they cover.  These identifiers are computed as follows:</t>
        <sourcecode type="tls"><![CDATA[
opaque HashReference<V>;

HashReference KeyPackageRef;
HashReference ProposalRef;
]]></sourcecode>
        <sourcecode type="pseudocode"><![CDATA[
MakeKeyPackageRef(value) = RefHash("MLS 1.0 KeyPackage Reference", value)
MakeProposalRef(value)   = RefHash("MLS 1.0 Proposal Reference", value)

RefHash(label, value) = Hash(RefHashInput)
]]></sourcecode>
        <t>Where RefHashInput is defined as:</t>
        <sourcecode type="tls"><![CDATA[
struct {
  opaque label<V>;
  opaque value<V>;
} RefHashInput;
]]></sourcecode>
        <t>And its fields set to:</t>
        <sourcecode type="pseudocode"><![CDATA[
label = label;
value = value;
]]></sourcecode>
        <t>For a KeyPackageRef, the <tt>value</tt> input is the encoded KeyPackage, and the
ciphersuite specified in the KeyPackage determines the KDF used.  For a
ProposalRef, the <tt>value</tt> input is the AuthenticatedContent carrying the
proposal.  In the latter two cases, the KDF is determined by the group's
ciphersuite.</t>
      </section>
      <section anchor="credentials">
        <name>Credentials</name>
        <t>Each member of a group presents a credential that provides one or more
identities for the member, and associates them with the member's signing key.
The identities and signing key are verified by the Authentication Service in use
for a group.</t>
        <t>It is up to the application to decide which identifier or identifiers to use at
the application level.  For example,
a certificate in an X509Credential may attest to several domain names or email
addresses in its subjectAltName extension.  An application may decide to
present all of these to a user, or if it knows a "desired" domain name or email
address, it can check that the desired identifier is among those attested.
Using the terminology from <xref target="RFC6125"/>, a Credential provides "presented
identifiers", and it is up to the application to supply a "reference identifier"
for the authenticated client, if any.</t>
        <sourcecode type="tls"><![CDATA[
// See IANA registry for registered values
uint16 CredentialType;

struct {
    opaque cert_data<V>;
} Certificate;

struct {
    CredentialType credential_type;
    select (Credential.credential_type) {
        case basic:
            opaque identity<V>;

        case x509:
            Certificate chain<V>;
    };
} Credential;
]]></sourcecode>
        <t>A "basic" credential is a bare assertion of an identity, without any additional
information.  The format of the encoded identity is defined by the application.</t>
        <t>For an X.509 credential, each entry in the chain represents a single DER-encoded
X.509 certificate. The chain is ordered such that the first entry (chain[0]) is
the end-entity certificate and each subsequent certificate in the chain MUST be
the issuer of the previous certificate.  The public key encoded in the
<tt>subjectPublicKeyInfo</tt> of the end-entity certificate MUST be identical to the
<tt>signature_key</tt> in the LeafNode containing this credential.</t>
        <section anchor="credential-validation">
          <name>Credential Validation</name>
          <t>The application using MLS is responsible for specifying which identifiers it
finds acceptable for each member in a group.  In other words, following the
model that <xref target="RFC6125"/> describes for TLS, the application maintains a list of
"reference identifiers" for the members of a group, and the credentials provide
"presented identifiers".  A member of a group is authenticated by first
validating that the member's credential legitimately represents some presented
identifiers, and then ensuring that the reference identifiers for the member are
authenticated by those presented identifiers.</t>
          <t>The parts of the system that perform these functions are collectively referred
to as the Authentication Service (AS) <xref target="I-D.ietf-mls-architecture"/>.  A
member's credential is said to be <em>validated with the AS</em> when the AS verifies
that the credential's presented identifiers are correctly associated with the
<tt>signature_key</tt> field in the member's LeafNode, and verifies that those
identifiers match the reference identifiers for the member.</t>
          <t>Whenever a new credential is introduced in the group, it MUST be validated with
the AS.  In particular, at the following events in the protocol:</t>
          <ul spacing="normal">
            <li>When a member receives a KeyPackage that it will use in an Add proposal to add
a new member to the group.</li>
            <li>When a member receives a GroupInfo object that it will use to join a group,
either via a Welcome or via an External Commit</li>
            <li>When a member receives an Add proposal adding a member to the group.</li>
            <li>When a member receives an Update proposal whose LeafNode has a new credential
for the member.</li>
            <li>When a member receives a Commit with an UpdatePath whose LeafNode has a new
credential for the committer.</li>
            <li>When an <tt>external_senders</tt> extension is added to the group, or an existing
<tt>external_senders</tt> extension is updated.</li>
          </ul>
          <t>In cases where a member's credential is being replaced, such as Update and
Commit cases above, the AS MUST also verify that the set of presented
identifiers in the new credential is valid as a successor to the set of
presented identifiers in the old credential, according to the application's
policy.</t>
        </section>
        <section anchor="credential-expiry-and-revocation">
          <name>Credential Expiry and Revocation</name>
          <t>In some credential schemes, a valid credential can "expire", or become invalid
after a certain point in time. For example, each X.509 certificate has a
<tt>notAfter</tt> field, expressing a time after which the certificate is not valid.</t>
          <t>Expired credentials can cause operational problems in light of the validation
requirements of <xref target="credential-validation"/>.  Applications can apply some
operational practices and adaptations to Authentication Service policies to
moderate these impacts.</t>
          <t>In general, to avoid operational problems such as new joiners rejecting expired
credentials in a group, applications that use such credentials should ensure to
the extent practical that all of the credentials in use in a group are valid at
all times.</t>
          <t>If a member finds that its credential has expired (or will soon), it should
issue an Update or Commit that replaces it with a valid credential.  For this
reason, members SHOULD accept Update proposals and Commits issued by members
with expired credentials, if the credential in the Update or Commit is valid.</t>
          <t>Similarly, when a client is processing messages sent some time in the past
(e.g., syncing up with a group after being offline), the client SHOULD accept
signatures from members with expired credentials, since the credential may
have been valid at the time the message was sent.</t>
          <t>If a member finds that another member's credential has expired, they may issue a
Remove that removes that member.  For example, an application could require a
member preparing to issue a Commit to check the tree for expired credentials and
include Remove proposals for those members in its Commit.  In situations where
the group tree is known to the DS, the DS could also monitor the tree for
expired credentials and issue external Remove proposals.</t>
          <t>Some credential schemes also allow credentials to be revoked.  Revocation is
similar to expiry, in that a previously valid credential becomes invalid.
As such, most of the considerations above also apply to revoked credentials.
However, applications may want to treat revoked credentials differently, e.g.,
removing members with revoked credentials while allowing members with expired
credentials time to update.</t>
        </section>
        <section anchor="uniquely-identifying-clients">
          <name>Uniquely Identifying Clients</name>
          <t>MLS implementations will presumably provide applications with a way to request
protocol operations with regard to other clients (e.g., removing clients).  Such
functions will need to refer to the other clients using some identifier.  MLS
clients have a few types of identifiers, with different operational properties.</t>
          <t>Internally to the protocol, group members are uniquely identified by their leaf
index. However, a leaf index is only valid for referring to members in a given
epoch. The same leaf index may represent a different member, or no member at
all, in a subsequent epoch.</t>
          <t>The Credentials presented by the clients in a group authenticate
application-level identifiers for the clients.  However, these identifiers may not
uniquely identify clients.  For example, if a user has multiple devices that are
all present in an MLS group, then those devices' clients could all present the
user's application-layer identifiers.</t>
          <t>If needed, applications may add application-specific identifiers to the
<tt>extensions</tt> field of a LeafNode object with the <tt>application_id</tt> extension.</t>
          <sourcecode type="tls"><![CDATA[
opaque application_id<V>;
]]></sourcecode>
          <t>However, applications SHOULD NOT rely on the data in an <tt>application_id</tt> extension
as if it were authenticated by the Authentication Service, and SHOULD gracefully
handle cases where the identifier presented is not unique.</t>
        </section>
      </section>
    </section>
    <section anchor="message-framing">
      <name>Message Framing</name>
      <t>Handshake and application messages use a common framing structure.
This framing provides encryption to ensure confidentiality within the
group, as well as signing to authenticate the sender.</t>
      <t>In most of the protocol, messages are handled in the form of
AuthenticatedContent objects.  These structures contain the content of the
message itself as well as information to authenticate the sender (see
<xref target="content-authentication"/>).  The additional protections required to transmit
these messages over an untrusted channel (group membership authentication or
AEAD encryption) are added by encoding the AuthenticatedContent as an
PublicMessage or PrivateMessage message, which can then be sent as an MLSMessage.
Likewise, these protections are enforced (via membership verification or AEAD
decryption) when decoding an PublicMessage or PrivateMessage into an
AuthenticatedContent object.</t>
      <t>PrivateMessage represents a signed and encrypted message, with
protections for both the content of the message and related
metadata.  PublicMessage represents a message that is only signed,
and not encrypted.  Applications MUST use PrivateMessage to encrypt
application messages and SHOULD use PrivateMessage to encode
handshake messages, but MAY transmit handshake messages encoded
as PublicMessage objects in cases where it is necessary for the
Delivery Service to examine such messages.</t>
      <sourcecode type="tls"><![CDATA[
enum {
    reserved(0),
    mls10(1),
    (65535)
} ProtocolVersion;

enum {
    reserved(0),
    application(1),
    proposal(2),
    commit(3),
    (255)
} ContentType;

enum {
    reserved(0),
    member(1),
    external(2),
    new_member_proposal(3),
    new_member_commit(4),
    (255)
} SenderType;

struct {
    SenderType sender_type;
    select (Sender.sender_type) {
        case member:
            uint32 leaf_index;
        case external:
            uint32 sender_index;
        case new_member_commit:
        case new_member_proposal:
            struct{};
    };
} Sender;

// See IANA registry for registered values
uint16 WireFormat;

struct {
    opaque group_id<V>;
    uint64 epoch;
    Sender sender;
    opaque authenticated_data<V>;

    ContentType content_type;
    select (FramedContent.content_type) {
        case application:
          opaque application_data<V>;
        case proposal:
          Proposal proposal;
        case commit:
          Commit commit;
    };
} FramedContent;

struct {
    ProtocolVersion version = mls10;
    WireFormat wire_format;
    select (MLSMessage.wire_format) {
        case mls_plaintext:
            PublicMessage plaintext;
        case mls_ciphertext:
            PrivateMessage ciphertext;
        case mls_welcome:
            Welcome welcome;
        case mls_group_info:
            GroupInfo group_info;
        case mls_key_package:
            KeyPackage key_package;
    };
} MLSMessage;
]]></sourcecode>
      <t>Messages from senders that aren't in the group are sent as PublicMessage. See
<xref target="external-proposals"/> and <xref target="joining-via-external-commits"/> for more details.</t>
      <t>The following structure is used to fully describe the data transmitted in
plaintexts or ciphertexts.</t>
      <sourcecode type="tls"><![CDATA[
struct {
    WireFormat wire_format;
    FramedContent content;
    FramedContentAuthData auth;
} AuthenticatedContent;
]]></sourcecode>
      <t>The following figure illustrates how the various structures described in this
section relate to each other, and the high-level operations used to produce and
consume them:</t>
      <artset>
        <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="512" width="728" viewBox="0 0 728 512" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
            <path d="M 32,416 L 32,448" fill="none" stroke="black"/>
            <path d="M 120,416 L 120,448" fill="none" stroke="black"/>
            <path d="M 208,416 L 208,448" fill="none" stroke="black"/>
            <path d="M 248,448 L 248,480" fill="none" stroke="black"/>
            <path d="M 272,48 L 272,64" fill="none" stroke="black"/>
            <path d="M 296,160 L 296,192" fill="none" stroke="black"/>
            <path d="M 296,224 L 296,240" fill="none" stroke="black"/>
            <path d="M 320,352 L 320,384" fill="none" stroke="black"/>
            <path d="M 320,416 L 320,448" fill="none" stroke="black"/>
            <path d="M 368,128 L 368,160" fill="none" stroke="black"/>
            <path d="M 368,240 L 368,272" fill="none" stroke="black"/>
            <path d="M 392,48 L 392,96" fill="none" stroke="black"/>
            <path d="M 392,128 L 392,272" fill="none" stroke="black"/>
            <path d="M 392,304 L 392,352" fill="none" stroke="black"/>
            <path d="M 464,352 L 464,384" fill="none" stroke="black"/>
            <path d="M 464,416 L 464,448" fill="none" stroke="black"/>
            <path d="M 512,48 L 512,64" fill="none" stroke="black"/>
            <path d="M 544,144 L 544,256" fill="none" stroke="black"/>
            <path d="M 544,320 L 544,384" fill="none" stroke="black"/>
            <path d="M 272,64 L 512,64" fill="none" stroke="black"/>
            <path d="M 296,160 L 368,160" fill="none" stroke="black"/>
            <path d="M 544,192 L 560,192" fill="none" stroke="black"/>
            <path d="M 296,240 L 368,240" fill="none" stroke="black"/>
            <path d="M 320,352 L 464,352" fill="none" stroke="black"/>
            <path d="M 544,352 L 560,352" fill="none" stroke="black"/>
            <path d="M 32,448 L 464,448" fill="none" stroke="black"/>
            <path d="M 528,128 C 536.83064,128 544,135.16936 544,144" fill="none" stroke="black"/>
            <path d="M 528,272 C 536.83064,272 544,264.83064 544,256" fill="none" stroke="black"/>
            <path d="M 528,304 C 536.83064,304 544,311.16936 544,320" fill="none" stroke="black"/>
            <path d="M 528,400 C 536.83064,400 544,392.83064 544,384" fill="none" stroke="black"/>
            <polygon class="arrowhead" points="472,384 460,378.4 460,389.6" fill="black" transform="rotate(90,464,384)"/>
            <polygon class="arrowhead" points="400,272 388,266.4 388,277.6" fill="black" transform="rotate(90,392,272)"/>
            <polygon class="arrowhead" points="400,96 388,90.4 388,101.6" fill="black" transform="rotate(90,392,96)"/>
            <polygon class="arrowhead" points="376,272 364,266.4 364,277.6" fill="black" transform="rotate(90,368,272)"/>
            <polygon class="arrowhead" points="328,384 316,378.4 316,389.6" fill="black" transform="rotate(90,320,384)"/>
            <polygon class="arrowhead" points="304,192 292,186.4 292,197.6" fill="black" transform="rotate(90,296,192)"/>
            <polygon class="arrowhead" points="256,480 244,474.4 244,485.6" fill="black" transform="rotate(90,248,480)"/>
            <g class="text">
              <text x="276" y="36">Proposal</text>
              <text x="396" y="36">Commit</text>
              <text x="504" y="36">Application</text>
              <text x="572" y="36">Data</text>
              <text x="384" y="116">FramedContent</text>
              <text x="612" y="196">Asymmetric</text>
              <text x="296" y="212">FramedContentAuthData</text>
              <text x="588" y="212">Sign</text>
              <text x="616" y="212">/</text>
              <text x="652" y="212">Verify</text>
              <text x="396" y="292">AuthenticatedContent</text>
              <text x="608" y="356">Symmetric</text>
              <text x="600" y="372">Protect</text>
              <text x="640" y="372">/</text>
              <text x="688" y="372">Unprotect</text>
              <text x="32" y="404">Welcome</text>
              <text x="116" y="404">KeyPackage</text>
              <text x="208" y="404">GroupInfo</text>
              <text x="320" y="404">PublicMessage</text>
              <text x="460" y="404">PrivateMessage</text>
              <text x="252" y="500">MLSMessage</text>
            </g>
          </svg>
        </artwork>
        <artwork type="ascii-art"><![CDATA[
                              Proposal        Commit     Application Data
                                 |              |              |
                                 +--------------+--------------+
                                                |
                                                V
                                         FramedContent
                                             |  |                -.
                                             |  |                  |
                                    +--------+  |                  |
                                    |           |                  |
                                    V           |                  +-- Asymmetric
                          FramedContentAuthData |                  |   Sign / Verify
                                    |           |                  |
                                    +--------+  |                  |
                                             |  |                  |
                                             V  V                -'
                                       AuthenticatedContent
                                                |                -.
                                                |                  |
                                                |                  |
                                       +--------+--------+         +-- Symmetric
                                       |                 |         |   Protect / Unprotect
                                       V                 V         |
Welcome  KeyPackage  GroupInfo   PublicMessage    PrivateMessage -'
   |          |          |             |                 |
   |          |          |             |                 |
   +----------+----------+----+--------+-----------------+
                              |
                              V
                          MLSMessage
]]></artwork>
      </artset>
      <section anchor="content-authentication">
        <name>Content Authentication</name>
        <t>FramedContent is authenticated using the FramedContentAuthData structure.</t>
        <sourcecode type="tls"><![CDATA[
struct {
    ProtocolVersion version = mls10;
    WireFormat wire_format;
    FramedContent content;
    select (FramedContentTBS.content.sender.sender_type) {
        case member:
        case new_member_commit:
            GroupContext context;
        case external:
        case new_member_proposal:
            struct{};
    };
} FramedContentTBS;

opaque MAC<V>;

struct {
    /* SignWithLabel(., "FramedContentTBS", FramedContentTBS) */
    opaque signature<V>;
    select (FramedContent.content_type) {
        case commit:
            /*
              MAC(confirmation_key,
                  GroupContext.confirmed_transcript_hash)
            */
            MAC confirmation_tag;
        case application:
        case proposal:
            struct{};
    };
} FramedContentAuthData;
]]></sourcecode>
        <t>The signature is computed using <tt>SignWithLabel</tt> with label
<tt>"FramedContentTBS"</tt> and with a content that covers the message content and
the wire format that will be used for this message. If the sender's
<tt>sender_type</tt> is <tt>member</tt>, the content also covers the GroupContext for the
current epoch so that signatures are specific to a given group and epoch.</t>
        <t>The sender MUST use the private key corresponding to the following signature key
depending on the sender's <tt>sender_type</tt>:</t>
        <ul spacing="normal">
          <li>
            <tt>member</tt>: The signature key contained in the LeafNode at the index
indicated by <tt>leaf_index</tt> in the ratchet tree.</li>
          <li>
            <tt>external</tt>: The signature key at the index
indicated by <tt>sender_index</tt> in the <tt>external_senders</tt> group context
extension (see <xref target="external-senders-extension"/>). The
<tt>content_type</tt> of the message MUST be <tt>proposal</tt>.</li>
          <li>
            <tt>new_member_commit</tt>: The signature key in the LeafNode in
  the Commit's path (see <xref target="joining-via-external-commits"/>). The
  <tt>content_type</tt> of the message MUST be <tt>commit</tt>.</li>
          <li>
            <tt>new_member_proposal</tt>: The signature key in the LeafNode in
  the KeyPackage embedded in an External Add Proposal. The
  <tt>content_type</tt> of the message MUST be <tt>proposal</tt> and the
  <tt>proposal_type</tt> of the Proposal MUST be <tt>add</tt>.</li>
        </ul>
        <t>Recipients of an MLSMessage MUST verify the signature with the key depending on
the <tt>sender_type</tt> of the sender as described above.</t>
        <t>The confirmation tag value confirms that the members of the group have arrived
at the same state of the group. A FramedContentAuthData is said to be valid when both
the <tt>signature</tt> and <tt>confirmation_tag</tt> fields are valid.</t>
      </section>
      <section anchor="encoding-and-decoding-a-public-message">
        <name>Encoding and Decoding a Public Message</name>
        <t>Messages that are authenticated but not encrypted are encoded using the PublicMessage structure.</t>
        <sourcecode type="tls"><![CDATA[
struct {
    FramedContent content;
    FramedContentAuthData auth;
    select (PublicMessage.content.sender.sender_type) {
        case member:
            MAC membership_tag;
        case external:
        case new_member_commit:
        case new_member_proposal:
            struct{};
    };
} PublicMessage;
]]></sourcecode>
        <t>The <tt>membership_tag</tt> field in the PublicMessage object authenticates the sender's
membership in the group. For messages sent by members, it MUST be set to the
following value:</t>
        <sourcecode type="tls"><![CDATA[
struct {
  FramedContentTBS content_tbs;
  FramedContentAuthData auth;
} AuthenticatedContentTBM;
]]></sourcecode>
        <sourcecode type="pseudocode"><![CDATA[
membership_tag = MAC(membership_key, AuthenticatedContentTBM)
]]></sourcecode>
        <t>When decoding an PublicMessage into an AuthenticatedContent,
the application MUST check <tt>membership_tag</tt> and MUST check that the
FramedContentAuthData is valid.</t>
      </section>
      <section anchor="encoding-and-decoding-a-private-message">
        <name>Encoding and Decoding a Private Message</name>
        <t>Authenticated and encrypted messages are encoded using the PrivateMessage structure.</t>
        <sourcecode type="tls"><![CDATA[
struct {
    opaque group_id<V>;
    uint64 epoch;
    ContentType content_type;
    opaque authenticated_data<V>;
    opaque encrypted_sender_data<V>;
    opaque ciphertext<V>;
} PrivateMessage;
]]></sourcecode>
        <t><tt>encrypted_sender_data</tt> and <tt>ciphertext</tt> are encrypted using the AEAD function
specified by the ciphersuite in use, using as input the structures SenderData
and PrivateContentTBE.</t>
        <section anchor="content-encryption">
          <name>Content Encryption</name>
          <t>Content to be encrypted is encoded in an PrivateContentTBE structure.</t>
          <sourcecode type="tls"><![CDATA[
struct {
    select (PrivateMessage.content_type) {
        case application:
          opaque application_data<V>;

        case proposal:
          Proposal proposal;

        case commit:
          Commit commit;
    };

    FramedContentAuthData auth;
    opaque padding[length_of_padding];
} PrivateContentTBE;
]]></sourcecode>
          <t>The <tt>padding</tt> field is set by the sender, by first encoding the content (via the
<tt>select</tt>) and the <tt>auth</tt> field, then appending the chosen number of zero bytes.
A receiver identifies the padding field in a plaintext decoded from
<tt>PrivateMessage.ciphertext</tt> by first decoding the content and the <tt>auth</tt> field;
then the <tt>padding</tt> field comprises any remaining octets of plaintext.  The
<tt>padding</tt> field MUST be filled with all zero bytes.  A receiver MUST verify that
there are no non-zero bytes in the <tt>padding</tt> field, and if this check fails, the
enclosing PrivateMessage MUST be rejected as malformed.  This check ensures that
the padding process is deterministic, so that, for example, padding cannot be
used as a covert channel.</t>
          <t>In the MLS key schedule, the sender creates two distinct key ratchets for
handshake and application messages for each member of the group. When encrypting
a message, the sender looks at the ratchets it derived for its own member and
chooses an unused generation from either the handshake or application ratchet
depending on the content type of the message. This generation of the ratchet is
used to derive a provisional nonce and key.</t>
          <t>Before use in the encryption operation, the nonce is XORed with a fresh random
value to guard against reuse.  Because the key schedule generates nonces
deterministically, a client MUST keep persistent state as to where in the key
schedule it is; if this persistent state is lost or corrupted, a client might
reuse a generation that has already been used, causing reuse of a key/nonce pair.</t>
          <t>To avoid this situation, the sender of a message MUST generate a fresh random
four-byte "reuse guard" value and XOR it with the first four bytes of the nonce
from the key schedule before using the nonce for encryption.  The sender MUST
include the reuse guard in the <tt>reuse_guard</tt> field of the sender data object, so
that the recipient of the message can use it to compute the nonce to be used for
decryption.</t>
          <artwork type="ascii-art"><![CDATA[
+-+-+-+-+---------...---+
|   Key Schedule Nonce  |
+-+-+-+-+---------...---+
           XOR
+-+-+-+-+---------...---+
| Guard |       0       |
+-+-+-+-+---------...---+
           ===
+-+-+-+-+---------...---+
| Encrypt/Decrypt Nonce |
+-+-+-+-+---------...---+
]]></artwork>
          <t>The Additional Authenticated Data (AAD) input to the encryption
contains an object of the following form, with the values used to
identify the key and nonce:</t>
          <sourcecode type="tls"><![CDATA[
struct {
    opaque group_id<V>;
    uint64 epoch;
    ContentType content_type;
    opaque authenticated_data<V>;
} PrivateContentAAD;
]]></sourcecode>
          <t>When decoding an PrivateContentTBE, the application MUST check that the
FramedContentAuthData is valid.</t>
          <t>It is up to the application to decide what <tt>authenticated_data</tt> to provide and
how much padding to add to a given message (if any).  The overall size of the
AAD and ciphertext MUST fit within the limits established for the group's AEAD
algorithm in [!I-D.irtf-cfrg-aead-limits].</t>
        </section>
        <section anchor="sender-data-encryption">
          <name>Sender Data Encryption</name>
          <t>The "sender data" used to look up the key for content encryption is
encrypted with the ciphersuite's AEAD with a key and nonce derived from both the
<tt>sender_data_secret</tt> and a sample of the encrypted content. Before being
encrypted, the sender data is encoded as an object of the following form:</t>
          <sourcecode type="tls"><![CDATA[
struct {
    uint32 leaf_index;
    uint32 generation;
    opaque reuse_guard[4];
} SenderData;
]]></sourcecode>
          <t>When constructing a SenderData object from a Sender object, the sender MUST verify
Sender.sender_type is <tt>member</tt> and use Sender.leaf_index for
SenderData.leaf_index.</t>
          <t>The <tt>reuse_guard</tt> field contains a fresh random value used to avoid nonce reuse
in the case of state loss or corruption, as described in <xref target="content-encryption"/>.</t>
          <t>The key and nonce provided to the AEAD are computed as the KDF of the first
<tt>KDF.Nh</tt> bytes of the ciphertext generated in the previous section. If the
length of the ciphertext is less than <tt>KDF.Nh</tt>, the whole ciphertext is used.
In pseudocode, the key and nonce are derived as:</t>
          <sourcecode type="pseudocode"><![CDATA[
ciphertext_sample = ciphertext[0..KDF.Nh-1]

sender_data_key = ExpandWithLabel(sender_data_secret, "key",
                      ciphertext_sample, AEAD.Nk)
sender_data_nonce = ExpandWithLabel(sender_data_secret, "nonce",
                      ciphertext_sample, AEAD.Nn)
]]></sourcecode>
          <t>The Additional Authenticated Data (AAD) for the SenderData ciphertext is the
first three fields of PrivateMessage:</t>
          <sourcecode type="tls"><![CDATA[
struct {
    opaque group_id<V>;
    uint64 epoch;
    ContentType content_type;
} SenderDataAAD;
]]></sourcecode>
          <t>When parsing a SenderData struct as part of message decryption, the recipient
MUST verify that the leaf index indicated in the <tt>leaf_index</tt> field identifies a
non-blank node.</t>
        </section>
      </section>
    </section>
    <section anchor="ratchet-tree-operations">
      <name>Ratchet Tree Operations</name>
      <t>The ratchet tree for an epoch describes the membership of a group in that epoch,
providing public-key encryption (HPKE) keys that can be used to encrypt to subsets of
the group as well as information to authenticate the members.  In order to
reflect changes to the membership of the group from one epoch to the next,
corresponding changes are made to the ratchet tree.  In this section, we
describe the content of the tree and the required operations.</t>
      <section anchor="parent-node-contents">
        <name>Parent Node Contents</name>
        <t>As discussed in <xref target="ratchet-tree-nodes"/>, the nodes of a ratchet tree contain
several types of data describing individual members (for leaf nodes) or
subgroups of the group (for parent nodes).  Parent nodes are simpler:</t>
        <sourcecode type="tls"><![CDATA[
struct {
    HPKEPublicKey encryption_key;
    opaque parent_hash<V>;
    uint32 unmerged_leaves<V>;
} ParentNode;
]]></sourcecode>
        <t>The <tt>encryption_key</tt> field contains an HPKE public key whose private key is held only
by the members at the leaves among its descendants.  The <tt>parent_hash</tt> field
contains a hash of this node's parent node, as described in <xref target="parent-hashes"/>.
The <tt>unmerged_leaves</tt> field lists the leaves under this parent node that are
unmerged, according to their indices among all the leaves in the tree.  The
entries in the <tt>unmerged_leaves</tt> vector MUST be sorted in increasing order.</t>
      </section>
      <section anchor="leaf-node-contents">
        <name>Leaf Node Contents</name>
        <t>A leaf node in the tree describes all the details of an individual client's
appearance in the group, signed by that client. It is also used in client
KeyPackage objects to store the information that will be needed to add a
client to a group.</t>
        <sourcecode type="tls"><![CDATA[
enum {
    reserved(0),
    key_package(1),
    update(2),
    commit(3),
    (255)
} LeafNodeSource;

struct {
    ProtocolVersion versions<V>;
    CipherSuite ciphersuites<V>;
    ExtensionType extensions<V>;
    ProposalType proposals<V>;
    CredentialType credentials<V>;
} Capabilities;

struct {
    uint64 not_before;
    uint64 not_after;
} Lifetime;

// See IANA registry for registered values
uint16 ExtensionType;

struct {
    ExtensionType extension_type;
    opaque extension_data<V>;
} Extension;

struct {
    HPKEPublicKey encryption_key;
    SignaturePublicKey signature_key;
    Credential credential;
    Capabilities capabilities;

    LeafNodeSource leaf_node_source;
    select (LeafNode.leaf_node_source) {
        case key_package:
            Lifetime lifetime;

        case update:
            struct{};

        case commit:
            opaque parent_hash<V>;
    };

    Extension extensions<V>;
    /* SignWithLabel(., "LeafNodeTBS", LeafNodeTBS) */
    opaque signature<V>;
} LeafNode;

struct {
    HPKEPublicKey encryption_key;
    SignaturePublicKey signature_key;
    Credential credential;
    Capabilities capabilities;

    LeafNodeSource leaf_node_source;
    select (LeafNodeTBS.leaf_node_source) {
        case key_package:
            Lifetime lifetime;

        case update:
            struct{};

        case commit:
            opaque parent_hash<V>;
    };

    Extension extensions<V>;

    select (LeafNodeTBS.leaf_node_source) {
        case key_package:
            struct{};

        case update:
            opaque group_id<V>;
            uint32 leaf_index;

        case commit:
            opaque group_id<V>;
            uint32 leaf_index;
    };
} LeafNodeTBS;
]]></sourcecode>
        <t>The <tt>encryption_key</tt> field contains an HPKE public key whose private key is held only
by the member occupying this leaf (or in the case of a LeafNode in a KeyPackage
object, the issuer of the KeyPackage). The <tt>signature_key</tt> field contains the
member's public signing key. The <tt>credential</tt> field contains information
authenticating both the member's identity and the provided signing key, as
described in <xref target="credentials"/>.</t>
        <t>The <tt>capabilities</tt> field indicates what protocol versions, ciphersuites,
extensions, credential types, and non-default proposal types are supported by a client.
Proposal and extension types defined in this document are considered "default" and thus need
not be listed, while any credential types the application wishes to use MUST
be listed. Extensions that appear in the <tt>extensions</tt> field of a LeafNode
MUST be included in the <tt>extensions</tt> field of the <tt>capabilities</tt> field, and the
credential type used in the LeafNode MUST be included in the <tt>credentials</tt> field
of the <tt>capabilities</tt> field.</t>
        <t>The <tt>leaf_node_source</tt> field indicates how this LeafNode came to be added to the
tree.  This signal tells other members of the group whether the leaf node is
required to have a <tt>lifetime</tt> or <tt>parent_hash</tt>, and whether the <tt>group_id</tt> is
added as context to the signature.  Whether these fields can be computed by the
client represented by the LeafNode depends on when the LeafNode was created.
For example, a KeyPackage is created before the client knows which group it will
be used with, so its signature can't bind to a <tt>group_id</tt>.</t>
        <t>In the case where the leaf was added to the tree based on a pre-published
KeyPackage, the <tt>lifetime</tt> field represents the times between which clients will
consider a LeafNode valid.  These times are represented as absolute times,
measured in seconds since the Unix epoch (1970-01-01T00:00:00Z).  Applications
MUST define a maximum total lifetime that is acceptable for a LeafNode, and
reject any LeafNode where the total lifetime is longer than this duration.</t>
        <t>In the case where the leaf node was inserted into the tree via a Commit message,
the <tt>parent_hash</tt> field contains the parent hash for this leaf node (see
<xref target="parent-hashes"/>).</t>
        <t>The LeafNodeTBS structure covers the fields above the signature in the LeafNode.
In addition, when the leaf node was created in the context of a group (the
update and commit cases), the group ID of the group is added as context to the
signature.</t>
        <t>LeafNode objects stored in the group's ratchet tree
are updated according to the evolution of the tree. Each modification of
LeafNode content MUST be reflected by a change in its signature. This allows other
members to verify the validity of the LeafNode at any time, particularly in the
case of a newcomer joining the group.</t>
      </section>
      <section anchor="leaf-node-validation">
        <name>Leaf Node Validation</name>
        <t>The validity of a LeafNode needs to be verified at a few stages:</t>
        <ul spacing="normal">
          <li>When a LeafNode is downloaded in a KeyPackage, before it is used
to add the client to the group</li>
          <li>When a LeafNode is received by a group member in an Add, Update, or Commit
message</li>
          <li>When a client validates a ratchet tree, e.g., when joining a group or after
processing a commit</li>
        </ul>
        <t>The client verifies the validity of a LeafNode using the following steps:</t>
        <ul spacing="normal">
          <li>Verify that the credential in the LeafNode is valid as described in
<xref target="credential-validation"/>.</li>
          <li>Verify that the signature on the LeafNode is valid using <tt>signature_key</tt>.</li>
          <li>Verify that the LeafNode is compatible with the group's parameters.  If the
GroupContext has a <tt>required_capabilities</tt> extension, then the required
extensions, proposals, and credential types MUST be listed in the LeafNode's
<tt>capabilities</tt> field.</li>
          <li>Verify that the credential type is supported by all members of the group, as
specified by the <tt>capabilities</tt> field of each member's LeafNode, and that the
<tt>capabilities</tt> field of this LeafNode indicates support for all the credential
types currently in use by other members.</li>
          <li>
            <t>Verify the <tt>lifetime</tt> field:
            </t>
            <ul spacing="normal">
              <li>If the LeafNode appears in a message being sent by the client, e.g., a
proposal or a commit, then the client MUST verify that the current time is within
the range of the <tt>lifetime</tt> field.</li>
              <li>If instead the LeafNode appears in a message being received by the client, e.g.,
a proposal, a commit, or a ratchet tree of the group the client is joining, it is
RECOMMENDED that the client verifies that the current time is within the range
of the <tt>lifetime</tt> field.</li>
            </ul>
          </li>
          <li>Verify that the extensions in the LeafNode are supported by checking that the
ID for each extension in the <tt>extensions</tt> field is listed in the
<tt>capabilities.extensions</tt> field of the LeafNode.</li>
          <li>
            <t>Verify the <tt>leaf_node_source</tt> field:
            </t>
            <ul spacing="normal">
              <li>If the LeafNode appears in a KeyPackage, verify that <tt>leaf_node_source</tt> is
set to <tt>key_package</tt>.</li>
              <li>If the LeafNode appears in an Update proposal, verify that <tt>leaf_node_source</tt>
is set to <tt>update</tt>.</li>
              <li>If the LeafNode appears in the <tt>leaf_node</tt> value of the UpdatePath in
a Commit, verify that <tt>leaf_node_source</tt> is set to <tt>commit</tt>.</li>
            </ul>
          </li>
          <li>
            <t>Verify that the following fields are unique among the members of the group:
            </t>
            <ul spacing="normal">
              <li>
                <tt>signature_key</tt></li>
              <li>
                <tt>encryption_key</tt></li>
            </ul>
          </li>
        </ul>
      </section>
      <section anchor="ratchet-tree-evolution">
        <name>Ratchet Tree Evolution</name>
        <t>Whenever a member initiates an epoch change (i.e., commits; see <xref target="commit"/>),
they may need to refresh the key pairs of their leaf and of the nodes on their
leaf's direct path in order to maintain forward secrecy and post-compromise
security.</t>
        <t>The member initiating the epoch change generates the fresh key pairs using the
following procedure. The procedure is designed in a way that allows group members to
efficiently communicate the fresh secret keys to other group members, as
described in <xref target="update-paths"/>.</t>
        <t>A member updates the nodes along its direct path as follows:</t>
        <ul spacing="normal">
          <li>Blank all the nodes on the direct path from the leaf to the root.</li>
          <li>Generate a fresh HPKE key pair for the leaf.</li>
          <li>Generate a sequence of path secrets, one for each node on the leaf's filtered direct
path, as follows. In this setting, <tt>path_secret[0]</tt> refers to the first parent node
in the filtered direct path, <tt>path_secret[1]</tt> to the second parent node, and so on.</li>
        </ul>
        <sourcecode type="pseudocode"><![CDATA[
path_secret[0] is sampled at random
path_secret[n] = DeriveSecret(path_secret[n-1], "path")
]]></sourcecode>
        <ul spacing="normal">
          <li>Compute the sequence of HPKE key pairs <tt>(node_priv,node_pub)</tt>, one for each
node on the leaf's direct path, as follows.</li>
        </ul>
        <sourcecode type="pseudocode"><![CDATA[
node_secret[n] = DeriveSecret(path_secret[n], "node")
node_priv[n], node_pub[n] = KEM.DeriveKeyPair(node_secret[n])
]]></sourcecode>
        <t>The node secret is derived as a temporary intermediate secret so that each
secret is only used with one algorithm: The path secret is used as an input to
DeriveSecret and the node secret is used as an input to DeriveKeyPair.</t>
        <t>For example, suppose there is a group with four members, with C an unmerged leaf
at Z:</t>
        <figure anchor="evolution-tree">
          <name>A full tree with one unmerged leaf</name>
          <artset>
            <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="176" width="120" viewBox="0 0 120 176" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
                <path d="M 56,48 L 56,64" fill="none" stroke="black"/>
                <path d="M 40,64 L 72,64" fill="none" stroke="black"/>
                <path d="M 72,64 L 80,80" fill="none" stroke="black"/>
                <path d="M 32,80 L 40,64" fill="none" stroke="black"/>
                <g class="text">
                  <text x="56" y="36">Y</text>
                  <text x="24" y="100">X</text>
                  <text x="100" y="100">Z[C]</text>
                  <text x="16" y="116">/</text>
                  <text x="32" y="116">\</text>
                  <text x="80" y="116">/</text>
                  <text x="96" y="116">\</text>
                  <text x="8" y="132">A</text>
                  <text x="40" y="132">B</text>
                  <text x="72" y="132">C</text>
                  <text x="104" y="132">D</text>
                  <text x="8" y="164">0</text>
                  <text x="40" y="164">1</text>
                  <text x="72" y="164">2</text>
                  <text x="104" y="164">3</text>
                </g>
              </svg>
            </artwork>
            <artwork type="ascii-art"><![CDATA[
      Y
      |
    .-+-.
   /     \
  X       Z[C]
 / \     / \
A   B   C   D

0   1   2   3
]]></artwork>
          </artset>
        </figure>
        <t>If member B subsequently generates an UpdatePath based on a secret
"leaf_secret", then it would generate the following sequence
of path secrets:</t>
        <artset>
          <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="272" width="560" viewBox="0 0 560 272" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
              <path d="M 48,64 L 48,96" fill="none" stroke="black"/>
              <path d="M 48,144 L 48,176" fill="none" stroke="black"/>
              <path d="M 128,32 L 152,32" fill="none" stroke="black"/>
              <path d="M 288,32 L 344,32" fill="none" stroke="black"/>
              <path d="M 128,112 L 152,112" fill="none" stroke="black"/>
              <path d="M 288,112 L 344,112" fill="none" stroke="black"/>
              <path d="M 104,192 L 152,192" fill="none" stroke="black"/>
              <path d="M 304,192 L 344,192" fill="none" stroke="black"/>
              <path d="M 368,224 L 416,224" fill="none" stroke="black"/>
              <path d="M 448,224 L 496,224" fill="none" stroke="black"/>
              <path d="M 368,224 C 359.16936,224 352,216.83064 352,208" fill="none" stroke="black"/>
              <path d="M 416,224 C 424.83064,224 432,231.16936 432,240" fill="none" stroke="black"/>
              <path d="M 448,224 C 439.16936,224 432,231.16936 432,240" fill="none" stroke="black"/>
              <path d="M 496,224 C 504.83064,224 512,216.83064 512,208" fill="none" stroke="black"/>
              <polygon class="arrowhead" points="352,192 340,186.4 340,197.6" fill="black" transform="rotate(0,344,192)"/>
              <polygon class="arrowhead" points="352,112 340,106.4 340,117.6" fill="black" transform="rotate(0,344,112)"/>
              <polygon class="arrowhead" points="352,32 340,26.4 340,37.6" fill="black" transform="rotate(0,344,32)"/>
              <polygon class="arrowhead" points="160,192 148,186.4 148,197.6" fill="black" transform="rotate(0,152,192)"/>
              <polygon class="arrowhead" points="160,112 148,106.4 148,117.6" fill="black" transform="rotate(0,152,112)"/>
              <polygon class="arrowhead" points="160,32 148,26.4 148,37.6" fill="black" transform="rotate(0,152,32)"/>
              <polygon class="arrowhead" points="56,144 44,138.4 44,149.6" fill="black" transform="rotate(270,48,144)"/>
              <polygon class="arrowhead" points="56,64 44,58.4 44,69.6" fill="black" transform="rotate(270,48,64)"/>
              <g class="text">
                <text x="60" y="36">path_secret[1]</text>
                <text x="220" y="36">node_secret[1]</text>
                <text x="408" y="36">node_priv[1],</text>
                <text x="512" y="36">node_pub[1]</text>
                <text x="60" y="116">path_secret[0]</text>
                <text x="220" y="116">node_secret[0]</text>
                <text x="408" y="116">node_priv[0],</text>
                <text x="512" y="116">node_pub[0]</text>
                <text x="48" y="196">leaf_secret</text>
                <text x="228" y="196">leaf_node_secret</text>
                <text x="396" y="196">leaf_priv,</text>
                <text x="476" y="196">leaf_pub</text>
                <text x="432" y="260">leaf_node</text>
              </g>
            </svg>
          </artwork>
          <artwork type="ascii-art"><![CDATA[
path_secret[1] ---> node_secret[1] -------> node_priv[1], node_pub[1]

     ^
     |
     |
path_secret[0] ---> node_secret[0] -------> node_priv[0], node_pub[0]

     ^
     |
     |
leaf_secret ------> leaf_node_secret --+--> leaf_priv, leaf_pub
                                           |                   |
                                            '-------. .-------'
                                                     |
                                                 leaf_node
]]></artwork>
        </artset>
        <t>After applying the UpdatePath, the tree will have the following structure:</t>
        <artset>
          <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="192" width="256" viewBox="0 0 256 192" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
              <path d="M 176,144 L 176,160" fill="none" stroke="black"/>
              <path d="M 192,48 L 192,64" fill="none" stroke="black"/>
              <path d="M 112,32 L 176,32" fill="none" stroke="black"/>
              <path d="M 176,64 L 208,64" fill="none" stroke="black"/>
              <path d="M 112,96 L 144,96" fill="none" stroke="black"/>
              <path d="M 88,160 L 176,160" fill="none" stroke="black"/>
              <path d="M 208,64 L 216,80" fill="none" stroke="black"/>
              <path d="M 168,80 L 176,64" fill="none" stroke="black"/>
              <polygon class="arrowhead" points="184,144 172,138.4 172,149.6" fill="black" transform="rotate(270,176,144)"/>
              <polygon class="arrowhead" points="184,32 172,26.4 172,37.6" fill="black" transform="rotate(0,176,32)"/>
              <polygon class="arrowhead" points="152,96 140,90.4 140,101.6" fill="black" transform="rotate(0,144,96)"/>
              <g class="text">
                <text x="52" y="36">node_priv[1]</text>
                <text x="196" y="36">Y'</text>
                <text x="52" y="100">node_priv[0]</text>
                <text x="164" y="100">X'</text>
                <text x="236" y="100">Z[C]</text>
                <text x="152" y="116">/</text>
                <text x="168" y="116">\</text>
                <text x="216" y="116">/</text>
                <text x="232" y="116">\</text>
                <text x="144" y="132">A</text>
                <text x="176" y="132">B</text>
                <text x="208" y="132">C</text>
                <text x="240" y="132">D</text>
                <text x="40" y="164">leaf_priv</text>
                <text x="144" y="180">0</text>
                <text x="176" y="180">1</text>
                <text x="208" y="180">2</text>
                <text x="240" y="180">3</text>
              </g>
            </svg>
          </artwork>
          <artwork type="ascii-art"><![CDATA[
node_priv[1] --------> Y'
                       |
                     .-+-.
                    /     \
node_priv[0] ----> X'      Z[C]
                  / \     / \
                 A   B   C   D
                     ^
leaf_priv -----------+
                 0   1   2   3
]]></artwork>
        </artset>
      </section>
      <section anchor="synchronizing-views-of-the-tree">
        <name>Synchronizing Views of the Tree</name>
        <t>After generating fresh key material and applying it to ratchet forward their
local tree state as described in the <xref target="ratchet-tree-evolution"/>, the
generator broadcasts
this update to other members of the group in a Commit message, who
apply it to keep their local views of the tree in
sync with the sender's.  More specifically, when a member commits a change to
the tree (e.g., to add or remove a member), it transmits an UpdatePath
containing a set of public keys and encrypted path secrets
for intermediate nodes in the filtered direct path of its leaf. The
other members of the group use these values to update
their view of the tree, aligning their copy of the tree to the
sender's.</t>
        <t>An UpdatePath contains
the following information for each node in the filtered direct path of the
sender's leaf, including the root:</t>
        <ul spacing="normal">
          <li>The public key for the node</li>
          <li>One or more encrypted copies of the path secret corresponding to
the node</li>
        </ul>
        <t>The path secret value for a given node is encrypted to the subtree
rooted at the parent's non-updated child, i.e., the child
on the copath of the sender's leaf node.
There is one encryption of the path secret to each public key in the resolution
of the non-updated child.</t>
        <t>A member of the group <em>updates their direct path</em> by computing new values for
their leaf node and the nodes along their filtered direct path:</t>
        <ol spacing="normal" type="1"><li>Blank all nodes along the direct path of the sender's leaf.</li>
          <li>
            <t>Compute updated path secrets and public keys for the nodes on the sender's
filtered direct path.
            </t>
            <ul spacing="normal">
              <li>Generate a sequence of path secrets of the same length as the filtered
direct path, as defined in <xref target="ratchet-tree-evolution"/></li>
              <li>For each node in the filtered direct path, replace the node's public key
with the <tt>node_pub[n]</tt> value derived from the corresponding path secret
<tt>path_secret[n]</tt>.</li>
            </ul>
          </li>
          <li>Compute the new parent hashes for the nodes along the filtered direct path
and the sender's leaf node.</li>
          <li>
            <t>Update the leaf node for the sender.
            </t>
            <ul spacing="normal">
              <li>Set the <tt>leaf_node_source</tt> to <tt>commit</tt>.</li>
              <li>Set the <tt>encryption_key</tt> to the public key of a freshly sampled key pair</li>
              <li>Set the parent hash to the parent hash for the leaf.</li>
              <li>Re-sign the leaf node with its new contents</li>
            </ul>
          </li>
        </ol>
        <t>Since the new leaf node effectively updates an existing leaf node in the group,
it MUST adhere to the same restrictions as LeafNodes used in <tt>Update</tt> proposals
(aside from <tt>leaf_node_source</tt>). The application MAY specify other changes to
the leaf node, e.g., providing a new signature key, updated capabilities, or
different extensions.</t>
        <t>The member then <em>encrypts path secrets to the group</em>.  For each node in the
member's filtered direct path, the member takes the following steps:</t>
        <ol spacing="normal" type="1"><li>Compute the resolution of the node's child that is on the copath of the
sender (the child that is not in the direct path of the sender).  Any new
member (from an Add proposal) added in the same Commit MUST be excluded from
this resolution.</li>
          <li>For each node in the resolution, encrypt the path secret for the direct
path node using the public key of the resolution node, as defined in
<xref target="update-paths"/></li>
        </ol>
        <t>The recipient of an UpdatePath performs the corresponding steps.  First, the
recipient <em>merges UpdatePath into the tree</em>:</t>
        <ol spacing="normal" type="1"><li>Blank all nodes on the direct path of the sender's leaf.</li>
          <li>
            <t>For all nodes on the filtered direct path of the sender's leaf,
            </t>
            <ul spacing="normal">
              <li>Set the public key to the public key in the UpdatePath.</li>
              <li>Set the list of unmerged leaves to the empty list.</li>
            </ul>
          </li>
          <li>
            <t>Compute parent hashes for the nodes in the sender's filtered direct path,
and verify that the <tt>parent_hash</tt> field of the leaf node matches the parent
hash for the first node in its filtered direct path.
            </t>
            <ul spacing="normal">
              <li>Note that these hashes are computed from root to leaf, so that
each hash incorporates all the non-blank nodes above it. The root node
always has a zero-length hash for its parent hash.</li>
            </ul>
          </li>
        </ol>
        <t>Second, the recipient <em>decrypts the path secrets</em>:</t>
        <ol spacing="normal" type="1"><li>Identify a node in the filtered direct path for which the recipient
is in the subtree of the non-updated child.</li>
          <li>Identify a node in the resolution of the copath node for
which the recipient has a private key.</li>
          <li>Decrypt the path secret for the parent of the copath node using
the private key from the resolution node.</li>
          <li>Derive path secrets for ancestors of that node in the sender's filtered
direct path using the algorithm described above.</li>
          <li>Derive the node secrets and node key pairs from the path secrets.</li>
          <li>Verify that the derived public keys are the same as the corresponding public
keys sent in the UpdatePath.</li>
          <li>Store the derived private keys in the corresponding ratchet tree nodes.</li>
        </ol>
        <t>For example, in order to communicate the example update described in
<xref target="ratchet-tree-evolution"/>, the member at node B would transmit the following
values:</t>
        <table>
          <thead>
            <tr>
              <th align="left">Public Key</th>
              <th align="left">Ciphertext(s)</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">
                <tt>node_pub[1]</tt></td>
              <td align="left">
                <tt>E(pk(Z), path_secret[1])</tt>, <tt>E(pk(C), path_secret[1]</tt>)</td>
            </tr>
            <tr>
              <td align="left">
                <tt>node_pub[0]</tt></td>
              <td align="left">
                <tt>E(pk(A), path_secret[0])</tt></td>
            </tr>
          </tbody>
        </table>
        <t>In this table, the value node_pub[i] represents the public key
derived from node_secret[i], pk(X) represents the current public key
of node X, and E(K, S) represents
the public-key encryption of the path secret S to the
public key K (using HPKE).</t>
        <t>A recipient at node A would decrypt <tt>E(pk(A), path_secret\[0\])</tt> to obtain
<tt>path_secret\[0\]</tt>, then use it to derive <tt>path_secret[1]</tt> and the resulting
node secrets and key pairs.  Thus A would have the private keys to nodes X'
and Y', in accordance with the tree invariant.</t>
        <t>Similarly, a recipient at node D would decrypt <tt>E(pk(Z), path_secret[1])</tt> to
obtain <tt>path_secret[1]</tt>, then use it to derive the node secret and and key pair
for the node Y'.  As required to maintain the tree invariant, node D does not
receive the private key for the node X', since X' is not an ancestor of D.</t>
        <t>After processing the update, each recipient MUST delete outdated key material,
specifically:</t>
        <ul spacing="normal">
          <li>The path secrets and node secrets used to derive each updated node key pair.</li>
          <li>Each outdated node key pair that was replaced by the update.</li>
        </ul>
      </section>
      <section anchor="update-paths">
        <name>Update Paths</name>
        <t>As described in <xref target="commit"/>, each Commit message may optionally contain an
UpdatePath, with a new LeafNode and set of parent nodes for the sender's
filtered direct path. For each parent node, the UpdatePath contains a new
public key and encrypted path secret. The parent nodes are kept in the same
order as the filtered direct path.</t>
        <sourcecode type="tls"><![CDATA[
struct {
    opaque kem_output<V>;
    opaque ciphertext<V>;
} HPKECiphertext;

struct {
    HPKEPublicKey encryption_key;
    HPKECiphertext encrypted_path_secret<V>;
} UpdatePathNode;

struct {
    LeafNode leaf_node;
    UpdatePathNode nodes<V>;
} UpdatePath;
]]></sourcecode>
        <t>For each <tt>UpdatePathNode</tt>, the resolution of the corresponding copath node MUST
exclude all new leaf nodes added as part of the current Commit. The length of
the <tt>encrypted_path_secret</tt> vector MUST be equal to the length of the resolution
of the copath node (excluding new leaf nodes), with each ciphertext being the
encryption to the respective resolution node.</t>
        <t>The HPKECiphertext values are encrypted and decrypted as follows:</t>
        <sourcecode type="pseudocode"><![CDATA[
(kem_output, ciphertext) =
  EncryptWithLabel(node_public_key, "UpdatePathNode",
                   group_context, path_secret)

path_secret =
  DecryptWithLabel(node_private_key, "UpdatePathNode",
                   group_context, kem_output, ciphertext)
]]></sourcecode>
        <t>Here <tt>node_public_key</tt> is the public key of the node for which the path secret is
encrypted, <tt>group_context</tt> is the provisional GroupContext object for
the group, and the <tt>EncryptWithLabel</tt> function is as defined in
<xref target="public-key-encryption"/>.</t>
      </section>
      <section anchor="adding-and-removing-leaves">
        <name>Adding and Removing Leaves</name>
        <t>In addition to the path-based updates to the tree described above, it is also
necessary to add and remove leaves of the tree in order to reflect changes to
the membership of the group (see <xref target="add"/> and <xref target="remove"/>).  Since the tree is
always full, adding or removing leaves corresponds to increasing or decreasing
the depth of the tree, resulting in the number of leaves being doubled or
halved. These operations are also known as <em>extending</em> and <em>truncating</em> the
tree.</t>
        <t>Leaves are always added and removed at the right edge of the tree.  When the
size of the tree needs to be increased, a new blank root node is added, whose
left subtree is the existing tree and right subtree is a new all-blank subtree.
This operation is typically done when adding a member to the group.</t>
        <figure>
          <name>Extending the tree to make room for a third member</name>
          <artwork type="ascii-art"><![CDATA[
                  _ <-- new blank root                    _
                __|__                                   __|__
               /     \                                 /     \
  X    ===>   X       _ <-- new blank subtree ===>    X       _
 / \         / \     / \                             / \     / \
A   B       A   B   _   _                           A   B   C   _
                                                            ^
                                                            |
                                                            +-- new member
]]></artwork>
        </figure>
        <t>When the right subtree of the tree no longer has any non-blank nodes, it can be
safely removed.  The root of the tree and the right subtree are discarded
(whether or not the root node is blank). The left child of the root becomes the
new root node, and the left subtree becomes the new tree.  This operation is
typically done after removing a member from the group.</t>
        <figure>
          <name>Cleaning up after removing member C</name>
          <artwork type="ascii-art"><![CDATA[
               Y                  Y
             __|__              __|__
            /     \            /     \
           X       _   ===>   X       _   ==>   X <-- new root
          / \     / \        / \     / \       / \
         A   B   C   _      A   B   _   _     A   B
                 ^
                 |
removed member --+
]]></artwork>
        </figure>
        <t>Concrete algorithms for these operations on array-based and link-based trees are
provided in <xref target="array-based-trees"/> and <xref target="link-based-trees"/>.  The concrete
algorithms are non-normative.  An implementation may use any algorithm that
produces the correct tree in its internal representation.</t>
      </section>
      <section anchor="tree-hashes">
        <name>Tree Hashes</name>
        <t>MLS hashes the contents of the tree in two ways to authenticate different
properties of the tree.  <em>Tree hashes</em> are defined in this section, and <em>parent
hashes</em> are defined in <xref target="parent-hashes"/>.</t>
        <t>Each node in a ratchet tree has a tree hash that summarizes the subtree below
that node.  The tree hash of the root is used in the GroupContext to confirm
that the group agrees on the whole tree.  Tree hashes are computed recursively
from the leaves up to the root.</t>
        <artset>
          <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="112" width="128" viewBox="0 0 128 112" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
              <path d="M 24,32 L 40,32" fill="none" stroke="black"/>
              <path d="M 72,48 L 88,80" fill="none" stroke="black"/>
              <path d="M 40,80 L 56,48" fill="none" stroke="black"/>
              <polygon class="arrowhead" points="80,48 68,42.4 68,53.6" fill="black" transform="rotate(243.43494882292202,72,48)"/>
              <polygon class="arrowhead" points="64,48 52,42.4 52,53.6" fill="black" transform="rotate(296.565051177078,56,48)"/>
              <polygon class="arrowhead" points="48,32 36,26.4 36,37.6" fill="black" transform="rotate(0,40,32)"/>
              <g class="text">
                <text x="8" y="36">P</text>
                <text x="72" y="36">th(P)</text>
                <text x="24" y="100">th(L)</text>
                <text x="104" y="100">th(R)</text>
              </g>
            </svg>
          </artwork>
          <artwork type="ascii-art"><![CDATA[
P --> th(P)
      ^ ^
     /   \
    /     \
th(L)     th(R)
]]></artwork>
        </artset>
        <t>The tree hash of an individual node is the hash of the node's <tt>TreeHashInput</tt>
object, which may contain either a <tt>LeafNodeHashInput</tt> or a
<tt>ParentNodeHashInput</tt> depending on the type of node. <tt>LeafNodeHashInput</tt> objects
contain the <tt>leaf_index</tt> and the <tt>LeafNode</tt> (if any). <tt>ParentNodeHashInput</tt>
objects contain the <tt>ParentNode</tt> (if any) and the tree hash of the node's left
and right children.  For both parent and leaf nodes, the optional node value
MUST be absent if the node is blank and present if the node contains a value.</t>
        <sourcecode type="tls"><![CDATA[
enum {
    reserved(0),
    leaf(1),
    parent(2),
    (255)
} NodeType;

struct {
  NodeType node_type;
  select (TreeHashInput.node_type) {
    case leaf:   LeafNodeHashInput leaf_node;
    case parent: ParentNodeHashInput parent_node;
  };
} TreeHashInput;

struct {
    uint32 leaf_index;
    optional<LeafNode> leaf_node;
} LeafNodeHashInput;

struct {
    optional<ParentNode> parent_node;
    opaque left_hash<V>;
    opaque right_hash<V>;
} ParentNodeHashInput;
]]></sourcecode>
        <t>The tree hash of an entire tree corresponds to the tree hash of the root node,
which is computed recursively by starting at the leaf nodes and building up.</t>
      </section>
      <section anchor="parent-hashes">
        <name>Parent Hashes</name>
        <t>While tree hashes summarize the state of a tree at point in time, parent hashes
capture information about how keys in the tree were populated.</t>
        <t>When a client sends a commit to change a group, it can include an UpdatePath to
assign new keys to the nodes along its filtered direct path.  When a client
computes an UpdatePath (as defined in <xref target="synchronizing-views-of-the-tree"/>), it
computes and signs a parent hash that summarizes the state of the tree after the
UpdatePath has been applied.  These summaries are constructed in a chain from
the root to the member's leaf so that the part of the chain closer to the root
can be overwritten as nodes set in one UpdatePath are reset by a later
UpdatePath.</t>
        <artset>
          <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="176" width="216" viewBox="0 0 216 176" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
              <path d="M 112,96 L 128,96" fill="none" stroke="black"/>
              <path d="M 160,112 L 176,144" fill="none" stroke="black"/>
              <path d="M 128,144 L 144,112" fill="none" stroke="black"/>
              <path d="M 160,80 L 176,48" fill="none" stroke="black"/>
              <polygon class="arrowhead" points="168,112 156,106.4 156,117.6" fill="black" transform="rotate(243.43494882292202,160,112)"/>
              <polygon class="arrowhead" points="168,80 156,74.4 156,85.6" fill="black" transform="rotate(116.56505117707799,160,80)"/>
              <polygon class="arrowhead" points="136,144 124,138.4 124,149.6" fill="black" transform="rotate(116.56505117707799,128,144)"/>
              <polygon class="arrowhead" points="136,96 124,90.4 124,101.6" fill="black" transform="rotate(0,128,96)"/>
              <g class="text">
                <text x="192" y="36">ph(Q)</text>
                <text x="52" y="100">P.public_key</text>
                <text x="160" y="100">ph(P)</text>
                <text x="80" y="164">N.parent_hash</text>
                <text x="192" y="164">th(S)</text>
              </g>
            </svg>
          </artwork>
          <artwork type="ascii-art"><![CDATA[
                     ph(Q)
                     /
                    /
                   V
P.public_key --> ph(P)
                 / ^
                /   \
               V     \
   N.parent_hash     th(S)
]]></artwork>
        </artset>
        <t>As a result, the signature over the parent hash in each member's leaf
effectively signs the subtree of the tree that hasn't been changed since that
leaf was last changed in an UpdatePath.  A new member joining the group uses
these parent hashes to verify that the parent nodes in the tree were set by
members of the group, not chosen by an external attacker.  For an example of how
this works, see <xref target="ph-evolution"/>.</t>
        <t>Consider a ratchet tree with a non-blank parent node P and children D and S (for
"parent", "direct path", and "sibling"), with D and P in the direct path of a
leaf node L (for "leaf"):</t>
        <figure anchor="parent-hash-inputs">
          <name>Inputs to a parent hash.</name>
          <artwork type="ascii-art"><![CDATA[
         ...
         /
        P
      __|__
     /     \
    D       S
   / \     / \
 ... ... ... ...
 /
L
]]></artwork>
        </figure>
        <t>The parent hash of P changes whenever an <tt>UpdatePath</tt> object is applied to
the ratchet tree along a path from a leaf L traversing node D (and hence also
P). The new "Parent hash of P (with copath child S)" is obtained by hashing P's
<tt>ParentHashInput</tt> struct.</t>
        <sourcecode type="tls"><![CDATA[
struct {
    HPKEPublicKey encryption_key;
    opaque parent_hash<V>;
    opaque original_sibling_tree_hash<V>;
} ParentHashInput;
]]></sourcecode>
        <t>The field <tt>encryption_key</tt> contains the HPKE public key of P. If P is the root,
then the <tt>parent_hash</tt> field is set to a zero-length octet string. Otherwise,
<tt>parent_hash</tt> is the Parent Hash of the next node after P on the filtered
direct path of the leaf L. This way, P's Parent Hash fixes
the new HPKE public key of each non-blank node on the path from P to the root. Note
that the path from P to the root may contain some blank nodes that are not
fixed by P's Parent Hash. However, for each node that has an HPKE key, this key
is fixed by P's Parent Hash.</t>
        <t>Finally, <tt>original_sibling_tree_hash</tt> is the tree hash of S in the ratchet tree
modified as follows: For each leaf L in <tt>P.unmerged_leaves</tt>, blank L and remove
it from the <tt>unmerged_leaves</tt> sets of all parent nodes.</t>
        <t>Observe that <tt>original_sibling_tree_hash</tt> does not change between updates of P.
This property is crucial for the correctness of the protocol.</t>
        <t>Note that <tt>original_sibling_tree_hash</tt> is the tree hash of S, not the parent
hash.  The <tt>parent_hash</tt> field in ParentHashInput captures information about the
nodes above P. the <tt>original_sibling_tree_hash</tt> captures information about the
subtree under S that is not being updated (and thus the subtree to which a path
secret for P would be encrypted according to <xref target="synchronizing-views-of-the-tree"/>).</t>
        <t>For example, in the following tree:</t>
        <figure anchor="parent-hash-tree">
          <name>A tree illustrating parent hash computations.</name>
          <artwork type="ascii-art"><![CDATA[
              W [F]
        ______|_____
       /             \
      U               Y [F]
    __|__           __|__
   /     \         /     \
  T       _       _       _
 / \     / \     / \     / \
A   B   C   D   E   F   G   _
]]></artwork>
        </figure>
        <t>With P = W and S = Y, <tt>original_sibling_tree_hash</tt> is the tree hash of the
following tree:</t>
        <artwork type="ascii-art"><![CDATA[
      Y
    __|__
   /     \
  _       _
 / \     / \
E   _   G   _
]]></artwork>
        <t>Because <tt>W.unmerged_leaves</tt> includes F, F is blanked and removed from
<tt>Y.unmerged_leaves</tt>.</t>
        <t>Note that no recomputation is needed if the tree hash of S is unchanged since
the last time P was updated. This is the case for computing or processing a
Commit whose UpdatePath traverses P, since the Commit itself resets P. (In
other words, it is only necessary to recompute the original sibling tree hash
when validating a group's tree on joining.) More generally, if none of the entries
in <tt>P.unmerged_leaves</tt> is in the subtree under S (and thus no leaves were blanked),
then the original tree hash at S is the tree hash of S in the current tree.</t>
        <t>If it is necessary to recompute the original tree hash of a node, the efficiency
of recomputation can be improved by caching intermediate tree hashes, to avoid
recomputing over the subtree when the subtree is included in multiple parent
hashes.  A subtree hash can be reused as long as the intersection of the
parent's unmerged leaves with the subtree is the same as in the earlier
computation.</t>
        <section anchor="using-parent-hashes">
          <name>Using Parent Hashes</name>
          <t>In ParentNode objects and LeafNode objects with <tt>leaf_node_source</tt> set to
<tt>commit</tt>, the value of the <tt>parent_hash</tt> field is the parent hash of the next
non-blank parent node above the node in question (the next node in the filtered
direct path).  Using the node labels in <xref target="parent-hash-inputs"/>, the
<tt>parent_hash</tt> field of D is equal to the parent hash of P with copath child S.
This is the case even when the node D is a leaf node.</t>
          <t>The <tt>parent_hash</tt> field of a LeafNode is signed by the member.  The signature of
such a LeafNode thus also attests to which keys the group member introduced into
the ratchet tree and to whom the corresponding secret keys were sent. This
prevents malicious insiders from constructing artificial ratchet trees with a
node D whose HPKE secret key is known to the insider yet where the insider isn't
assigned a leaf in the subtree rooted at D. Indeed, such a ratchet tree would
violate the tree invariant.</t>
        </section>
        <section anchor="verifying-parent-hashes">
          <name>Verifying Parent Hashes</name>
          <t>Parent hashes are verified at two points in the protocol: When joining a group
and when processing a Commit.</t>
          <t>The parent hash in a node D is valid with respect to a parent node P if the
following criteria hold.  Here C and S are the children of P (for "child" and
"sibling"), with C being the child that is on the direct path of D (possibly D
itself) and S the other child:</t>
          <ul spacing="normal">
            <li>D is a descendant of P in the tree.</li>
            <li>The <tt>parent_hash</tt> field of D is equal to the parent hash of P with copath
child S.</li>
            <li>D is in the resolution of C, and the intersection of P's <tt>unmerged_leaves</tt>
with the subtree under C is equal to the resolution of C with D removed.</li>
          </ul>
          <t>These checks verify that D and P were updated at the same time (in the same
UpdatePath), and that they were neighbors in the UpdatePath because the nodes in
between them would have omitted from the filtered direct path.</t>
          <t>A parent node P is "parent-hash valid" if it can be chained back to a leaf node
in this way.  That is, if there is leaf node L and a sequence of parent nodes
P_1, ..., P_N such that P_N = P and each step in the chain is authenticated
by a parent hash: L's parent hash is valid with respect to P_1, P_1's parent
hash is valid with respect to P_2, and so on.</t>
          <t>When joining a group, the new member MUST authenticate that each non-blank
parent node P is parent-hash valid.  This can be done "bottom up" by building
chains up from leaves and verifying that all non-blank parent nodes are covered
by exactly one such chain, or "top down" by verifying that there is exactly one
descendant of each non-blank parent node for which the parent node is
parent-hash valid.</t>
          <t>When processing a Commit message that includes an UpdatePath, clients MUST
recompute the expected value of <tt>parent_hash</tt> for the committer's new leaf and
verify that it matches the <tt>parent_hash</tt> value in the supplied <tt>leaf_node</tt>.
After being merged into the tree, the nodes in the UpdatePath form a parent-hash
chain from the committer's leaf to the root.</t>
        </section>
      </section>
    </section>
    <section anchor="key-schedule">
      <name>Key Schedule</name>
      <t>Group keys are derived using the <tt>Extract</tt> and <tt>Expand</tt> functions from the KDF
for the group's ciphersuite, as well as the functions defined below:</t>
      <sourcecode type="pseudocode"><![CDATA[
ExpandWithLabel(Secret, Label, Context, Length) =
    KDF.Expand(Secret, KDFLabel, Length)

DeriveSecret(Secret, Label) =
    ExpandWithLabel(Secret, Label, "", KDF.Nh)
]]></sourcecode>
      <t>Where KDFLabel is specified as:</t>
      <sourcecode type="tls"><![CDATA[
struct {
    uint16 length = Length;
    opaque label<V> = "MLS 1.0 " + Label;
    opaque context<V> = Context;
} KDFLabel;
]]></sourcecode>
      <t>The value <tt>KDF.Nh</tt> is the size of an output from <tt>KDF.Extract</tt>, in bytes.  In
the below diagram:</t>
      <ul spacing="normal">
        <li>KDF.Extract takes its salt argument from the top and its Input
Key Material (IKM) argument from the left</li>
        <li>DeriveSecret takes its Secret argument from the incoming arrow</li>
        <li>
          <tt>0</tt> represents an all-zero byte string of length <tt>KDF.Nh</tt>.</li>
      </ul>
      <t>When processing a handshake message, a client combines the
following information to derive new epoch secrets:</t>
      <ul spacing="normal">
        <li>The init secret from the previous epoch</li>
        <li>The commit secret for the current epoch</li>
        <li>The GroupContext object for current epoch</li>
      </ul>
      <t>Given these inputs, the derivation of secrets for an epoch
proceeds as shown in the following diagram:</t>
      <artset>
        <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="656" width="584" viewBox="0 0 584 656" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
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            <path d="M 216,112 L 216,144" fill="none" stroke="black"/>
            <path d="M 216,176 L 216,208" fill="none" stroke="black"/>
            <path d="M 216,232 L 216,272" fill="none" stroke="black"/>
            <path d="M 216,304 L 216,384" fill="none" stroke="black"/>
            <path d="M 216,416 L 216,448" fill="none" stroke="black"/>
            <path d="M 216,472 L 216,560" fill="none" stroke="black"/>
            <path d="M 216,592 L 216,624" fill="none" stroke="black"/>
            <path d="M 152,96 L 168,96" fill="none" stroke="black"/>
            <path d="M 152,288 L 168,288" fill="none" stroke="black"/>
            <path d="M 216,336 L 240,336" fill="none" stroke="black"/>
            <path d="M 216,512 L 240,512" fill="none" stroke="black"/>
            <polygon class="arrowhead" points="248,512 236,506.4 236,517.6" fill="black" transform="rotate(0,240,512)"/>
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            <g class="text">
              <text x="232" y="36">init_secret_[n-1]</text>
              <text x="88" y="100">commit_secret</text>
              <text x="224" y="100">KDF.Extract</text>
              <text x="220" y="164">ExpandWithLabel(.,</text>
              <text x="336" y="164">"joiner",</text>
              <text x="448" y="164">GroupContext_[n],</text>
              <text x="552" y="164">KDF.Nh)</text>
              <text x="224" y="228">joiner_secret</text>
              <text x="44" y="292">psk_secret</text>
              <text x="104" y="292">(or</text>
              <text x="132" y="292">0)</text>
              <text x="224" y="292">KDF.Extract</text>
              <text x="312" y="340">DeriveSecret(.,</text>
              <text x="420" y="340">"welcome")</text>
              <text x="256" y="356">=</text>
              <text x="324" y="356">welcome_secret</text>
              <text x="220" y="404">ExpandWithLabel(.,</text>
              <text x="332" y="404">"epoch",</text>
              <text x="440" y="404">GroupContext_[n],</text>
              <text x="544" y="404">KDF.Nh)</text>
              <text x="220" y="468">epoch_secret</text>
              <text x="312" y="516">DeriveSecret(.,</text>
              <text x="412" y="516">&lt;label&gt;)</text>
              <text x="256" y="532">=</text>
              <text x="300" y="532">&lt;secret&gt;</text>
              <text x="224" y="580">DeriveSecret(.,</text>
              <text x="320" y="580">"init")</text>
              <text x="224" y="644">init_secret_[n]</text>
            </g>
          </svg>
        </artwork>
        <artwork type="ascii-art"><![CDATA[
                    init_secret_[n-1]
                          |
                          |
                          V
    commit_secret --> KDF.Extract
                          |
                          |
                          V
                  ExpandWithLabel(., "joiner", GroupContext_[n], KDF.Nh)
                          |
                          |
                          V
                     joiner_secret
                          |
                          |
                          V
psk_secret (or 0) --> KDF.Extract
                          |
                          |
                          +--> DeriveSecret(., "welcome")
                          |    = welcome_secret
                          |
                          V
                  ExpandWithLabel(., "epoch", GroupContext_[n], KDF.Nh)
                          |
                          |
                          V
                     epoch_secret
                          |
                          |
                          +--> DeriveSecret(., <label>)
                          |    = <secret>
                          |
                          V
                    DeriveSecret(., "init")
                          |
                          |
                          V
                    init_secret_[n]
]]></artwork>
      </artset>
      <t>A number of values are derived from the epoch secret for different purposes:</t>
      <table anchor="epoch-derived-secrets">
        <name>Epoch-derived secrets</name>
        <thead>
          <tr>
            <th align="left">Label</th>
            <th align="left">Secret</th>
            <th align="left">Purpose</th>
          </tr>
        </thead>
        <tbody>
          <tr>
            <td align="left">"sender data"</td>
            <td align="left">
              <tt>sender_data_secret</tt></td>
            <td align="left">Deriving keys to encrypt sender data</td>
          </tr>
          <tr>
            <td align="left">"encryption"</td>
            <td align="left">
              <tt>encryption_secret</tt></td>
            <td align="left">Deriving message encryption keys (via the secret tree)</td>
          </tr>
          <tr>
            <td align="left">"exporter"</td>
            <td align="left">
              <tt>exporter_secret</tt></td>
            <td align="left">Deriving exported secrets</td>
          </tr>
          <tr>
            <td align="left">"external"</td>
            <td align="left">
              <tt>external_secret</tt></td>
            <td align="left">Deriving the external init key</td>
          </tr>
          <tr>
            <td align="left">"confirm"</td>
            <td align="left">
              <tt>confirmation_key</tt></td>
            <td align="left">Computing the confirmation MAC for an epoch</td>
          </tr>
          <tr>
            <td align="left">"membership"</td>
            <td align="left">
              <tt>membership_key</tt></td>
            <td align="left">Computing the membership MAC for an PublicMessage</td>
          </tr>
          <tr>
            <td align="left">"resumption"</td>
            <td align="left">
              <tt>resumption_psk</tt></td>
            <td align="left">Proving membership in this epoch (via a PSK injected later)</td>
          </tr>
          <tr>
            <td align="left">"authentication"</td>
            <td align="left">
              <tt>epoch_authenticator</tt></td>
            <td align="left">Confirming that two clients have the same view of the group</td>
          </tr>
        </tbody>
      </table>
      <t>The <tt>external_secret</tt> is used to derive an HPKE key pair whose private key is
held by the entire group:</t>
      <sourcecode type="pseudocode"><![CDATA[
external_priv, external_pub = KEM.DeriveKeyPair(external_secret)
]]></sourcecode>
      <t>The public key <tt>external_pub</tt> can be published as part of the GroupInfo struct
in order to allow non-members to join the group using an external commit.</t>
      <section anchor="group-context">
        <name>Group Context</name>
        <t>Each member of the group maintains a GroupContext object that
summarizes the state of the group:</t>
        <sourcecode type="tls"><![CDATA[
struct {
    ProtocolVersion version = mls10;
    CipherSuite cipher_suite;
    opaque group_id<V>;
    uint64 epoch;
    opaque tree_hash<V>;
    opaque confirmed_transcript_hash<V>;
    Extension extensions<V>;
} GroupContext;
]]></sourcecode>
        <t>The fields in this state have the following semantics:</t>
        <ul spacing="normal">
          <li>The <tt>cipher_suite</tt> is the cipher suite used by the group.</li>
          <li>The <tt>group_id</tt> field is an application-defined identifier for the
group.</li>
          <li>The <tt>epoch</tt> field represents the current version of the group.</li>
          <li>The <tt>tree_hash</tt> field contains a commitment to the contents of the
group's ratchet tree and the credentials for the members of the
group, as described in <xref target="tree-hashes"/>.</li>
          <li>The <tt>confirmed_transcript_hash</tt> field contains a running hash over
the messages that led to this state.</li>
          <li>The <tt>extensions</tt> field contains the details of any protocol extensions that
apply to the group.</li>
        </ul>
        <t>When a new member is added to the group, an existing member of the
group provides the new member with a Welcome message.  The Welcome
message provides the information the new member needs to initialize
its GroupContext.</t>
        <t>Different changes to the group will have different effects on the group state.
These effects are described in their respective subsections of <xref target="proposals"/>.
The following general rules apply:</t>
        <ul spacing="normal">
          <li>The <tt>group_id</tt> field is constant.</li>
          <li>The <tt>epoch</tt> field increments by one for each Commit message that
is processed.</li>
          <li>The <tt>tree_hash</tt> is updated to represent the current tree and
credentials.</li>
          <li>The <tt>confirmed_transcript_hash</tt> field is updated with the data for an
AuthenticatedContent encoding a Commit message as described below.</li>
          <li>The <tt>extensions</tt> field changes when a GroupContextExtensions proposal is
committed.</li>
        </ul>
      </section>
      <section anchor="transcript-hashes">
        <name>Transcript Hashes</name>
        <t>The transcript hashes computed in MLS represent a running hash over all Proposal
and Commit messages that have ever been sent in a group.  Commit messages are
included directly. Proposal messages are indirectly included via the Commit that
applied them. Both types of message are included by hashing the AuthenticatedContent
object in which they were sent.</t>
        <t>The transcript hash comprises two individual hashes:</t>
        <ul spacing="normal">
          <li>A <tt>confirmed_transcript_hash</tt> that represents a transcript over the whole
history of Commit messages, up to and including the signature of the most
recent Commit.</li>
          <li>An <tt>interim_transcript_hash</tt> that covers the confirmed transcript hash plus
the <tt>confirmation_tag</tt> of the most recent Commit.</li>
        </ul>
        <t>New members compute the interim transcript hash using the <tt>confirmation_tag</tt>
field of the GroupInfo struct, while existing members can compute it directly.</t>
        <t>Each Commit message updates these hashes by way of its enclosing
AuthenticatedContent.  The AuthenticatedContent struct is split into
ConfirmedTranscriptHashInput and InterimTranscriptHashInput. The former is used to
update the confirmed transcript hash and the latter to update the interim
transcript hash.</t>
        <sourcecode type="tls"><![CDATA[
struct {
    WireFormat wire_format;
    FramedContent content; /* with content_type == commit */
    opaque signature<V>;
} ConfirmedTranscriptHashInput;

struct {
    MAC confirmation_tag;
} InterimTranscriptHashInput;
]]></sourcecode>
        <sourcecode type="pseudocode"><![CDATA[
confirmed_transcript_hash_[epoch] = ""; /* zero-length octet string */

interim_transcript_hash_[epoch] =
    Hash(confirmed_transcript_hash_[epoch] ||
        InterimTranscriptHashInput_[epoch]);

confirmed_transcript_hash_[epoch+1] =
    Hash(interim_transcript_hash_[epoch] ||
        ConfirmedTranscriptHashInput_[epoch+1]);
]]></sourcecode>
        <t>In this notation, <tt>InterimTranscriptHashInput_[epoch]</tt> and
<tt>ConfirmedTranscriptHashInput_[epoch+1]</tt> are based on the Commit that initiated
the epoch with epoch number <tt>epoch</tt>.  (Note that the <tt>epoch</tt> field in this
Commit will be set to <tt>epoch - 1</tt>, since it is sent within the previous epoch.)</t>
      </section>
      <section anchor="external-initialization">
        <name>External Initialization</name>
        <t>In addition to initializing a new epoch via KDF invocations as described above,
an MLS group can also initialize a new epoch via an asymmetric interaction using
the external key pair for the previous epoch.  This is done when an new member
is joining via an external commit.</t>
        <t>In this process, the joiner sends a new <tt>init_secret</tt> value to the group using
the HPKE export method.  The joiner then uses that <tt>init_secret</tt> with
information provided in the GroupInfo and an external Commit to initialize
their copy of the key schedule for the new epoch.</t>
        <sourcecode type="pseudocode"><![CDATA[
kem_output, context = SetupBaseS(external_pub, "")
init_secret = context.export("MLS 1.0 external init secret", KDF.Nh)
]]></sourcecode>
        <t>Members of the group receive the <tt>kem_output</tt> in an ExternalInit proposal and
perform the corresponding calculation to retrieve the <tt>init_secret</tt> value.</t>
        <sourcecode type="pseudocode"><![CDATA[
context = SetupBaseR(kem_output, external_priv, "")
init_secret = context.export("MLS 1.0 external init secret", KDF.Nh)
]]></sourcecode>
        <t>In both cases, the <tt>info</tt> input to HPKE is set to the GroupInfo for the
previous epoch, encoded using the TLS serialization.</t>
      </section>
      <section anchor="pre-shared-keys">
        <name>Pre-Shared Keys</name>
        <t>Groups which already have an out-of-band mechanism to generate
shared group secrets can inject those into the MLS key schedule to seed
the MLS group secrets computations by this external entropy.</t>
        <t>Injecting an external PSK can improve security in the case
where having a full run of Updates across members is too expensive, or if
the external group key establishment mechanism provides
stronger security against classical or quantum adversaries.</t>
        <t>Note that, as a PSK may have a different lifetime than an Update, it does not
necessarily provide the same Forward Secrecy (FS) or Post-Compromise Security
(PCS) guarantees as a Commit message.  Unlike the key pairs populated in the
tree by an Update or Commit, which are always freshly generated, PSKs may be
pre-distributed and stored. This creates the risk that a PSK may be compromised
in the process of distribution and storage. The security that the group gets
from injecting a PSK thus depends on both the entropy of the PSK and the risk of
compromise.  These factors are outside of the scope of this document, but should
be considered by application designers relying on PSKs.</t>
        <t>Each PSK in MLS has a type that designates how it was provisioned.
External PSKs are provided by the application, while resumption PSKs
are derived from the MLS key schedule and used in cases where it is
necessary to authenticate a member's participation in a prior epoch.</t>
        <t>The injection of one or more PSKs into the key schedule is signaled in two ways:
Existing members are informed via PreSharedKey proposals covered by a Commit,
and new members added in the Commit are informed by the GroupSecrets object in the
Welcome message corresponding to the Commit.  To ensure that existing and new
members compute the same PSK input to the key schedule, the Commit and
GroupSecrets objects MUST indicate the same set of PSKs, in the same order.</t>
        <sourcecode type="tls"><![CDATA[
enum {
  reserved(0),
  external(1),
  resumption(2),
  (255)
} PSKType;

enum {
  reserved(0),
  application(1),
  reinit(2),
  branch(3),
  (255)
} ResumptionPSKUsage;

struct {
  PSKType psktype;
  select (PreSharedKeyID.psktype) {
    case external:
      opaque psk_id<V>;

    case resumption:
      ResumptionPSKUsage usage;
      opaque psk_group_id<V>;
      uint64 psk_epoch;
  };
  opaque psk_nonce<V>;
} PreSharedKeyID;
]]></sourcecode>
        <t>Each time a client injects a PSK into a group, the <tt>psk_nonce</tt> of its
PreSharedKeyID MUST be set to a fresh random value of length <tt>KDF.Nh</tt>, where
<tt>KDF</tt> is the KDF for the ciphersuite of the group into which the PSK is being
injected. This ensures that even when a PSK is used multiple times, the value
used as an input into the key schedule is different each time.</t>
        <t>Upon receiving a Commit with a <tt>PreSharedKey</tt> proposal or a GroupSecrets object
with the <tt>psks</tt> field set, the receiving Client includes them in the key
schedule in the order listed in the Commit, or in the <tt>psks</tt> field respectively.
For resumption PSKs, the PSK is defined as the <tt>resumption_psk</tt> of the group and
epoch specified in the <tt>PreSharedKeyID</tt> object. Specifically, <tt>psk_secret</tt> is
computed as follows:</t>
        <sourcecode type="tls"><![CDATA[
struct {
    PreSharedKeyID id;
    uint16 index;
    uint16 count;
} PSKLabel;
]]></sourcecode>
        <sourcecode type="pseudocode"><![CDATA[
psk_extracted_[i] = KDF.Extract(0, psk_[i])
psk_input_[i] = ExpandWithLabel(psk_extracted_[i], "derived psk",
                  PSKLabel, KDF.Nh)

psk_secret_[0] = 0
psk_secret_[i] = KDF.Extract(psk_input_[i-1], psk_secret_[i-1])
psk_secret     = psk_secret_[n]
]]></sourcecode>
        <t>Here <tt>0</tt> represents the all-zero vector of length <tt>KDF.Nh</tt>. The <tt>index</tt> field in
<tt>PSKLabel</tt> corresponds to the index of the PSK in the <tt>psk</tt> array, while the
<tt>count</tt> field contains the total number of PSKs.  In other words, the PSKs are
chained together with KDF.Extract invocations (labeled "Extract" for brevity
in the diagram), as follows:</t>
        <artset>
          <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="256" width="568" viewBox="0 0 568 256" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
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              <path d="M 184,80 L 200,80" fill="none" stroke="black"/>
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                <text x="144" y="36">0</text>
                <text x="400" y="36">0</text>
                <text x="440" y="36">=</text>
                <text x="508" y="36">psk_secret_[0]</text>
                <text x="144" y="52">|</text>
                <text x="400" y="52">|</text>
                <text x="32" y="84">psk_[0]</text>
                <text x="144" y="84">Extract</text>
                <text x="272" y="84">ExpandWithLabel</text>
                <text x="400" y="84">Extract</text>
                <text x="440" y="84">=</text>
                <text x="508" y="84">psk_secret_[1]</text>
                <text x="144" y="116">0</text>
                <text x="144" y="132">|</text>
                <text x="32" y="164">psk_[1]</text>
                <text x="144" y="164">Extract</text>
                <text x="272" y="164">ExpandWithLabel</text>
                <text x="400" y="164">Extract</text>
                <text x="440" y="164">=</text>
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                <text x="400" y="180">|</text>
                <text x="144" y="196">0</text>
                <text x="392" y="196">.</text>
                <text x="408" y="196">.</text>
                <text x="144" y="212">|</text>
                <text x="40" y="244">psk_[n-1]</text>
                <text x="144" y="244">Extract</text>
                <text x="272" y="244">ExpandWithLabel</text>
                <text x="400" y="244">Extract</text>
                <text x="440" y="244">=</text>
                <text x="508" y="244">psk_secret_[n]</text>
              </g>
            </svg>
          </artwork>
          <artwork type="ascii-art"><![CDATA[
                 0                               0    = psk_secret_[0]
                 |                               |
                 V                               V
psk_[0]   --> Extract --> ExpandWithLabel --> Extract = psk_secret_[1]
                                                 |
                 0                               |
                 |                               |
                 V                               V
psk_[1]   --> Extract --> ExpandWithLabel --> Extract = psk_secret_[2]
                                                 |
                 0                              ...
                 |                               |
                 V                               V
psk_[n-1] --> Extract --> ExpandWithLabel --> Extract = psk_secret_[n]
]]></artwork>
        </artset>
        <t>In particular, if there are no PreSharedKey proposals in a given Commit, then
the resulting <tt>psk_secret</tt> is <tt>psk_secret_[0]</tt>, the all-zero vector.</t>
      </section>
      <section anchor="exporters">
        <name>Exporters</name>
        <t>The main MLS key schedule provides an <tt>exporter_secret</tt> which can
be used by an application to derive new secrets for use outside of MLS.</t>
        <sourcecode type="pseudocode"><![CDATA[
MLS-Exporter(Label, Context, Length) =
       ExpandWithLabel(DeriveSecret(exporter_secret, Label),
                         "exporter", Hash(Context), Length)
]]></sourcecode>
        <t>Applications SHOULD provide a unique label to <tt>MLS-Exporter</tt> that
identifies the secret's intended purpose. This is to help prevent the same
secret from being generated and used in two different places. To help avoid
the same label being used in different applications, an IANA registry for these
labels has been defined in <xref target="mls-exporter-labels"/>.</t>
        <t>The exported values are bound to the group epoch from which the
<tt>exporter_secret</tt> is derived, and hence reflect a particular state of
the group.</t>
        <t>It is RECOMMENDED for the application generating exported values
to refresh those values after a Commit is processed.</t>
      </section>
      <section anchor="resumption-psk">
        <name>Resumption PSK</name>
        <t>The main MLS key schedule provides a <tt>resumption_psk</tt> that is used as a PSK
to inject entropy from one epoch into another.  This functionality is used in the
reinitialization and branching processes described in <xref target="reinitialization"/> and
<xref target="subgroup-branching"/>, but may be used by applications for other purposes.</t>
        <t>Some uses of resumption PSKs might call for the use of PSKs from historical
epochs. The application SHOULD specify an upper limit on the number of past
epochs for which the <tt>resumption_psk</tt> may be stored.</t>
      </section>
      <section anchor="epoch-authenticators">
        <name>Epoch Authenticators</name>
        <t>The main MLS key schedule provides a per-epoch <tt>epoch_authenticator</tt>. If one
member of the group is being impersonated by an active attacker, the
<tt>epoch_authenticator</tt> computed by their client will differ from those computed
by the other group members.</t>
        <t>This property can be used to construct defenses against impersonation attacks
that are effective even if members' signature keys are compromised. As a trivial
example, if the users of the clients in an MLS group were to meet in person and
reliably confirm that their epoch authenticator values were equal (using some
suitable user interface), then each user would be assured that the others were
not being impersonated in the current epoch. As soon as the epoch changed,
though, they would need to re-do this confirmation. The state of the group would
have changed, possibly introducing an attacker.</t>
        <t>More generally, in order for the members of an MLS group to obtain concrete
authentication protections using the <tt>epoch_authenticator</tt>, they will need to
use it in some secondary protocol (such as the face-to-face protocol above).
The details of that protocol will then determine the specific authentication
protections provided to the MLS group.</t>
      </section>
    </section>
    <section anchor="secret-tree">
      <name>Secret Tree</name>
      <t>For the generation of encryption keys and nonces, the key schedule begins with
the <tt>encryption_secret</tt> at the root and derives a tree of secrets with the same
structure as the group's ratchet tree. Each leaf in the Secret Tree is
associated with the same group member as the corresponding leaf in the ratchet
tree.</t>
      <t>If N is a parent node in the Secret Tree then the secrets of the children of N
are defined as follows (where left(N) and right(N) denote the children of N):</t>
      <artset>
        <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="160" width="456" viewBox="0 0 456 160" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
            <path d="M 72,40 L 72,128" fill="none" stroke="black"/>
            <path d="M 248,80 L 248,88" fill="none" stroke="black"/>
            <path d="M 72,80 L 96,80" fill="none" stroke="black"/>
            <path d="M 72,128 L 96,128" fill="none" stroke="black"/>
            <polygon class="arrowhead" points="104,128 92,122.4 92,133.6" fill="black" transform="rotate(0,96,128)"/>
            <polygon class="arrowhead" points="104,80 92,74.4 92,85.6" fill="black" transform="rotate(0,96,80)"/>
            <g class="text">
              <text x="84" y="36">tree_node_[N]_secret</text>
              <text x="176" y="84">ExpandWithLabel(.</text>
              <text x="288" y="84">"tree",</text>
              <text x="352" y="84">"left",</text>
              <text x="416" y="84">KDF.Nh)</text>
              <text x="112" y="100">=</text>
              <text x="228" y="100">tree_node_[left(N)]_secret</text>
              <text x="180" y="132">ExpandWithLabel(.,</text>
              <text x="288" y="132">"tree",</text>
              <text x="356" y="132">"right",</text>
              <text x="424" y="132">KDF.Nh)</text>
              <text x="112" y="148">=</text>
              <text x="232" y="148">tree_node_[right(N)]_secret</text>
            </g>
          </svg>
        </artwork>
        <artwork type="ascii-art"><![CDATA[
tree_node_[N]_secret
        |
        |
        +--> ExpandWithLabel(., "tree", "left", KDF.Nh)
        |    = tree_node_[left(N)]_secret
        |
        +--> ExpandWithLabel(., "tree", "right", KDF.Nh)
             = tree_node_[right(N)]_secret
]]></artwork>
      </artset>
      <t>The secret in the leaf of the Secret Tree is used to initiate two symmetric hash
ratchets, from which a sequence of single-use keys and nonces are derived, as
described in <xref target="encryption-keys"/>. The root of each ratchet is computed as:</t>
      <artset>
        <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="160" width="472" viewBox="0 0 472 160" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
            <path d="M 72,40 L 72,128" fill="none" stroke="black"/>
            <path d="M 72,80 L 96,80" fill="none" stroke="black"/>
            <path d="M 72,128 L 96,128" fill="none" stroke="black"/>
            <polygon class="arrowhead" points="104,128 92,122.4 92,133.6" fill="black" transform="rotate(0,96,128)"/>
            <polygon class="arrowhead" points="104,80 92,74.4 92,85.6" fill="black" transform="rotate(0,96,80)"/>
            <g class="text">
              <text x="84" y="36">tree_node_[N]_secret</text>
              <text x="180" y="84">ExpandWithLabel(.,</text>
              <text x="308" y="84">"handshake",</text>
              <text x="376" y="84">"",</text>
              <text x="424" y="84">KDF.Nh)</text>
              <text x="112" y="100">=</text>
              <text x="252" y="100">handshake_ratchet_secret_[N]_[0]</text>
              <text x="180" y="132">ExpandWithLabel(.,</text>
              <text x="316" y="132">"application",</text>
              <text x="392" y="132">"",</text>
              <text x="440" y="132">KDF.Nh)</text>
              <text x="112" y="148">=</text>
              <text x="260" y="148">application_ratchet_secret_[N]_[0]</text>
            </g>
          </svg>
        </artwork>
        <artwork type="ascii-art"><![CDATA[
tree_node_[N]_secret
        |
        |
        +--> ExpandWithLabel(., "handshake", "", KDF.Nh)
        |    = handshake_ratchet_secret_[N]_[0]
        |
        +--> ExpandWithLabel(., "application", "", KDF.Nh)
             = application_ratchet_secret_[N]_[0]
]]></artwork>
      </artset>
      <section anchor="encryption-keys">
        <name>Encryption Keys</name>
        <t>As described in <xref target="message-framing"/>, MLS encrypts three different
types of information:</t>
        <ul spacing="normal">
          <li>Metadata (sender information)</li>
          <li>Handshake messages (Proposal and Commit)</li>
          <li>Application messages</li>
        </ul>
        <t>The sender information used to look up the key for content encryption is
encrypted with an AEAD where the key and nonce are derived from both
<tt>sender_data_secret</tt> and a sample of the encrypted message content.</t>
        <t>For handshake and application messages, a sequence of keys is derived via a
"sender ratchet".  Each sender has their own sender ratchet, and each step along
the ratchet is called a "generation".</t>
        <t>The following figure shows a secret tree for a four-member group, with the
handshake and application ratchets that member D will use for sending and the
first two application keys and nonces.</t>
        <figure anchor="secret-tree-example">
          <name>Secret tree for a four-member group</name>
          <artset>
            <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="320" width="200" viewBox="0 0 200 320" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
                <path d="M 56,48 L 56,64" fill="none" stroke="black"/>
                <path d="M 128,176 L 128,208" fill="none" stroke="black"/>
                <path d="M 128,240 L 128,272" fill="none" stroke="black"/>
                <path d="M 160,160 L 160,192" fill="none" stroke="black"/>
                <path d="M 160,224 L 160,256" fill="none" stroke="black"/>
                <path d="M 40,64 L 72,64" fill="none" stroke="black"/>
                <path d="M 144,160 L 176,160" fill="none" stroke="black"/>
                <path d="M 160,192 L 176,192" fill="none" stroke="black"/>
                <path d="M 144,224 L 176,224" fill="none" stroke="black"/>
                <path d="M 160,256 L 176,256" fill="none" stroke="black"/>
                <path d="M 72,64 L 80,80" fill="none" stroke="black"/>
                <path d="M 32,80 L 40,64" fill="none" stroke="black"/>
                <g class="text">
                  <text x="56" y="36">G</text>
                  <text x="24" y="100">E</text>
                  <text x="88" y="100">F</text>
                  <text x="16" y="116">/</text>
                  <text x="32" y="116">\</text>
                  <text x="80" y="116">/</text>
                  <text x="96" y="116">\</text>
                  <text x="8" y="132">A</text>
                  <text x="40" y="132">B</text>
                  <text x="72" y="132">C</text>
                  <text x="104" y="132">D</text>
                  <text x="96" y="148">/</text>
                  <text x="112" y="148">\</text>
                  <text x="88" y="164">HR0</text>
                  <text x="128" y="164">AR0</text>
                  <text x="188" y="164">K0</text>
                  <text x="188" y="196">N0</text>
                  <text x="128" y="228">AR1</text>
                  <text x="188" y="228">K1</text>
                  <text x="188" y="260">N1</text>
                  <text x="128" y="292">AR2</text>
                </g>
              </svg>
            </artwork>
            <artwork type="ascii-art"><![CDATA[
       G
       |
     .-+-.
    /     \
   E       F
  / \     / \
 A   B   C   D
            / \
          HR0  AR0--+--K0
                |   |
                |   +--N0
                |
               AR1--+--K1
                |   |
                |   +--N1
                |
               AR2
]]></artwork>
          </artset>
        </figure>
        <t>A sender ratchet starts from a per-sender base secret derived from a Secret
Tree, as described in <xref target="secret-tree"/>. The base secret initiates a symmetric
hash ratchet which generates a sequence of keys and nonces. The sender uses the
j-th key/nonce pair in the sequence to encrypt (using the AEAD) the j-th message
they send during that epoch. Each key/nonce pair MUST NOT be used to encrypt
more than one message.</t>
        <t>Keys, nonces, and the secrets in ratchets are derived using
DeriveTreeSecret. The context in a given call consists of the current position
in the ratchet.</t>
        <sourcecode type="pseudocode"><![CDATA[
DeriveTreeSecret(Secret, Label, Generation, Length) =
    ExpandWithLabel(Secret, Label, Generation, Length)
]]></sourcecode>
        <t>Where <tt>Generation</tt> is encoded as a big endian uint32.</t>
        <artset>
          <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="208" width="416" viewBox="0 0 416 208" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
              <path d="M 56,40 L 56,160" fill="none" stroke="black"/>
              <path d="M 56,64 L 80,64" fill="none" stroke="black"/>
              <path d="M 56,112 L 80,112" fill="none" stroke="black"/>
              <polygon class="arrowhead" points="88,112 76,106.4 76,117.6" fill="black" transform="rotate(0,80,112)"/>
              <polygon class="arrowhead" points="88,64 76,58.4 76,69.6" fill="black" transform="rotate(0,80,64)"/>
              <polygon class="arrowhead" points="64,160 52,154.4 52,165.6" fill="black" transform="rotate(90,56,160)"/>
              <g class="text">
                <text x="92" y="36">ratchet_secret_[N]_[j]</text>
                <text x="168" y="68">DeriveTreeSecret(.,</text>
                <text x="284" y="68">"nonce",</text>
                <text x="332" y="68">j,</text>
                <text x="380" y="68">AEAD.Nn)</text>
                <text x="96" y="84">=</text>
                <text x="192" y="84">ratchet_nonce_[N]_[j]</text>
                <text x="168" y="116">DeriveTreeSecret(.,</text>
                <text x="276" y="116">"key",</text>
                <text x="316" y="116">j,</text>
                <text x="372" y="116">AEAD.Nk)</text>
                <text x="96" y="132">=</text>
                <text x="184" y="132">ratchet_key_[N]_[j]</text>
                <text x="80" y="180">DeriveTreeSecret(.,</text>
                <text x="200" y="180">"secret",</text>
                <text x="252" y="180">j,</text>
                <text x="296" y="180">KDF.Nh)</text>
                <text x="8" y="196">=</text>
                <text x="116" y="196">ratchet_secret_[N]_[j+1]</text>
              </g>
            </svg>
          </artwork>
          <artwork type="ascii-art"><![CDATA[
ratchet_secret_[N]_[j]
      |
      +--> DeriveTreeSecret(., "nonce", j, AEAD.Nn)
      |    = ratchet_nonce_[N]_[j]
      |
      +--> DeriveTreeSecret(., "key", j,  AEAD.Nk)
      |    = ratchet_key_[N]_[j]
      |
      V
DeriveTreeSecret(., "secret", j, KDF.Nh)
= ratchet_secret_[N]_[j+1]
]]></artwork>
        </artset>
        <t>Here, <tt>AEAD.Nn</tt> and <tt>AEAD.Nk</tt> denote the lengths
in bytes of the nonce and key for the AEAD scheme defined by
the ciphersuite.</t>
      </section>
      <section anchor="deletion-schedule">
        <name>Deletion Schedule</name>
        <t>It is important to delete all security-sensitive values as soon as they are
<em>consumed</em>. A sensitive value S is said to be <em>consumed</em> if</t>
        <ul spacing="normal">
          <li>S was used to encrypt or (successfully) decrypt a message, or if</li>
          <li>a key, nonce, or secret derived from S has been consumed. (This goes for
values derived via DeriveSecret as well as ExpandWithLabel.)</li>
        </ul>
        <t>Here, S may be the <tt>init_secret</tt>, <tt>commit_secret</tt>, <tt>epoch_secret</tt>,
<tt>encryption_secret</tt> as well as any secret in a Secret Tree or one of the
ratchets.</t>
        <t>As soon as a group member consumes a value they MUST immediately delete
(all representations of) that value. This is crucial to ensuring
forward secrecy for past messages. Members MAY keep unconsumed values around
for some reasonable amount of time to handle out-of-order message delivery.</t>
        <t>For example, suppose a group member encrypts or (successfully) decrypts an
application message using the j-th key and nonce in the ratchet of leaf node
L in some epoch n. Then, for that member, at least the following
values have been consumed and MUST be deleted:</t>
        <ul spacing="normal">
          <li>the <tt>commit_secret</tt>, <tt>joiner_secret</tt>, <tt>epoch_secret</tt>, <tt>encryption_secret</tt> of
that epoch n as well as the <tt>init_secret</tt> of the previous epoch n-1,</li>
          <li>all node secrets in the Secret Tree on the path from the root to the leaf with
node L,</li>
          <li>the first j secrets in the application data ratchet of node L and</li>
          <li>
            <tt>application_ratchet_nonce_[L]_[j]</tt> and <tt>application_ratchet_key_[L]_[j]</tt>.</li>
        </ul>
        <t>Concretely, consider the Secret Tree shown in <xref target="secret-tree-example"/>.  Client
A, B, or C would generate the illustrated values on receiving a message from D
with generation equal to 1, having not received a message with generation 0
(e.g., due to out-of-order delivery).  In such a case, the following values
would be consumed:</t>
        <ul spacing="normal">
          <li>The key K1 and nonce N1 used to decrypt the message</li>
          <li>The application ratchet secrets AR1 and AR0</li>
          <li>The tree secrets D, F, G (recall that G is the <tt>encryption_secret</tt> for the
epoch)</li>
          <li>The <tt>epoch_secret</tt>, <tt>commit_secret</tt>, <tt>psk_secret</tt>, and <tt>joiner_secret</tt> for the
current epoch</li>
        </ul>
        <t>Other values may be retained (not consumed):</t>
        <ul spacing="normal">
          <li>K0 and N0 for decryption of an out-of-order message with generation 0</li>
          <li>AR2 for derivation of further message decryption keys and nonces</li>
          <li>HR0 for protection of handshake messages from D</li>
          <li>E and C for deriving secrets used by senders A, B, and C</li>
        </ul>
      </section>
    </section>
    <section anchor="key-packages">
      <name>Key Packages</name>
      <t>In order to facilitate the asynchronous addition of clients to a
group, key packages are pre-published that
provide some public information about a user. A KeyPackage object specifies:</t>
      <ol spacing="normal" type="1"><li>A protocol version and ciphersuite that the client supports,</li>
        <li>a public key that others can use to encrypt a Welcome message to this client
(an "init key"), and</li>
        <li>the content of the leaf node that should be added to the tree to represent
this client.</li>
      </ol>
      <t>KeyPackages are intended to be used only once and SHOULD NOT
be reused except in the case of last resort (see <xref target="keypackage-reuse"/>).
Clients MAY generate and publish multiple KeyPackages to
support multiple ciphersuites.</t>
      <t>The value for <tt>init_key</tt> MUST be a public key for the asymmetric encryption
scheme defined by <tt>cipher_suite</tt>, and it MUST be unique among the set of
KeyPackages created by this client.  Likewise, the <tt>leaf_node</tt> field MUST be
valid for the ciphersuite, including both the <tt>encryption_key</tt> and
<tt>signature_key</tt> fields.  The whole structure is signed using the client's
signature key. A KeyPackage object with an invalid signature field MUST be
considered malformed.</t>
      <t>The signature is computed by the function <tt>SignWithLabel</tt> with a label
<tt>KeyPackageTBS</tt> and a content comprising of all of the fields except for the
signature field.</t>
      <sourcecode type="tls"><![CDATA[
struct {
    ProtocolVersion version;
    CipherSuite cipher_suite;
    HPKEPublicKey init_key;
    LeafNode leaf_node;
    Extension extensions<V>;
    /* SignWithLabel(., "KeyPackageTBS", KeyPackageTBS) */
    opaque signature<V>;
} KeyPackage;

struct {
    ProtocolVersion version;
    CipherSuite cipher_suite;
    HPKEPublicKey init_key;
    LeafNode leaf_node;
    Extension extensions<V>;
} KeyPackageTBS;
]]></sourcecode>
      <t>If a client receives a KeyPackage carried within an MLSMessage object, then it
MUST verify that the <tt>version</tt> field of the KeyPackage has the same value as the
<tt>version</tt> field of the MLSMessage.  The <tt>version</tt> field in the KeyPackage
provides an explicit signal of the intended version to the other members of
group when they receive the KeyPackage in an Add proposal.</t>
      <t>The field <tt>leaf_node.capabilities</tt> indicates what protocol versions,
ciphersuites, credential types, and non-default proposal/extension types are supported
by the client.  (Proposal and extension types defined in this document are considered
"default" and not listed.)  This information allows MLS session
establishment to be safe from downgrade attacks on the parameters described (as
discussed in <xref target="group-creation"/>), while still only advertising one version /
ciphersuite per KeyPackage.</t>
      <t>The field <tt>leaf_node.leaf_node_source</tt> of the LeafNode in a KeyPackage MUST be
set to <tt>key_package</tt>.</t>
      <t>Extension included in the <tt>extensions</tt> or <tt>leaf_node.extensions</tt> fields MUST be
included in the <tt>leaf_node.capabilities</tt> field.</t>
      <section anchor="keypackage-validation">
        <name>KeyPackage Validation</name>
        <t>The validity of a KeyPackage needs to be verified at a few stages:</t>
        <ul spacing="normal">
          <li>When a KeyPackage is downloaded by a group member, before it is used
to add the client to the group</li>
          <li>When a KeyPackage is received by a group member in an Add message</li>
        </ul>
        <t>The client verifies the validity of a KeyPackage using the following steps:</t>
        <ul spacing="normal">
          <li>Verify that the ciphersuite and protocol version of the KeyPackage match
those in the <tt>GroupContext</tt>.</li>
          <li>Verify that the <tt>leaf_node</tt> of the KeyPackage is valid for a KeyPackage
according to <xref target="leaf-node-validation"/>.</li>
          <li>Verify that the signature on the KeyPackage is valid using the public key
in <tt>leaf_node.credential</tt>.</li>
          <li>Verify that the value of <tt>leaf_node.encryption_key</tt> is different from the value of
the <tt>init_key</tt> field.</li>
        </ul>
      </section>
    </section>
    <section anchor="group-creation">
      <name>Group Creation</name>
      <t>A group is always created with a single member, the "creator".  Other members
are then added to the group using the usual Add/Commit mechanism.</t>
      <t>The creator of a group is responsible for setting the group ID, ciphersuite, and
initial extensions for the group.  If the creator intends to add other members
at the time of creation, then it SHOULD Fetch KeyPackages for the members to be
added, and select a ciphersuite and extensions according to the capabilities of
the members.  To protect against downgrade attacks, the creator MUST use the
<tt>capabilities</tt> information in these KeyPackages to verify that the chosen
version and ciphersuite is the best option supported by all members.</t>
      <t>Group IDs SHOULD be constructed in such a way that there's an overwhelmingly low
probability of honest group creators generating the same group ID, even without
assistance from the Delivery Service. For example, by making the group ID a
freshly generated random value of size <tt>KDF.Nh</tt>. The Delivery Service MAY
attempt to ensure that group IDs are globally unique by rejecting the creation
of new groups with a previously used ID.</t>
      <t>The creator of a group MUST take the following steps to initialize the group:</t>
      <ul spacing="normal">
        <li>
          <t>Initialize a one-member group with the following initial values:
          </t>
          <ul spacing="normal">
            <li>Ratchet tree: A tree with a single node, a leaf containing an HPKE public
key and credential for the creator</li>
            <li>Group ID: A value set by the creator</li>
            <li>Epoch: 0</li>
            <li>Tree hash: The root hash of the above ratchet tree</li>
            <li>Confirmed transcript hash: The zero-length octet string</li>
            <li>Epoch secret: A fresh random value of size <tt>KDF.Nh</tt></li>
            <li>Extensions: Any values of the creator's choosing</li>
          </ul>
        </li>
        <li>
          <t>Calculate the interim transcript hash:
          </t>
          <ul spacing="normal">
            <li>Derive the <tt>confirmation_key</tt> for the epoch as described in
<xref target="key-schedule"/>.</li>
            <li>Compute a <tt>confirmation_tag</tt> over the empty <tt>confirmed_transcript_hash</tt>
using the <tt>confirmation_key</tt> as described in <xref target="content-authentication"/>.</li>
            <li>Compute the updated <tt>interim_transcript_hash</tt> from the
<tt>confirmed_transcript_hash</tt> and the <tt>confirmation_tag</tt> as described in
<xref target="transcript-hashes"/></li>
          </ul>
        </li>
      </ul>
      <t>At this point, the creator's state represents a one-member group with a fully
initialized key schedule, transcript hashes, etc.  Proposals and Commits can be
generated for this group state just like any other state of the group, such as
Add proposals and Commits to add other members to the group.  A GroupInfo object
for this group state can also be published to facilitate external joins.</t>
      <t>Members other than the creator join either by being sent a Welcome message (as
described in <xref target="joining-via-welcome-message"/>) or by sending an external Commit
(see <xref target="joining-via-external-commits"/>).</t>
      <t>In principle, the above process could be streamlined by having the
creator directly create a tree and choose a random value for first
epoch's epoch secret.  We follow the steps above because it removes
unnecessary choices, by which, for example, bad randomness could be
introduced.  The only choices the creator makes here are its own
KeyPackage and the leaf secret from which the Commit is built.</t>
      <section anchor="required-capabilities">
        <name>Required Capabilities</name>
        <t>The configuration of a group imposes certain requirements on clients in the
group.  At a minimum, all members of the group need to support the ciphersuite
and protocol version in use.  Additional requirements can be imposed by
including a <tt>required_capabilities</tt> extension in the GroupContext.</t>
        <sourcecode type="tls"><![CDATA[
struct {
    ExtensionType extension_types<V>;
    ProposalType proposal_types<V>;
    CredentialType credential_types<V>;
} RequiredCapabilities;
]]></sourcecode>
        <t>This extension lists the extensions, proposals, and credential types that must be supported by
all members of the group. The "default" proposal and extension types defined in this
document are assumed to be implemented by all clients, and need not be listed in
RequiredCapabilities in order to be safely used. Note that this is not true for
credential types.</t>
        <t>For new members, support for required capabilities is enforced by existing
members during the application of Add commits.  Existing members should of
course be in compliance already.  In order to ensure this continues to be the
case even as the group's extensions are updated, a GroupContextExtensions
proposal is deemed invalid if it contains a <tt>required_capabilities</tt> extension that
requires non-default capabilities not supported by all current members.</t>
      </section>
      <section anchor="reinitialization">
        <name>Reinitialization</name>
        <t>A group may be reinitialized by creating a new group with the same membership
and different parameters, and linking it to the old group via a resumption PSK.
The members of a group reinitialize it using the following steps:</t>
        <ol spacing="normal" type="1"><li>A member of the old group sends a ReInit proposal (see <xref target="reinit"/>)</li>
          <li>A member of the old group sends a Commit covering the ReInit proposal</li>
          <li>
            <t>A member of the old group creates an initial Commit setting up a new group
that matches the ReInit and sends a Welcome message
            </t>
            <ul spacing="normal">
              <li>The <tt>group_id</tt>, <tt>version</tt>, <tt>cipher_suite</tt>, and <tt>extensions</tt> fields in the Welcome
message MUST be the same as the corresponding fields in the ReInit
proposal. The <tt>epoch</tt> in the Welcome message MUST be 1.</li>
              <li>The Welcome MUST specify a PreSharedKeyID of type <tt>resumption</tt> with usage
<tt>reinit</tt>, where the <tt>group_id</tt> field matches the old group and the <tt>epoch</tt>
field indicates the epoch after the Commit covering the ReInit.</li>
            </ul>
          </li>
        </ol>
        <t>Note that these three steps may be done by the same group member or different
members.  For example, if a group member sends a Commit with an inline ReInit
proposal (steps 1 and 2) but then goes offline, another group member may
recreate the group instead.  This flexibility avoids situations where a group
gets stuck between steps 2 and 3.</t>
        <t>Resumption PSKs with usage <tt>reinit</tt> MUST NOT be used in other contexts.  A
PreSharedKey proposal with type <tt>resumption</tt> and usage <tt>reinit</tt> MUST be
considered invalid.</t>
      </section>
      <section anchor="subgroup-branching">
        <name>Subgroup Branching</name>
        <t>A new group can be formed from a subset of an existing group's members, using
the same parameters as the old group.</t>
        <t>A member can create a subgroup by performing the following steps:</t>
        <ol spacing="normal" type="1"><li>Fetch a new KeyPackage for each group member that should be included in the
subgroup.</li>
          <li>Create an initial Commit message that sets up the new group and contains a
PreSharedKey proposal of type <tt>resumption</tt> with usage <tt>branch</tt>. To avoid key
re-use, the <tt>psk_nonce</tt> included in the <tt>PreSharedKeyID</tt> object MUST be a
randomly sampled nonce of length <tt>KDF.Nh</tt>.</li>
          <li>Send the corresponding Welcome message to the subgroup members.</li>
        </ol>
        <t>A client receiving a Welcome including a PreSharedKey of type <tt>resumption</tt> with
usage <tt>branch</tt> MUST verify that the new group reflects a subgroup branched from
the referenced group by checking:</t>
        <ul spacing="normal">
          <li>The <tt>version</tt> and <tt>ciphersuite</tt> values in the Welcome are the same as
those used by the old group.</li>
          <li>The <tt>epoch</tt> in the Welcome message MUST be 1.</li>
          <li>Each LeafNode in a new subgroup MUST match some LeafNode in the original
group. In this context, a pair of LeafNodes is said to "match" if the
identifiers presented by their respective credentials are considered
equivalent by the application.</li>
        </ul>
        <t>Resumption PSKs with usage <tt>branch</tt> MUST NOT be used in other contexts.  A
PreSharedKey proposal with type <tt>resumption</tt> and usage <tt>branch</tt> MUST be
considered invalid.</t>
      </section>
    </section>
    <section anchor="group-evolution">
      <name>Group Evolution</name>
      <t>Over the lifetime of a group, its membership can change, and existing members
might want to change their keys in order to achieve post-compromise security.
In MLS, each such change is accomplished by a two-step process:</t>
      <ol spacing="normal" type="1"><li>A proposal to make the change is broadcast to the group in a Proposal message</li>
        <li>A member of the group or a new member broadcasts a Commit message that causes
one or more proposed changes to enter into effect</li>
      </ol>
      <t>In cases where the Proposal and Commit are sent by the same member, these two steps
can be combined by sending the proposals in the commit.</t>
      <t>The group thus evolves from one cryptographic state to another each time a
Commit message is sent and processed.  These states are referred to as "epochs"
and are uniquely identified among states of the group by eight-octet epoch values.
When a new group is initialized, its initial state epoch is 0x0000000000000000.  Each time
a state transition occurs, the epoch number is incremented by one.</t>
      <section anchor="proposals">
        <name>Proposals</name>
        <t>Proposals are included in a FramedContent by way of a Proposal structure
that indicates their type:</t>
        <sourcecode type="tls"><![CDATA[
// See IANA registry for registered values
uint16 ProposalType;

struct {
    ProposalType msg_type;
    select (Proposal.msg_type) {
        case add:                      Add;
        case update:                   Update;
        case remove:                   Remove;
        case psk:                      PreSharedKey;
        case reinit:                   ReInit;
        case external_init:            ExternalInit;
        case group_context_extensions: GroupContextExtensions;
    };
} Proposal;
]]></sourcecode>
        <t>On receiving a FramedContent containing a Proposal, a client MUST verify the
signature inside FramedContentAuthData and that the <tt>epoch</tt> field of the enclosing
FramedContent is equal to the <tt>epoch</tt> field of the current GroupContext object.
If the verification is successful, then the Proposal should be cached in such a way
that it can be retrieved by hash (as a ProposalOrRef object) in a later Commit message.</t>
        <section anchor="add">
          <name>Add</name>
          <t>An Add proposal requests that a client with a specified KeyPackage be added
to the group.</t>
          <sourcecode type="tls"><![CDATA[
struct {
    KeyPackage key_package;
} Add;
]]></sourcecode>
          <t>An Add proposal is invalid if the KeyPackage is invalid according to
<xref target="keypackage-validation"/>.</t>
          <t>An Add is applied after being included in a Commit message.  The position of the
Add in the list of proposals determines the leaf node where the new member will
be added.  For the first Add in the Commit, the corresponding new member will be
placed in the leftmost empty leaf in the tree, for the second Add, the next
empty leaf to the right, etc. If no empty leaf exists, the tree is extended to
the right.</t>
          <ul spacing="normal">
            <li>Identify the leaf L for the new member: if there are empty leaves in the tree,
L is the leftmost empty leaf.  Otherwise, the tree is extended to the right
by one leaf node and L is the new leaf.</li>
            <li>For each non-blank intermediate node along the path from the leaf L
to the root, add L's leaf index to the <tt>unmerged_leaves</tt> list for the node.</li>
            <li>Set the leaf node L to a new node containing the LeafNode object carried in
the <tt>leaf_node</tt> field of the KeyPackage in the Add.</li>
          </ul>
        </section>
        <section anchor="update">
          <name>Update</name>
          <t>An Update proposal is a similar mechanism to Add with the distinction
that it replaces the sender's LeafNode in the tree instead of adding a new leaf
to the tree.</t>
          <sourcecode type="tls"><![CDATA[
struct {
    LeafNode leaf_node;
} Update;
]]></sourcecode>
          <t>An Update proposal is invalid if the LeafNode is invalid for an Update
proposal according to <xref target="leaf-node-validation"/>.</t>
          <t>A member of the group applies an Update message by taking the following steps:</t>
          <ul spacing="normal">
            <li>Replace the sender's LeafNode with the one contained in the Update proposal</li>
            <li>Blank the intermediate nodes along the path from the sender's leaf to the root</li>
          </ul>
        </section>
        <section anchor="remove">
          <name>Remove</name>
          <t>A Remove proposal requests that the member with the leaf index <tt>removed</tt> be removed
from the group.</t>
          <sourcecode type="tls"><![CDATA[
struct {
    uint32 removed;
} Remove;
]]></sourcecode>
          <t>A Remove proposal is invalid if the <tt>removed</tt> field does not identify a non-blank
leaf node.</t>
          <t>A member of the group applies a Remove message by taking the following steps:</t>
          <ul spacing="normal">
            <li>Identify the leaf node matching <tt>removed</tt>.  Let L be this leaf node.</li>
            <li>Replace the leaf node L with a blank node</li>
            <li>Blank the intermediate nodes along the path from L to the root</li>
            <li>Truncate the tree by removing the right subtree until there is at least one
non-blank leaf node in the right subtree.  If the rightmost non-blank leaf has
index L, then this will result in the tree having <tt>2^d</tt> leaves, where <tt>d</tt> is
the smallest value such that <tt>2^d &gt; L</tt>.</li>
          </ul>
        </section>
        <section anchor="presharedkey">
          <name>PreSharedKey</name>
          <t>A PreSharedKey proposal can be used to request that a pre-shared key be
injected into the key schedule in the process of advancing the epoch.</t>
          <sourcecode type="tls"><![CDATA[
struct {
    PreSharedKeyID psk;
} PreSharedKey;
]]></sourcecode>
          <t>A PreSharedKey proposal is invalid if any of the following is true:</t>
          <ul spacing="normal">
            <li>The <tt>psktype</tt> in the PreSharedKeyID struct is set to <tt>resumption</tt> and
the <tt>usage</tt> is <tt>reinit</tt> or <tt>branch</tt>.</li>
            <li>The <tt>psk_nonce</tt> is not of length <tt>KDF.Nh</tt>.</li>
          </ul>
          <t>The <tt>psk_nonce</tt> MUST be randomly sampled. When processing
a Commit message that includes one or more PreSharedKey proposals, group
members derive <tt>psk_secret</tt> as described in <xref target="pre-shared-keys"/>, where the
order of the PSKs corresponds to the order of the <tt>PreSharedKey</tt> proposals
in the Commit.</t>
        </section>
        <section anchor="reinit">
          <name>ReInit</name>
          <t>A ReInit proposal represents a request to reinitialize the group with different
parameters, for example, to increase the version number or to change the
ciphersuite. The reinitialization is done by creating a completely new group
and shutting down the old one.</t>
          <sourcecode type="tls"><![CDATA[
struct {
    opaque group_id<V>;
    ProtocolVersion version;
    CipherSuite cipher_suite;
    Extension extensions<V>;
} ReInit;
]]></sourcecode>
          <t>A ReInit proposal is invalid if the <tt>version</tt> field is less than the version
for the current group.</t>
          <t>A member of the group applies a ReInit proposal by waiting for the committer to
send the Welcome message that matches the ReInit, according to the criteria in
<xref target="reinitialization"/>.</t>
        </section>
        <section anchor="externalinit">
          <name>ExternalInit</name>
          <t>An ExternalInit proposal is used by new members that want to join a group by
using an external commit. This proposal can only be used in that context.</t>
          <sourcecode type="tls"><![CDATA[
struct {
  opaque kem_output<V>;
} ExternalInit;
]]></sourcecode>
          <t>A member of the group applies an ExternalInit message by initializing the next
epoch using an init secret computed as described in <xref target="external-initialization"/>.
The <tt>kem_output</tt> field contains the required KEM output.</t>
        </section>
        <section anchor="groupcontextextensions">
          <name>GroupContextExtensions</name>
          <t>A GroupContextExtensions proposal is used to update the list of extensions in
the GroupContext for the group.</t>
          <sourcecode type="tls"><![CDATA[
struct {
  Extension extensions<V>;
} GroupContextExtensions;
]]></sourcecode>
          <t>A GroupContextExtensions proposal is invalid if it includes a
<tt>required_capabilities</tt> extension and some members of the group do not support
some of the required capabilities (including those added in the same commit,
and excluding those removed).</t>
          <t>A member of the group applies a GroupContextExtensions proposal with the
following steps:</t>
          <ul spacing="normal">
            <li>Remove all of the existing extensions from the GroupContext object for the
group and replacing them with the list of extensions in the proposal.  (This
is a wholesale replacement, not a merge. An extension is only carried over if
the sender of the proposal includes it in the new list.)</li>
          </ul>
          <t>Note that once the GroupContext is updated, its inclusion in the
confirmation_tag by way of the key schedule will confirm that all members of the
group agree on the extensions in use.</t>
        </section>
        <section anchor="external-proposals">
          <name>External Proposals</name>
          <t>Add and Remove proposals can be constructed and sent to the group by a party
that is outside the group in two cases. One case, indicated by an <tt>external</tt> SenderType
is useful in cases where, for example, an automated service might propose to
remove a member of a group who has been inactive for a long time, or propose adding
a newly-hired staff member to a group representing a real-world team.</t>
          <t>ReInit proposals can also be sent to the group by an <tt>external</tt> sender, for
example to enforce a changed policy regarding MLS version or ciphersuite.</t>
          <t>The <tt>external</tt> SenderType requires that signers are pre-provisioned
to the clients within a group and can only be used if the
<tt>external_senders</tt> extension is present in the group's GroupContext.</t>
          <t>The other case, indicated by a <tt>new_member_proposal</tt> SenderType is useful when
existing members of the group can independently authorize the addition of an
MLS client proposing it be added to the group. External proposals which are not
authorized are considered invalid.</t>
          <t>An external proposal MUST be sent as a PublicMessage object, since the sender
will not have the keys necessary to construct a PrivateMessage object.</t>
          <section anchor="external-senders-extension">
            <name>External Senders Extension</name>
            <t>The <tt>external_senders</tt> extension is a group context extension that contains
the credentials and signature keys of senders that are permitted to send
external proposals to the group.</t>
            <sourcecode type="tls"><![CDATA[
struct {
  SignaturePublicKey signature_key;
  Credential credential;
} ExternalSender;

ExternalSender external_senders<V>;
]]></sourcecode>
          </section>
        </section>
      </section>
      <section anchor="proposal-list-validation">
        <name>Proposal List Validation</name>
        <t>A group member creating a commit and a group member processing a commit
MUST verify that the list of committed proposals is valid using one of the following
procedures, depending on whether the commit is external or not.</t>
        <t>For a regular, i.e. not external, commit the list is invalid if any of the following
occurs:</t>
        <ul spacing="normal">
          <li>It contains an individual proposal that is invalid as specified in <xref target="proposals"/>.</li>
          <li>It contains an Update proposal generated by the committer.</li>
          <li>It contains a Remove proposal that removes the committer.</li>
          <li>It contains multiple Update and/or Remove proposals that apply to the same leaf.
If the committer has received multiple such proposals they SHOULD prefer any Remove
received, or the most recent Update if there are no Removes.</li>
          <li>It contains multiple Add proposals that contain KeyPackages that represent the same
client according to the application (for example, identical signature keys).</li>
          <li>It contains an Add proposal with a KeyPackage that represents a client already
in the group according to the application, unless there is a Remove proposal
in the list removing the matching client from the group.</li>
          <li>It contains multiple PreSharedKey proposals that reference the same PreSharedKeyID.</li>
          <li>It contains multiple GroupContextExtensions proposals.</li>
          <li>It contains a ReInit proposal together with any other proposal. If the committer has
received other proposals during the epoch, they SHOULD prefer them over the
ReInit proposal, allowing the ReInit to be resent and applied in a subsequent
epoch.</li>
          <li>It contains an ExternalInit proposal.</li>
          <li>It contains a proposal with a non-default proposal type that is not supported by some
members of the group that will process the Commit (i.e., members being added
or removed by the Commit do not need to support the proposal type).</li>
          <li>After processing the commit the ratchet tree is invalid, in particular, if it
contains any leaf node that is invalid according to <xref target="leaf-node-validation"/>.</li>
        </ul>
        <t>An application may extend the above procedure by additional rules, for example,
requiring application-level permissions to add members, or rules concerning
non-default proposal types.</t>
        <t>For an external commit, the list is valid if it contains only the following proposals
(not necessarily in this order):</t>
        <ul spacing="normal">
          <li>Exactly one ExternalInit</li>
          <li>At most one Remove proposal, with which the joiner removes an
old version of themselves. If a Remove proposal is present, then the LeafNode in the
<tt>path</tt> field of the external commit MUST meet the same criteria as would the LeafNode
in an Update for the removed leaf (see <xref target="update"/>). In particular, the <tt>credential</tt>
in the LeafNode MUST present a set of identifiers that is acceptable to the
application for the removed participant.</li>
          <li>Zero or more PreSharedKey proposals.</li>
          <li>No other proposals.</li>
        </ul>
        <t>Proposal types defined in the future may make updates to the above validation
logic to incorporate considerations related to proposals of the new type.</t>
      </section>
      <section anchor="applying-a-proposal-list">
        <name>Applying a Proposal List</name>
        <t>The sections above defining each proposal type describe how each individual
proposals is applied.  When creating or processing a Commit, a client applies a
list of proposals to the ratchet tree and GroupContext. The client MUST apply
the proposals in the list in the following order:</t>
        <ul spacing="normal">
          <li>If there is a GroupContextExtensions proposal, replace the <tt>extensions</tt> field
of the GroupContext for the group with the contents of the proposal.  The
new <tt>extensions</tt> MUST be used for evaluating other proposals in this list. For
example, if a GroupContextExtensions proposal adds a <tt>required_capabilities</tt>
extension, then any Add proposals need to indicate support for those
capabilities.</li>
          <li>Apply any Update proposals to the ratchet tree, in any order.</li>
          <li>Apply any Remove proposals to the ratchet tree, in any order.</li>
          <li>Apply any Add proposals to the ratchet tree, in the order they appear in the list.</li>
          <li>Look up the PSK secrets for any PreSharedKey proposals, in the order they
appear in the list.  These secrets are then used to advance the key schedule
later in Commit processing.</li>
          <li>If there is an ExternalInit proposal, use it to derive the <tt>init_secret</tt> for
use later in Commit processing.</li>
          <li>If there is a ReInit proposal, note its parameters for application later in
Commit processing.</li>
        </ul>
        <t>Proposal types defined in the future MUST specify how the above steps are to be
adjusted to accommodate the application of proposals of the new type.</t>
      </section>
      <section anchor="commit">
        <name>Commit</name>
        <t>A Commit message initiates a new epoch for the group, based on a collection of
Proposals. It instructs group members to update their representation of the
state of the group by applying the proposals and advancing the key schedule.</t>
        <t>Each proposal covered by the Commit is included by a ProposalOrRef value, which
identifies the proposal to be applied by value or by reference.  Commits that
refer to new Proposals from the committer can be included by value. Commits
for previously sent proposals from anyone (including the committer) can be sent
by reference.  Proposals sent by reference are specified by including the hash of
the AuthenticatedContent object in which the proposal was sent (see <xref target="hash-based-identifiers"/>).</t>
        <sourcecode type="tls"><![CDATA[
enum {
  reserved(0),
  proposal(1),
  reference(2),
  (255)
} ProposalOrRefType;

struct {
  ProposalOrRefType type;
  select (ProposalOrRef.type) {
    case proposal:  Proposal proposal;
    case reference: ProposalRef reference;
  };
} ProposalOrRef;

struct {
    ProposalOrRef proposals<V>;
    optional<UpdatePath> path;
} Commit;
]]></sourcecode>
        <t>A group member that has observed one or more valid proposals within an epoch MUST send
a Commit message before sending application data. This ensures, for example,
that any members whose removal was proposed during the epoch are actually
removed before any application data is transmitted.</t>
        <t>A sender and a receiver of a Commit MUST verify that the committed list of
proposals is valid as specified in <xref target="proposal-list-validation"/>. A list is invalid if, for example,
it includes an Update and a Remove for the same member, or an Add when the sender does not have
the application-level permission to add new users.</t>
        <t>The sender of a Commit SHOULD include all proposals that it has received
during the current epoch, that are valid according to the rules for their
proposal types and according to application policy, as long as this results in
a valid proposal list.</t>
        <t>Due to the asynchronous nature of proposals, receivers of a Commit SHOULD NOT enforce
that all valid proposals sent within the current epoch are referenced by the next
Commit. In the event that a valid proposal is omitted from the next Commit, and
that proposal is still valid in the current epoch, the sender of the proposal
MAY resend it after updating it to reflect the current epoch.</t>
        <t>A member of the group MAY send a Commit that references no proposals at all,
which would thus have an empty <tt>proposals</tt> vector.  Such
a Commit resets the sender's leaf and the nodes along its direct path, and
provides forward secrecy and post-compromise security with regard to the sender
of the Commit.  An Update proposal can be regarded as a "lazy" version of this
operation, where only the leaf changes and intermediate nodes are blanked out.</t>
        <t>By default, the <tt>path</tt> field of a Commit MUST be populated.  The <tt>path</tt> field
MAY be omitted if (a) it covers at least one proposal and (b) none of the proposals
covered by the Commit are of "path required" types.  A proposal type requires a
path if it cannot change the group membership in a way that requires the forward
secrecy and post-compromise security guarantees that an UpdatePath provides.
The only proposal types defined in this document that do not require a path are:</t>
        <ul spacing="normal">
          <li>
            <tt>add</tt></li>
          <li>
            <tt>psk</tt></li>
          <li>
            <tt>reinit</tt></li>
        </ul>
        <t>New proposal types MUST state whether they require a path. If any instance of a
proposal type requires a path, then the proposal type requires a path. This
attribute of a proposal type is reflected in the "Path Required" field of the
proposal type registry defined in <xref target="mls-proposal-types"/>.</t>
        <t>Update and Remove proposals are the clearest examples of proposals that require
a path.  An UpdatePath is required to evict the removed member or the old
appearance of the updated member.</t>
        <t>In pseudocode, the logic for validating the <tt>path</tt> field of a Commit is as
follows:</t>
        <sourcecode type="pseudocode"><![CDATA[
pathRequiredTypes = [
    update,
    remove,
    external_init,
    group_context_extensions
]

pathRequired = false

for i, id in commit.proposals:
    proposal = proposalCache[id]
    assert(proposal != null)

    pathRequired = pathRequired ||
                   (proposal.msg_type in pathRequiredTypes)

if len(commit.proposals) == 0 || pathRequired:
    assert(commit.path != null)
]]></sourcecode>
        <t>To summarize, a Commit can have three different configurations, with different
uses:</t>
        <ol spacing="normal" type="1"><li>An "empty" Commit that references no proposals, which updates the committer's
contribution to the group and provides PCS with regard to the committer.</li>
          <li>A "partial" Commit that references proposals that do not require a path, and
where the path is empty. Such a commit doesn't provide PCS with regard to the
committer.</li>
          <li>A "full" Commit that references proposals of any type, which provides FS with
regard to any removed members and PCS for the committer and any updated
members.</li>
        </ol>
        <section anchor="creating-a-commit">
          <name>Creating a Commit</name>
          <t>When creating or processing a Commit, a client updates the ratchet tree and
GroupContext for the group.  These values advance from an "old" state reflecting
the current epoch to a "new" state reflecting the new epoch initiated by the
Commit.  When the Commit includes an UpdatePath, a "provisional" group context
is constructed that reflects changes due to the proposals and UpdatePath, but
with the old confirmed transcript hash.</t>
          <t>A member of the group creates a Commit message and the corresponding Welcome
message at the same time, by taking the following steps:</t>
          <ul spacing="normal">
            <li>Verify that the list of proposals to be committed is valid as specified in
<xref target="proposal-list-validation"/>.</li>
            <li>Construct an initial Commit object with the <tt>proposals</tt>
field populated from Proposals received during the current epoch, and an empty
<tt>path</tt> field.</li>
            <li>Create the new ratchet tree and GroupContext by applying the list of proposals
to the old ratchet tree and GroupContext, as defined in
<xref target="applying-a-proposal-list"/></li>
            <li>Decide whether to populate the <tt>path</tt> field: If the <tt>path</tt> field is required
based on the proposals that are in the commit (see above), then it MUST be
populated.  Otherwise, the sender MAY omit the <tt>path</tt> field at its discretion.</li>
            <li>
              <t>If populating the <tt>path</tt> field:  </t>
              <ul spacing="normal">
                <li>If this is an external commit, assign the sender the leftmost blank leaf
node in the new ratchet tree.  If there are no blank leaf nodes in the new
ratchet tree, add a blank leaf to the right side of the new ratchet tree and
assign it to the sender.</li>
                <li>Update the sender's direct path in the ratchet tree as described in
<xref target="synchronizing-views-of-the-tree"/>.  Define
<tt>commit_secret</tt> as the value <tt>path_secret[n+1]</tt> derived from the
last path secret value (<tt>path_secret[n]</tt>) derived for the UpdatePath.</li>
                <li>
                  <t>Construct a provisional GroupContext object containing the following values:
                  </t>
                  <ul spacing="normal">
                    <li>
                      <tt>group_id</tt>: Same as the old GroupContext</li>
                    <li>
                      <tt>epoch</tt>: The epoch number for the new epoch</li>
                    <li>
                      <tt>tree_hash</tt>: The tree hash of the new ratchet tree</li>
                    <li>
                      <tt>confirmed_transcript_hash</tt>: Same as the old GroupContext</li>
                    <li>
                      <tt>extensions</tt>: The new GroupContext extensions (possibly updated by a
GroupContextExtensions proposal)</li>
                  </ul>
                </li>
                <li>Encrypt the path secrets resulting from the tree update to the group as
described in <xref target="synchronizing-views-of-the-tree"/>, using the provisional
group context as the context for HPKE encryption.</li>
                <li>Create an UpdatePath containing the sender's new leaf node and the new
public keys and encrypted path secrets along the sender's filtered direct
path.  Assign this UpdatePath to the <tt>path</tt> field in the Commit.</li>
              </ul>
            </li>
            <li>If not populating the <tt>path</tt> field: Set the <tt>path</tt> field in the Commit to the
null optional.  Define <tt>commit_secret</tt> as the all-zero vector of length
<tt>KDF.Nh</tt> (the same length as a <tt>path_secret</tt> value would be).</li>
            <li>Derive the <tt>psk_secret</tt> as specified in <xref target="pre-shared-keys"/>, where the order
of PSKs in the derivation corresponds to the order of PreSharedKey proposals
in the <tt>proposals</tt> vector.</li>
            <li>
              <t>Construct a FramedContent object containing the Commit object. Sign the
FramedContent using the old GroupContext as context.
              </t>
              <ul spacing="normal">
                <li>Use the FramedContent to update the confirmed transcript hash and update
the new GroupContext.</li>
                <li>Use the <tt>init_secret</tt> from the previous epoch, the <tt>commit_secret</tt> and the
<tt>psk_secret</tt> as defined in the previous steps, and the new GroupContext to
compute the new <tt>joiner_secret</tt>, <tt>welcome_secret</tt>, <tt>epoch_secret</tt>, and
derived secrets for the new epoch.</li>
                <li>Use the <tt>confirmation_key</tt> for the new epoch to compute the
<tt>confirmation_tag</tt> value.</li>
                <li>Calculate the interim transcript hash using the new confirmed transcript
hash and the <tt>confirmation_tag</tt> from the FramedContentAuthData.</li>
              </ul>
            </li>
            <li>
              <t>Protect the AuthenticatedContent object using keys from the old epoch:
              </t>
              <ul spacing="normal">
                <li>If encoding as PublicMessage, compute the <tt>membership_tag</tt> value using the
<tt>membership_key</tt>.</li>
                <li>If encoding as an PrivateMessage, encrypt the message using the
<tt>sender_data_secret</tt> and the next (key, nonce) pair from the sender's
handshake ratchet.</li>
              </ul>
            </li>
            <li>
              <t>Construct a GroupInfo reflecting the new state:
              </t>
              <ul spacing="normal">
                <li>Group ID, epoch, tree, confirmed transcript hash, interim transcript
hash, and group context extensions from the new state</li>
                <li>The confirmation_tag from the FramedContentAuthData object</li>
                <li>Other extensions as defined by the application</li>
                <li>Optionally derive an external keypair as described in <xref target="key-schedule"/>
(required for External Commits, see <xref target="joining-via-external-commits"/>)</li>
                <li>Sign the GroupInfo using the member's private signing key</li>
                <li>Encrypt the GroupInfo using the key and nonce derived from the <tt>joiner_secret</tt>
for the new epoch (see <xref target="joining-via-welcome-message"/>)</li>
              </ul>
            </li>
            <li>
              <t>For each new member in the group:
              </t>
              <ul spacing="normal">
                <li>Identify the lowest common ancestor in the tree of the new member's
leaf node and the member sending the Commit</li>
                <li>If the <tt>path</tt> field was populated above: Compute the path secret
corresponding to the common ancestor node</li>
                <li>Compute an EncryptedGroupSecrets object that encapsulates the <tt>init_secret</tt>
for the current epoch and the path secret (if present).</li>
              </ul>
            </li>
            <li>Construct one or more Welcome messages from the encrypted GroupInfo object,
the encrypted key packages, and any PSKs for which a proposal was included in
the Commit. The order of the <tt>psks</tt> MUST be the same as the order of
PreSharedKey proposals in the <tt>proposals</tt> vector.  As discussed on
<xref target="joining-via-welcome-message"/>, the committer is free to choose how many
Welcome messages to construct.  However, the set of Welcome messages produced
in this step MUST cover every new member added in the Commit.</li>
            <li>
              <t>If a ReInit proposal was part of the Commit, the committer MUST create a new
group with the parameters specified in the ReInit proposal,
and with the same members as the original group.
The Welcome message MUST include a <tt>PreSharedKeyID</tt> with the following
parameters:
              </t>
              <ul spacing="normal">
                <li>
                  <tt>psktype</tt>: <tt>resumption</tt></li>
                <li>
                  <tt>usage</tt>: <tt>reinit</tt></li>
                <li>
                  <tt>group_id</tt>: The group ID for the current group</li>
                <li>
                  <tt>epoch</tt>: The epoch that the group will be in after this Commit</li>
              </ul>
            </li>
          </ul>
        </section>
        <section anchor="processing-a-commit">
          <name>Processing a Commit</name>
          <t>A member of the group applies a Commit message by taking the following steps:</t>
          <ul spacing="normal">
            <li>Verify that the <tt>epoch</tt> field of the enclosing FramedContent is equal
to the <tt>epoch</tt> field of the current GroupContext object</li>
            <li>
              <t>Unprotect the Commit using the keys from the current epoch:
              </t>
              <ul spacing="normal">
                <li>If the message is encoded as PublicMessage, verify the membership MAC using
the <tt>membership_key</tt></li>
                <li>If the message is encoded as PrivateMessage, decrypt the message using the
<tt>sender_data_secret</tt> and the (key, nonce) pair from the step on the sender's
hash ratchet indicated by the <tt>generation</tt> field.</li>
              </ul>
            </li>
            <li>Verify that the signature on the FramedContent message as described in
Section <xref target="content-authentication"/>.</li>
            <li>Verify that the <tt>proposals</tt> vector is valid as specified in <xref target="proposal-list-validation"/>.</li>
            <li>Verify that all PreSharedKey proposals in the <tt>proposals</tt> vector are available.</li>
            <li>Create the new ratchet tree and GroupContext by applying the list of proposals
to the old ratchet tree and GroupContext, as defined in
<xref target="applying-a-proposal-list"/></li>
            <li>Verify that the <tt>path</tt> value is populated if the <tt>proposals</tt> vector contains
any Update or Remove proposals, or if it's empty. Otherwise, the <tt>path</tt> value
MAY be omitted.</li>
            <li>
              <t>If the <tt>path</tt> value is populated, validate it and apply it to the tree:  </t>
              <ul spacing="normal">
                <li>If this is an external commit, assign the sender the leftmost blank leaf
node in the new ratchet tree.  If there are no blank leaf nodes in the new
ratchet tree, add a blank leaf to the right side of the new ratchet tree and
assign it to the sender.</li>
                <li>Validate the LeafNode as specified in <xref target="leaf-node-validation"/>.  The
<tt>leaf_node_source</tt> field MUST be set to <tt>commit</tt>.</li>
                <li>Verify that the <tt>encryption_key</tt> value in the LeafNode is different from the
committer's current leaf node.</li>
                <li>Merge the UpdatePath into the new ratchet tree as described in
<xref target="synchronizing-views-of-the-tree"/>.</li>
                <li>
                  <t>Construct a provisional GroupContext object containing the following values:
                  </t>
                  <ul spacing="normal">
                    <li>
                      <tt>group_id</tt>: Same as the old GroupContext</li>
                    <li>
                      <tt>epoch</tt>: The epoch number for the new epoch</li>
                    <li>
                      <tt>tree_hash</tt>: The tree hash of the new ratchet tree</li>
                    <li>
                      <tt>confirmed_transcript_hash</tt>: Same as the old GroupContext</li>
                    <li>
                      <tt>extensions</tt>: The new GroupContext extensions (possibly updated by a
GroupContextExtensions proposal)</li>
                  </ul>
                </li>
                <li>Decrypt the path secrets for UpdatePath as described in
<xref target="synchronizing-views-of-the-tree"/>, using the provisional GroupContext as
the context for HPKE decryption.</li>
                <li>Define <tt>commit_secret</tt> as the value <tt>path_secret[n+1]</tt> derived from the
last path secret value (<tt>path_secret[n]</tt>) derived for the UpdatePath.</li>
              </ul>
            </li>
            <li>If the <tt>path</tt> value is not populated: Define <tt>commit_secret</tt> as the all-zero
vector of length <tt>KDF.Nh</tt> (the same length as a <tt>path_secret</tt> value would be).</li>
            <li>Update the confirmed and interim transcript hashes using the new Commit, and
generate the new GroupContext.</li>
            <li>Derive the <tt>psk_secret</tt> as specified in <xref target="pre-shared-keys"/>, where the order
of PSKs in the derivation corresponds to the order of PreSharedKey proposals
in the <tt>proposals</tt> vector.</li>
            <li>Use the <tt>init_secret</tt> from the previous epoch, the <tt>commit_secret</tt> and the
<tt>psk_secret</tt> as defined in the previous steps, and the new GroupContext to
compute the new <tt>joiner_secret</tt>, <tt>welcome_secret</tt>, <tt>epoch_secret</tt>, and
derived secrets for the new epoch.</li>
            <li>Use the <tt>confirmation_key</tt> for the new epoch to compute the confirmation tag
for this message, as described below, and verify that it is the same as the
<tt>confirmation_tag</tt> field in the FramedContentAuthData object.</li>
            <li>If the above checks are successful, consider the new GroupContext object
as the current state of the group.</li>
            <li>If the Commit included a ReInit proposal, the client MUST NOT use the group to
send messages anymore. Instead, it MUST wait for a Welcome message from the committer
meeting the requirements of <xref target="reinitialization"/>.</li>
          </ul>
          <t>Note that clients need to be prepared to receive a valid Commit message which removes
them from the group. In this case, the client cannot send any more messages in the
group and SHOULD promptly delete its group state and secret tree. (A client might keep
the secret tree for a short time to decrypt late messages in the previous epoch.)</t>
        </section>
        <section anchor="adding-members-to-the-group">
          <name>Adding Members to the Group</name>
          <t>New members can join the group in two ways. Either by being added by a group
member, or by adding themselves through an external Commit. In both cases, the
new members need information to bootstrap their local group state.</t>
          <sourcecode type="tls"><![CDATA[
struct {
    GroupContext group_context;
    Extension extensions<V>;
    MAC confirmation_tag;
    uint32 signer;
    /* SignWithLabel(., "GroupInfoTBS", GroupInfoTBS) */
    opaque signature<V>;
} GroupInfo;
]]></sourcecode>
          <t>The <tt>group_context</tt> field represents the current state of the group.  The
<tt>extensions</tt> field allows the sender to provide additional data that might be
useful to new joiners.  The <tt>confirmation_tag</tt> represents the  confirmation tag
from the Commit that initiated the current epoch, or for epoch 0, the
confirmation tag computed in the creation of the group (see <xref target="group-creation"/>).
(In either case, the creator of a GroupInfo may recompute the confirmation tag
as <tt>MAC(confirmation_key, confirmed_transcript_hash)</tt>.)</t>
          <t>New members MUST verify that <tt>group_id</tt> is unique among the groups they're
currently participating in.</t>
          <t>New members also MUST verify the <tt>signature</tt> using the public key taken from the
leaf node of the ratchet tree with leaf index <tt>signer</tt>. The
signature covers the following structure, comprising all the fields in the
GroupInfo above <tt>signature</tt>:</t>
          <sourcecode type="tls"><![CDATA[
struct {
    GroupContext group_context;
    Extension extensions<V>;
    MAC confirmation_tag;
    uint32 signer;
} GroupInfoTBS;
]]></sourcecode>
          <section anchor="joining-via-welcome-message">
            <name>Joining via Welcome Message</name>
            <t>The sender of a Commit message is responsible for sending a Welcome message to
each new member added via Add proposals.  The format of the Welcome message
allows a single Welcome message to be encrypted for multiple new members.  It is
up to the committer to decide how many Welcome messages to create for a given
Commit. The committer could create one Welcome that is encrypted for all new
members, a different Welcome for each new member, or Welcome messages for
batches of new members (according to some batching scheme that works well for
the application).  The processes for creating and processing the Welcome are the
same in all cases, aside from the set of new members for whom a given Welcome is
encrypted.</t>
            <t>The Welcome message provides the new
members with the current state of the group after the application of the Commit
message.  The new members will not be able to decrypt or verify the Commit
message, but will have the secrets they need to participate in the epoch
initiated by the Commit message.</t>
            <t>In order to allow the same Welcome message to be sent to multiple new members,
information describing the group is encrypted with a symmetric key and nonce
derived from the <tt>joiner_secret</tt> for the new epoch.  The <tt>joiner_secret</tt> is
then encrypted to each new member using HPKE.  In the same encrypted package,
the committer transmits the path secret for the lowest (closest to the leaf) node
which is contained in the direct paths of both the committer and the new member.
This allows the new
member to compute private keys for nodes in its direct path that are being
reset by the corresponding Commit.</t>
            <t>If the sender of the Welcome message wants the receiving member to include a PSK
in the derivation of the <tt>epoch_secret</tt>, they can populate the <tt>psks</tt> field
indicating which PSK to use.</t>
            <sourcecode type="tls"><![CDATA[
struct {
  opaque path_secret<V>;
} PathSecret;

struct {
  opaque joiner_secret<V>;
  optional<PathSecret> path_secret;
  PreSharedKeyID psks<V>;
} GroupSecrets;

struct {
  KeyPackageRef new_member;
  HPKECiphertext encrypted_group_secrets;
} EncryptedGroupSecrets;

struct {
  CipherSuite cipher_suite;
  EncryptedGroupSecrets secrets<V>;
  opaque encrypted_group_info<V>;
} Welcome;
]]></sourcecode>
            <t>The client processing a Welcome message will need to have a copy of the group's
ratchet tree.  The tree can be provided in the Welcome message, in an extension
of type <tt>ratchet_tree</tt>.  If it is sent otherwise (e.g., provided by a caching
service on the Delivery Service), then the client MUST download the tree before
processing the Welcome.</t>
            <t>On receiving a Welcome message, a client processes it using the following steps:</t>
            <ul spacing="normal">
              <li>Identify an entry in the <tt>secrets</tt> array where the <tt>new_member</tt>
value corresponds to one of this client's KeyPackages, using the hash
indicated by the <tt>cipher_suite</tt> field. If no such field exists, or if the
ciphersuite indicated in the KeyPackage does not match the one in the
Welcome message, return an error.</li>
              <li>Decrypt the <tt>encrypted_group_secrets</tt> value with the algorithms indicated by
the ciphersuite and the private key <tt>init_key_priv</tt> corresponding to
<tt>init_key</tt> in the referenced KeyPackage.</li>
            </ul>
            <sourcecode type="pseudocode"><![CDATA[
encrypted_group_secrets = EncryptWithLabel(init_key, "Welcome",
                                           encrypted_group_info, group_secrets)

group_secrets = DecryptWithLabel(kem_output, init_key_priv, "Welcome",
                                 encrypted_group_info, ciphertext)
]]></sourcecode>
            <ul spacing="normal">
              <li>If a <tt>PreSharedKeyID</tt> is part of the GroupSecrets and the client is not in
possession of the corresponding PSK, return an error. Additionally, if a
<tt>PreSharedKeyID</tt> has type <tt>resumption</tt> with usage <tt>reinit</tt> or <tt>branch</tt>, verify
that it is the only such PSK.</li>
              <li>From the <tt>joiner_secret</tt> in the decrypted GroupSecrets object and the PSKs
specified in the <tt>GroupSecrets</tt>, derive the <tt>welcome_secret</tt> and using that
the <tt>welcome_key</tt> and <tt>welcome_nonce</tt>. Use the key and nonce to decrypt the
<tt>encrypted_group_info</tt> field.</li>
            </ul>
            <sourcecode type="pseudocode"><![CDATA[
welcome_nonce = KDF.Expand(welcome_secret, "nonce", AEAD.Nn)
welcome_key = KDF.Expand(welcome_secret, "key", AEAD.Nk)
]]></sourcecode>
            <ul spacing="normal">
              <li>Verify the signature on the GroupInfo object. The signature input comprises
all of the fields in the GroupInfo object except the signature field. The
public key is taken from the LeafNode of the
ratchet tree with leaf index <tt>signer</tt>. If the node is blank or if
signature verification fails, return an error.</li>
              <li>Verify that the <tt>group_id</tt> is unique among the groups that the client is
currently participating in.</li>
              <li>Verify that the <tt>cipher_suite</tt> in the GroupInfo matches the <tt>cipher_suite</tt> in
the KeyPackage.</li>
              <li>
                <t>Verify the integrity of the ratchet tree.  </t>
                <ul spacing="normal">
                  <li>Verify that the tree hash of the ratchet tree matches the <tt>tree_hash</tt> field
in GroupInfo.</li>
                  <li>For each non-empty parent node, verify that it is "parent-hash valid",
as described in <xref target="verifying-parent-hashes"/>.</li>
                  <li>For each non-empty leaf node, validate the LeafNode as described in
<xref target="leaf-node-validation"/>.</li>
                  <li>
                    <t>For each non-empty parent node and each entry in the node's
<tt>unmerged_leaves</tt> field:      </t>
                    <ul spacing="normal">
                      <li>Verify that the entry represents a non-blank leaf node that is a
descendant of the parent node.</li>
                      <li>Verify that every non-blank intermediate node beween the leaf node and the
parent node also has an entry for the leaf node in its <tt>unmerged_leaves</tt>.</li>
                    </ul>
                  </li>
                </ul>
              </li>
              <li>Identify a leaf whose LeafNode is
identical to the one in the KeyPackage.  If no such field exists, return an
error.  Let <tt>my_leaf</tt> represent this leaf in the tree.</li>
              <li>
                <t>Construct a new group state using the information in the GroupInfo object.
                </t>
                <ul spacing="normal">
                  <li>The GroupContext is the <tt>group_context</tt> field from the GroupInfo object.</li>
                  <li>The new member's position in the tree is at the leaf <tt>my_leaf</tt>, as defined
above.</li>
                  <li>Update the leaf <tt>my_leaf</tt> with the private key corresponding to the
public key in the node.</li>
                  <li>If the <tt>path_secret</tt> value is set in the GroupSecrets object: Identify the
lowest common ancestor of the leaf node <tt>my_leaf</tt> and of the node of
the member with leaf index <tt>GroupInfo.signer</tt>. Set the private key for
this node to the private key derived from the <tt>path_secret</tt>.</li>
                  <li>For each parent of the common ancestor, up to the root of the tree, derive
a new path secret and set the private key for the node to the private key
derived from the path secret.  The private key MUST be the private key
that corresponds to the public key in the node.</li>
                </ul>
              </li>
              <li>Use the <tt>joiner_secret</tt> from the GroupSecrets object to generate the epoch secret
and other derived secrets for the current epoch.</li>
              <li>Set the confirmed transcript hash in the new state to the value of the
<tt>confirmed_transcript_hash</tt> in the GroupInfo.</li>
              <li>Verify the confirmation tag in the GroupInfo using the derived confirmation
key and the <tt>confirmed_transcript_hash</tt> from the GroupInfo.</li>
              <li>Use the confirmed transcript hash and confirmation tag to compute the interim
transcript hash in the new state.</li>
              <li>
                <t>If a <tt>PreSharedKeyID</tt> was used that has type <tt>resumption</tt> with usage <tt>reinit</tt>
or <tt>branch</tt>, verify that the <tt>epoch</tt> field in the GroupInfo is equal to 1.  </t>
                <ul spacing="normal">
                  <li>For usage <tt>reinit</tt>, verify that the last Commit to the referenced group
contains a ReInit proposal and that the <tt>group_id</tt>, <tt>version</tt>,
<tt>cipher_suite</tt>, and <tt>group_context.extensions</tt> fields of the GroupInfo match
the ReInit proposal. Additionally, verify that all the members of the old
group are also members of the new group, according to the application.</li>
                  <li>For usage <tt>branch</tt>, verify that the <tt>version</tt> and <tt>cipher_suite</tt> of the new
group match those of the old group, and that the members of the new group
compose a subset of the members of the old group, according to the
application.</li>
                </ul>
              </li>
            </ul>
          </section>
          <section anchor="joining-via-external-commits">
            <name>Joining via External Commits</name>
            <t>External Commits are a mechanism for new members (external parties that want to
become members of the group) to add themselves to a group, without requiring
that an existing member has to come online to issue a Commit that references an
Add Proposal.</t>
            <t>Whether existing members of the group will accept or reject an External Commit
follows the same rules that are applied to other handshake messages.</t>
            <t>New members can create and issue an External Commit if they have access to the
following information for the group's current epoch:</t>
            <ul spacing="normal">
              <li>group ID</li>
              <li>epoch ID</li>
              <li>ciphersuite</li>
              <li>public tree hash</li>
              <li>confirmed transcript hash</li>
              <li>confirmation tag of the most recent Commit</li>
              <li>group extensions</li>
              <li>external public key</li>
            </ul>
            <t>In other words, to join a group via an External Commit, a new member needs a
GroupInfo with an <tt>external_pub</tt> extension present in its <tt>extensions</tt> field.</t>
            <sourcecode type="tls"><![CDATA[
struct {
    HPKEPublicKey external_pub;
} ExternalPub;
]]></sourcecode>
            <t>Thus, a member of the group can enable new clients to join by making a GroupInfo
object available to them. Note that because a GroupInfo object is specific to an
epoch, it will need to be updated as the group advances. In particular, each
GroupInfo object can be used for one external join, since that external join
will cause the epoch to change.</t>
            <t>Note that the <tt>tree_hash</tt> field is used the same way as in the Welcome message.
The full tree can be included via the <tt>ratchet_tree</tt> extension
<xref target="ratchet-tree-extension"/>.</t>
            <t>The information in a GroupInfo is not generally public information, but applications
can choose to make it available to new members in order to allow External
Commits.</t>
            <t>In principle, External Commits work like regular Commits. However, their content
has to meet a specific set of requirements:</t>
            <ul spacing="normal">
              <li>External Commits MUST contain a <tt>path</tt> field (and is therefore a "full"
Commit).  The joiner is added at the leftmost free leaf node (just as if they
were added with an Add proposal), and the path is calculated relative to that
leaf node.</li>
              <li>The Commit MUST NOT include any proposals by reference, since an external
joiner cannot determine the validity of proposals sent within the group</li>
              <li>External Commits MUST be signed by the new member.  In particular, the
signature on the enclosing AuthenticatedContent MUST verify using the public key for
the credential in the <tt>leaf_node</tt> of the <tt>path</tt> field.</li>
              <li>When processing a Commit, both existing and new members MUST use the external
init secret as described in <xref target="external-initialization"/>.</li>
              <li>The sender type for the AuthenticatedContent encapsulating the External Commit MUST be
<tt>new_member_commit</tt>.</li>
            </ul>
            <t>External Commits come in two "flavors" -- a "join" commit that
adds the sender to the group or a "resync" commit that replaces a member's prior
appearance with a new one.</t>
            <t>Note that the "resync" operation allows an attacker that has compromised a
member's signature private key to introduce themselves into the group and remove the
prior, legitimate member in a single Commit.  Without resync, this
can still be done, but requires two operations, the external Commit to join and
a second Commit to remove the old appearance.  Applications for whom this
distinction is salient can choose to disallow external commits that contain a
Remove, or to allow such resync commits only if they contain a "reinit" PSK
proposal that demonstrates the joining member's presence in a prior epoch of the
group.  With the latter approach, the attacker would need to compromise the PSK
as well as the signing key, but the application will need to ensure that
continuing, non-resynchronizing members have the required PSK.</t>
          </section>
          <section anchor="ratchet-tree-extension">
            <name>Ratchet Tree Extension</name>
            <t>By default, a GroupInfo message only provides the joiner with a hash of
the group's ratchet tree.  In order to process or generate handshake
messages, the joiner will need to get a copy of the ratchet tree from some other
source.  (For example, the DS might provide a cached copy.)  The inclusion of
the tree hash in the GroupInfo message means that the source of the ratchet
tree need not be trusted to maintain the integrity of tree.</t>
            <t>In cases where the application does not wish to provide such an external source,
the whole public state of the ratchet tree can be provided in an extension of
type <tt>ratchet_tree</tt>, containing a <tt>ratchet_tree</tt> object of the following form:</t>
            <sourcecode type="tls"><![CDATA[
struct {
    NodeType node_type;
    select (Node.node_type) {
        case leaf:   LeafNode leaf_node;
        case parent: ParentNode parent_node;
    };
} Node;

optional<Node> ratchet_tree<V>;
]]></sourcecode>
            <t>Each entry in the <tt>ratchet_tree</tt> vector provides the value for a node in the
tree, or the null optional for a blank node.</t>
            <t>The nodes are listed in the order specified by a left-to-right in-order
traversal of the ratchet tree. Each node is listed between its left subtree and
its right subtree.  (This is the same ordering as specified for the array-based
trees outlined in <xref target="array-based-trees"/>.)</t>
            <t>If the tree has <tt>2^d</tt> leaves, then it has <tt>2^(d+1) - 1</tt> nodes.  The
<tt>ratchet_tree</tt> vector logically has this number of entries, but the sender
SHOULD NOT include blank nodes after the last non-blank node.  If a receiver
encounters a vector whose length <tt>L</tt> is not of the form <tt>2^(d+1) - 1</tt>, then the
receiver MUST extend it to the right with blank values until it has such a
length, adding the minimum number of blank values possible.  (Obviously, this
may be done "virtually", by synthesizing blank nodes when required, as opposed
to actually changing the structure in memory.)</t>
            <t>The leaves of the tree are stored in even-numbered entries in the array (the
leaf with index <tt>L</tt> in array position <tt>2*L</tt>). The root node of the tree is at
position <tt>2^d - 1</tt> of the array. Intermediate parent nodes can be identified by
performing the same calculation to the subarrays to the left and right of the
root, following something like the following algorithm:</t>
            <sourcecode type="python"><![CDATA[
# Assuming a class Node that has left and right members
def subtree_root(nodes):
    # If there is only one node in the array return it
    if len(nodes) == 1:
        return Node(nodes[0])

    # Otherwise, the length of the array MUST be odd
    if len(nodes) % 2 == 0:
        raise Exception("Malformed node array {}", len(nodes))

    # Identify the root of the subtree
    d = 0
    while (2**(d+1)) < len(nodes):
       d += 1
    R = 2**d - 1
    root = Node(nodes[R])
    root.left = subtree_root(nodes[:R])
    root.right = subtree_root(nodes[(R+1):])
    return root
]]></sourcecode>
            <t>(Note that this is the same ordering of nodes as in the array-based tree representation
described in <xref target="array-based-trees"/>.  The algorithms in that section may be used to
simplify decoding this extension into other representations.)</t>
            <t>For example, the following tree with six non-blank leaves would be represented
as an array of eleven elements, <tt>[A, W, B, X, C, _, D, Y, E, Z, F]</tt>.  The above
decoding procedure would identify the subtree roots as follows (using R to
represent a subtree root):</t>
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            <t>The presence of a <tt>ratchet_tree</tt> extension in a GroupInfo message does not
result in any changes to the GroupContext extensions for the group.  The ratchet
tree provided is simply stored by the client and used for MLS operations.</t>
            <t>If this extension is not provided in a Welcome message, then the client will
need to fetch the ratchet tree over some other channel before it can generate or
process Commit messages.  Applications should ensure that this out-of-band
channel is provided with security protections equivalent to the protections that
are afforded to Proposal and Commit messages.  For example, an application that
encrypts Proposal and Commit messages might distribute ratchet trees encrypted
using a key exchanged over the MLS channel.</t>
            <t>Regardless of how the client obtains the tree, the client MUST verify that the
root hash of the ratchet tree matches the <tt>tree_hash</tt> of the GroupContext before
using the tree for MLS operations.</t>
          </section>
        </section>
      </section>
    </section>
    <section anchor="extensibility">
      <name>Extensibility</name>
      <t>The base MLS protocol can be extended in a few ways.  New ciphersuites can be
added to enable the use of new cryptographic algorithms.  New types of proposals
can be used to perform new actions within an epoch.  Extension fields can be
used to add additional information to the protocol.  In this section, we discuss
some constraints on these extensibility mechanisms that are necessary to ensure
broad interoperability.</t>
      <section anchor="additional-ciphersuites">
        <name>Additional Ciphersuites</name>
        <t>As discussed in <xref target="ciphersuites"/>, MLS allows the participants in a group to
negotiate the cryptographic algorithms used within the group.  This
extensibility is important for maintaining the security of the protocol over
time <xref target="RFC7696"/>.  It also creates a risk of interoperability failure due to
clients not supporting a common ciphersuite.</t>
        <t>The ciphersuite registry defined in <xref target="mls-ciphersuites"/> attempts to strike a
balance on this point.  On the one hand, the base policy for the registry is
Specification Required, a fairly low bar designed to avoid the need for
standards work in cases where different ciphers are needed for niche
applications.  There is a higher bar (Standards Action) for ciphers to set the
Recommended field in the registry.  This higher bar is there in part to ensure
that the interoperability implications of new ciphersuites are considered.</t>
        <t>MLS ciphersuites are defined independent of MLS versions, so that in principle
the same ciphersuite can be used across versions.  Standards work defining new
versions of MLS should consider whether it is desirable for the new version to
be compatible with existing ciphersuites, or whether the new version should rule
out some ciphersuites. For example, a new version could follow the example of
HTTP/2, which restricted the set of allowed TLS ciphers (see Section 9.2.2 of
<xref target="RFC7540"/>.</t>
      </section>
      <section anchor="proposals-1">
        <name>Proposals</name>
        <t>Commit messages do not have an extension field because the set of proposals is
extensible.  As discussed in <xref target="commit"/>, Proposals with a non-default proposal
type MUST NOT be included in a commit unless the proposal type is supported by
all the members of the group that will process the Commit.</t>
      </section>
      <section anchor="credential-extensibility">
        <name>Credential Extensibility</name>
        <t>In order to ensure that MLS provides meaningful authentication it is important
that each member is able to authenticate some identity information for each
other member.  Identity information is encoded in Credentials, so this property
is provided by ensuring that members use compatible credential types.</t>
        <t>The types of credential that may be used in a group is restricted to what all
members of the group support, as specified by the <tt>capabilities</tt> field of each
LeafNode in the ratchet tree. An application can introduce new credential types
by choosing an unallocated identifier from the registry in
<xref target="mls-credential-types"/> and indicating support for the credential type in
published LeafNodes, whether in Update proposals to existing groups or
KeyPackages that are added to new groups. Once all members in a group indicate
support for the credential type, members can start using LeafNodes with the new
credential. Application may enforce that certain credential types always remain
supported by adding a <tt>required_capabilities</tt> extension to the group's
GroupContext, which would prevent any member from being added to the group that
doesn't support them.</t>
        <t>In future extensions to MLS, it may be useful to allow a member to present more
than one credential.  For example, such credentials might present different
attributes attested by different authorities.  To be consistent with the general
principle stated at the beginning of this section, such an extension would need
to ensure that each member can authenticate some identity for each other member.
For each pair of members (Alice, Bob), Alice would need to present at least one
credential of a type that Bob supports.</t>
      </section>
      <section anchor="extensions">
        <name>Extensions</name>
        <t>This protocol includes a mechanism for negotiating extension parameters similar
to the one in TLS <xref target="RFC8446"/>.  In TLS, extension negotiation is one-to-one: The
client offers extensions in its ClientHello message, and the server expresses
its choices for the session with extensions in its ServerHello and
EncryptedExtensions messages.  In MLS, extensions appear in the following
places:</t>
        <ul spacing="normal">
          <li>In KeyPackages, to describe additional information related to the client</li>
          <li>In LeafNodes, to describe additional information about the client or its
participation in the group (once in the ratchet tree)</li>
          <li>In the GroupInfo, to tell new members of a group what parameters are
being used by the group, and to provide any additional details required to
join the group</li>
          <li>In the GroupContext object, to ensure that all members of the group have the
same view of the parameters in use</li>
        </ul>
        <t>In other words, an application can use GroupContext extensions to ensure that
all members of the group agree on a set of parameters. Clients indicate their
support for parameters in the <tt>capabilities</tt> field of their LeafNode. New
members of a group are informed of the group's GroupContext extensions via the
<tt>extensions</tt> field in the <tt>group_context</tt> field of the GroupInfo object. The
<tt>extensions</tt> field in a GroupInfo object (outside of the <tt>group_context</tt> field)
can be used to provide additional parameters to new joiners that are used to
join the group.</t>
        <t>This extension mechanism is designed to allow for the secure and forward-compatible
negotiation of extensions.  For this to work, implementations MUST correctly
handle extensible fields:</t>
        <ul spacing="normal">
          <li>A client that posts a KeyPackage MUST support all parameters advertised in
it.  Otherwise, another client might fail to interoperate by selecting one of
those parameters.</li>
          <li>A client initiating a group MUST ignore all unrecognized ciphersuites,
extensions, and other parameters.  Otherwise, it may fail to interoperate with
newer clients.</li>
          <li>Any field containing a list of extensions MUST NOT have more than one extension of any given type.</li>
          <li>A client adding a new member to a group MUST verify that the LeafNode for the
new member is compatible with the group's extensions.  The <tt>capabilities</tt>
field MUST indicate support for each extension in the GroupContext.</li>
          <li>If any extension in a GroupInfo message is unrecognized (i.e., not contained
in the <tt>capabilities</tt> of the corresponding KeyPackage), then the client MUST
reject the Welcome message and not join the group.</li>
        </ul>
        <t>Note that the latter two requirements mean that all MLS extensions are
mandatory, in the sense that an extension in use by the group MUST be supported
by all members of the group.</t>
        <t>The parameters of a group may be changed by sending a GroupContextExtensions
proposal to enable additional extensions, or by reinitializing the group as
described in <xref target="reinitialization"/>.</t>
      </section>
    </section>
    <section anchor="sequencing">
      <name>Sequencing of State Changes</name>
      <t>Each Commit message is premised on a given starting state,
indicated by the <tt>epoch</tt> field of the enclosing FramedContent.
If the changes implied by a Commit message are made
starting from a different state, the results will be incorrect.</t>
      <t>This need for sequencing is not a problem as long as each time a
group member sends a Commit message, it is based on the most
current state of the group.  In practice, however, there is a risk
that two members will generate Commit messages simultaneously
based on the same state.</t>
      <t>Applications MUST have an established way to resolve conflicting Commit messages
for the same epoch. They can do this either by preventing conflicting messages
from occurring in the first place, or by developing rules for deciding which
Commit out of several sent in an epoch will be canonical. The approach chosen
MUST minimize the amount of time that forked or previous group states are kept
in memory, and promptly delete them once they're no longer necessary to ensure
forward secrecy.</t>
      <t>The generation of Commit messages MUST NOT modify a client's state, since the
client doesn't know at that time whether the changes implied by the Commit
message will conflict with another Commit or not. Similarly, the Welcome
message corresponding to a Commit MUST NOT be delivered to a new
joiner until it's clear that the Commit has been accepted.</t>
      <t>Regardless of how messages are kept in sequence, there is a risk that
in a sufficiently busy group, a given member may never
be able to send a Commit message because they always lose to other
members. The degree to which this is a practical problem will depend
on the dynamics of the application.</t>
    </section>
    <section anchor="application-messages">
      <name>Application Messages</name>
      <t>The primary purpose of handshake messages are to provide an authenticated group
key exchange to clients. In order to protect application messages sent among the
members of a group, the <tt>encryption_secret</tt> provided by the key schedule is used
to derive a sequence of nonces and keys for message encryption. Every epoch
moves the key schedule forward which triggers the creation of a new secret
tree, as described in <xref target="secret-tree"/>, along with a new set of symmetric
ratchets of nonces and keys for each member.</t>
      <t>Each client maintains their own local copy of the key
schedule for each epoch during which they are a group member. They
derive new keys, nonces, and secrets as needed while deleting old
ones as soon as they have been used.</t>
      <t>The group identifier and epoch allow a recipient to know which group secrets
should be used and from which <tt>epoch_secret</tt> to start computing other secrets.
The sender identifier and content type is used to identify which
symmetric ratchet to use from the secret tree. The
<tt>generation</tt> counter determines how far into the ratchet to iterate in
order to produce the required nonce and key for encryption or decryption.</t>
      <section anchor="padding">
        <name>Padding</name>
        <t>Application messages MAY be padded to provide some resistance
against traffic analysis techniques over encrypted traffic
<xref target="CLINIC"/>
          <xref target="HCJ16"/>.
While MLS might deliver the same payload less frequently across
a lot of ciphertexts than traditional web servers, it might still provide
the attacker enough information to mount an attack. If Alice asks Bob
"When are we going to the movie?", then the answer "Wednesday" could be leaked
to an adversary solely by the ciphertext length.</t>
        <t>The length of the <tt>padding</tt> field in <tt>PrivateContentTBE</tt> can be
chosen by the sender at the time of message encryption. Senders may use padding
to reduce the ability of attackers outside the group to infer the size of the
encrypted content.  Note, however, that the transports used to carry MLS
messages may have maximum message sizes, so padding schemes SHOULD avoid
increasing message size beyond any such limits that exist in a given
deployment scenario.</t>
      </section>
      <section anchor="restrictions">
        <name>Restrictions</name>
        <t>During each epoch, senders MUST NOT encrypt more data than permitted by the
security bounds of the AEAD scheme used <xref target="I-D.irtf-cfrg-aead-limits"/>.</t>
        <t>Note that each change to the group through a handshake message will also set a
new <tt>encryption_secret</tt>. Hence this change MUST be applied before encrypting
any new application message. This is required both to ensure that any users
removed from the group can no longer receive messages and to (potentially)
recover confidentiality and authenticity for future messages despite a past
state compromise.</t>
      </section>
      <section anchor="delayed-and-reordered-application-messages">
        <name>Delayed and Reordered Application messages</name>
        <t>Since each application message contains the group identifier, the epoch, and a
generation counter, a client can receive messages out of order. When messages
are received out of order, the client moves the sender ratchet forward to match
the received generation counter. Any unused nonce and key pairs from the ratchet
are potentially stored so that they can be used to decrypt the messages which
were delayed or reordered.</t>
        <t>Applications SHOULD define a policy on how long to keep unused nonce and key
pairs for a sender, and the maximum number to keep. This is in addition to
ensuring that these secrets are deleted according to the deletion schedule
defined in <xref target="deletion-schedule"/>. Applications SHOULD also define a policy
limiting the maximum number of steps that clients will move the ratchet forward
in response to a new message.  Messages received with a generation counter
that's too much higher than the last message received would then be rejected.
This avoids causing a denial-of-service attack by requiring the recipient to
perform an excessive number of key derivations. For example, a malicious group
member could send a message with <tt>generation = 0xffffffff</tt> at the beginning of a
new epoch, forcing recipients to perform billions of key derivations unless they
apply limits of the type discussed above.</t>
      </section>
    </section>
    <section anchor="security-considerations">
      <name>Security Considerations</name>
      <t>The security goals of MLS are described in <xref target="I-D.ietf-mls-architecture"/>.
We describe here how the protocol achieves its goals at a high level,
though a complete security analysis is outside of the scope of this
document.  The Security Considerations section of <xref target="I-D.ietf-mls-architecture"/>
provides some citations to detailed security analyses.</t>
      <section anchor="confidentiality-of-the-group-secrets">
        <name>Confidentiality of the Group Secrets</name>
        <t>Group secrets are partly derived from the output of a ratchet tree. Ratchet
trees work by assigning each member of the group to a leaf in the tree and
maintaining the following property: the private key of a node in the tree is
known only to members of the group that are assigned a leaf in the node's
subtree. This is called the <em>ratchet tree invariant</em> and it makes it possible to
encrypt to all group members except one, with a number of ciphertexts that is
logarithmic in the number of group members.</t>
        <t>The ability to efficiently encrypt to all members except one allows members to
be securely removed from a group. It also allows a member to rotate their
keypair such that the old private key can no longer be used to decrypt new
messages.</t>
      </section>
      <section anchor="confidentiality-of-sender-data">
        <name>Confidentiality of Sender Data</name>
        <t>The MLSCiphertext framing encrypts "sender data" that identifies which group
member sent an encrypted message, as described in <xref target="sender-data-encryption"/>.
As with the QUIC header protection scheme <xref section="5.4" sectionFormat="comma" target="RFC9001"/>, this scheme
is a variant of the HN1 construction analyzed in <xref target="NAN"/>.  A sample of the
ciphertext is combined with a <tt>sender_data_secret</tt> to derive a key and nonce
that are used for AEAD encryption of the sender data.</t>
        <t><tt>pseudocode
(key, nonce) = PRF(sender_data_secret, sample)
encrypted_sender_data =
  AEAD.Seal(key, nonce, sender_data_aad, sender_data)
</tt></t>
        <t>The only differences between this construction and HN1 as described in <xref target="NAN"/> are
(1) that it uses authenticated encryption instead of unauthenticated encryption
and (2) that it protects information used to derive a nonce instead of the nonce
itself.</t>
        <t>Since the <tt>sender_data_secret</tt> is distinct from the content encryption key, it
follows that the sender data encryption scheme achieves AE2 security as defined
in <xref target="NAN"/>, and therefore guarantees the confidentiality of the sender data.</t>
        <t>Use of the same <tt>sender_data_secret</tt> and ciphertext sample more than once risks
compromising sender data protection by reusing an AEAD (key, nonce) pair.  For
example, in many AEAD schemes, reusing a key and nonce reveals the exclusive OR
of the two plaintexts. Assuming the ciphertext output of the AEAD algorithm is
indistinguishable from random data (i.e., the AEAD is AE1-secure in the phrasing
of <xref target="NAN"/>), the odds of two ciphertext samples being identical is roughly
2<sup>-L/2</sup>, i.e., the birthday bound.</t>
        <t>The AEAD algorithms for ciphersuites defined in this document all provide this
property. The size of the sample depends on the ciphersuite's hash function, but
in all cases, the probability of collision is no more than 2<sup>-128</sup>.
Any future ciphersuite MUST use an AE1-secure AEAD algorithm.</t>
      </section>
      <section anchor="confidentiality-of-group-metadata">
        <name>Confidentiality of Group Metadata</name>
        <t>MLS does not provide confidentiality protection to some messages and fields
within messages:</t>
        <ul spacing="normal">
          <li>KeyPackage messages</li>
          <li>GroupInfo messages</li>
          <li>The unencrypted portion of a Welcome message</li>
          <li>Any Proposal or Commit messages sent as PublicMessage messages</li>
          <li>The unencrypted header fields in PrivateMessage messages</li>
          <li>The lengths of encrypted Welcome and PrivateMessage messages</li>
        </ul>
        <t>The only mechanism MLS provides for confidentially distributing a group's
ratchet tree to new members is to send it in a Welcome message as a
<tt>ratchet_tree</tt> extension.  If an application distributes the tree in some other
way, its security will depend on that application mechanism.</t>
        <t>A party observing these fields might be able to infer certain properties of the
group:</t>
        <ul spacing="normal">
          <li>Group ID</li>
          <li>Current epoch and frequency of epoch changes</li>
          <li>Frequency of messages within an epoch</li>
          <li>Group extensions</li>
          <li>Group membership</li>
        </ul>
        <t>The amount of metadata exposed to parties outside the group, and thus the
ability of these parties to infer the group's properties, depends on several
aspects of the DS design, such as:</t>
        <ul spacing="normal">
          <li>How KeyPackages are distributed</li>
          <li>How the ratchet tree is distributed</li>
          <li>How prospective external joiners get a GroupInfo object for the group</li>
          <li>Whether Proposal and Commit messages are sent as PublicMessage or PrivateMessage</li>
        </ul>
        <t>In the remainder of this section, we note the ways that the above properties of
the group are reflected in unprotected group messages, as a guide to
understanding how they might be exposed or protected in a given application.</t>
        <section anchor="groupid-epoch-and-message-frequency">
          <name>GroupID, Epoch, and Message Frequency</name>
          <t>MLS provides no mechanism to protect the group ID and epoch of a message from
the DS, so the group ID and the frequency of messages and epoch changes are not
protected against inspection by the DS.</t>
        </section>
        <section anchor="group-extensions">
          <name>Group Extensions</name>
          <t>A group's extensions are first set by the group's creator and then updated by
GroupContextExtensions proposals.  A GroupContextExtension proposal sent as
a PublicMessage leaks the groups' extensions.</t>
          <t>A new member learns the group's extensions via a GroupInfo object.  When the new
member joins via a Welcome message, the Welcome message's encryption protects
the GroupInfo message.  When the new member joins via an external join, they
must be provided with a GroupInfo object.  Protection of this GroupInfo object
is up to the application -- if it is transmitted over a channel that is not
confidential to the group and the new joiner, then it will leak the group's
extensions.</t>
        </section>
        <section anchor="group-membership">
          <name>Group Membership</name>
          <t>The group's membership is represented directly by its ratchet tree, since each
member's LeafNode contains members' cryptographic keys, a credential that
contains information about the member's identity, and possibly other
identifiers.  Applications that expose the group's ratchet tree outside the
group also leak the group's membership.</t>
          <t>Changes to the group's membership are made by means of Add and Remove proposals.
If these proposals are sent as PublicMessage, then information will be leaked
about the corresponding changes to the group's membership.  A party that sees
all of these changes can reconstruct the group membership.</t>
          <t>Welcome messages contain a hash of each KeyPackage for which the Welcome message
is encrypted.  If a party has access to a pool of KeyPackages and observes a
Welcome message, then they can identify the KeyPackage representing the new
member.  If the party can also associate the Welcome with a group, then the
party can infer that the identified new member was added to that group.</t>
          <t>Note that these information leaks reveal the group's membership only to the degree
that that membership is revealed by the contents of a member's LeafNode in the
ratchet tree.  In some cases, this may be quite direct, e.g., due to credentials
attesting to identifiers such as email addresses.  An application could
construct a member's leaf node to be less identifying, e.g., by using a
pseudonymous credential and frequently rotating encryption and signature keys.</t>
        </section>
      </section>
      <section anchor="authentication">
        <name>Authentication</name>
        <t>The first form of authentication we provide is that group members can verify a
message originated from one of the members of the group. For encrypted messages,
this is guaranteed because messages are encrypted with an AEAD under a key
derived from the group secrets. For plaintext messages, this is guaranteed by
the use of a <tt>membership_tag</tt> which constitutes a MAC over the message, under a
key derived from the group secrets.</t>
        <t>The second form of authentication is that group members can verify a message
originated from a particular member of the group. This is guaranteed by a
digital signature on each message from the sender's signature key.</t>
        <t>The signature keys held by group members are critical to the security of MLS
against active attacks.  If a member's signature key is compromised, then an
attacker can create LeafNodes and KeyPackages impersonating the member; depending on the
application, this can then allow the attacker to join the group with the
compromised member's identity.  For example, if a group has enabled external
parties to join via external commits, then an attacker that has compromised a
member's signature key could use an external commit to insert themselves into
the group -- even using a "resync"-style external commit to replace the
compromised member in the group.</t>
        <t>Applications can mitigate the risks of signature key compromise using pre-shared
keys.  If a group requires joiners to know a PSK in addition to authenticating
with a credential, then in order to mount an impersonation attack, the attacker
would need to compromise the relevant PSK as well as the victim's signature key.
The cost of this mitigation is that the application needs some external
arrangement that ensures that the legitimate members of the group have the
required PSKs.</t>
      </section>
      <section anchor="forward-secrecy-and-post-compromise-security">
        <name>Forward Secrecy and Post-Compromise Security</name>
        <t>Forward secrecy and post-compromise security are important security notions for
long-lived MLS groups.  Forward secrecy means that messages sent at a certain
point in time are secure in the face of later compromise of a group member.
Post-compromise security means that messages are secure even if a group member
was compromised at some point in the past.</t>
        <artset>
          <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="176" width="448" viewBox="0 0 448 176" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
              <path d="M 152,80 L 152,160" fill="none" stroke="black"/>
              <path d="M 192,48 L 192,88" fill="none" stroke="black"/>
              <path d="M 232,80 L 232,160" fill="none" stroke="black"/>
              <path d="M 8,96 L 144,96" fill="none" stroke="black"/>
              <path d="M 160,96 L 224,96" fill="none" stroke="black"/>
              <path d="M 240,96 L 440,96" fill="none" stroke="black"/>
              <path d="M 8,128 L 144,128" fill="none" stroke="black"/>
              <path d="M 240,128 L 368,128" fill="none" stroke="black"/>
              <polygon class="arrowhead" points="448,96 436,90.4 436,101.6" fill="black" transform="rotate(0,440,96)"/>
              <polygon class="arrowhead" points="376,128 364,122.4 364,133.6" fill="black" transform="rotate(0,368,128)"/>
              <polygon class="arrowhead" points="200,88 188,82.4 188,93.6" fill="black" transform="rotate(90,192,88)"/>
              <polygon class="arrowhead" points="16,128 4,122.4 4,133.6" fill="black" transform="rotate(180,8,128)"/>
              <g class="text">
                <text x="196" y="36">Compromise</text>
                <text x="420" y="116">Time</text>
                <text x="48" y="148">Forward</text>
                <text x="112" y="148">Secrecy</text>
                <text x="304" y="148">Post-Compromise</text>
                <text x="292" y="164">Security</text>
              </g>
            </svg>
          </artwork>
          <artwork type="ascii-art"><![CDATA[
                   Compromise
                       |
                       |
                  |    V    |
------------------|---------|------------------------->
                  |         |                     Time
<-----------------|         |---------------->
  Forward Secrecy |         | Post-Compromise
                  |         |   Security
]]></artwork>
        </artset>
        <t>Post-compromise security is provided between epochs by members regularly
updating their leaf key in the ratchet tree. Updating their leaf key prevents
group secrets from continuing to be encrypted to public keys whose private keys
had previously been compromised.</t>
        <t>Forward secrecy between epochs is provided by deleting private keys from past
versions of the ratchet tree, as this prevents old group secrets from being
re-derived. Forward secrecy <em>within</em> an epoch is provided by deleting message
encryption keys once they've been used to encrypt or decrypt a message.</t>
        <t>New groups are also at risk of using previously compromised keys (as with
post-compromise security), if a member is added to a new group via an old
KeyPackage whose corresponding private key has been compromised.  This risk can
be mitigated by having clients regularly generate new KeyPackages and upload
them to the Delivery Service.  This way, the key material used to add a member
to a new group is more likely to be fresh and less likely to be compromised.</t>
      </section>
      <section anchor="keypackage-reuse">
        <name>KeyPackage Reuse</name>
        <t>KeyPackages are intended to be used only once.  That is, once a KeyPackage
has been used to introduce the corresponding client to a group, it SHOULD be
deleted from the KeyPackage publication system.  Reuse of KeyPackages can lead
to replay attacks.</t>
        <t>An application MAY allow for reuse of a "last resort" KeyPackage in order to
prevent denial-of-service attacks.  Since a KeyPackage is needed to add a
client to a new group, an attacker could prevent a client being added to new
groups by exhausting all available KeyPackages. To prevent such a denial-of-service
attack, the KeyPackage publication system SHOULD rate-limit KeyPackage
requests, especially if not authenticated.</t>
      </section>
      <section anchor="group-fragmentation-by-malicious-insiders">
        <name>Group Fragmentation by Malicious Insiders</name>
        <t>It is possible for a malicious member of a group to "fragment" the group by
crafting an invalid UpdatePath.  Recall that an UpdatePath encrypts a sequence
of path secrets to different subtrees of the group's ratchet trees.  These path
secrets should be derived in a sequence as described in
<xref target="ratchet-tree-evolution"/>, but the UpdatePath syntax allows the sender to
encrypt arbitrary, unrelated secrets.  The syntax also does not guarantee that
the encrypted path secret for a given node corresponds to the public
key provided for that node.</t>
        <t>Both of these types of corruption will cause processing of a Commit to fail for
some members of the group.  If the public key for a node does not match the path
secret, then the members that decrypt that path secret will reject the commit
based on this mismatch.  If the path secret sequence is incorrect at some point,
then members that can decrypt nodes before that point will compute a different
public key for the mismatched node than the one in the UpdatePath, which also
causes the Commit to fail.  Applications SHOULD provide mechanisms for failed
commits to be reported, so that group members who were not able to recognize the
error themselves can reinitialize the group if necessary.</t>
        <t>Even with such an error reporting mechanism in place, however, it is still
possible for members to get locked out of the group by a malformed commit.
Since malformed Commits can only be recognized by certain members of the group,
in an asynchronous application, it may be the case that all members that could
detect a fault in a Commit are offline.  In such a case, the Commit will be
accepted by the group, and the resulting state possibly used as the basis for
further Commits.  When the affected members come back online, they will reject
the first commit, and thus be unable to catch up with the group. These members
will either need to add themselves back with an external Commit, or reinitialize
the group from scratch.</t>
        <t>Applications can address this risk by requiring certain members of the group to
acknowledge successful processing of a Commit before the group regards the
Commit as accepted.  The minimum set of acknowledgements necessary to verify
that a Commit is well-formed comprises an acknowledgement from one member per
node in the UpdatePath, that is, one member from each subtree rooted in the
copath node corresponding to the node in the UpdatePath.</t>
      </section>
    </section>
    <section anchor="iana-considerations">
      <name>IANA Considerations</name>
      <t>This document requests the creation of the following new IANA registries:</t>
      <ul spacing="normal">
        <li>MLS Ciphersuites (<xref target="mls-ciphersuites"/>)</li>
        <li>MLS Wire Formats (<xref target="mls-wire-formats"/>)</li>
        <li>MLS Extension Types (<xref target="mls-extension-types"/>)</li>
        <li>MLS Proposal Types (<xref target="mls-proposal-types"/>)</li>
        <li>MLS Credential Types (<xref target="mls-credential-types"/>)</li>
        <li>MLS Signature Labels (<xref target="mls-signature-labels"/>)</li>
        <li>MLS Public Key Encryption Labels (<xref target="mls-public-key-encryption-labels"/>)</li>
        <li>MLS Exporter Labels (<xref target="mls-exporter-labels"/>)</li>
      </ul>
      <t>All of these registries should be under a heading of "Messaging Layer Security",
and assignments are made via the Specification Required policy <xref target="RFC8126"/>. See
<xref target="de"/> for additional information about the MLS Designated Experts (DEs).</t>
      <t>RFC EDITOR: Please replace XXXX throughout with the RFC number assigned to
this document</t>
      <section anchor="mls-ciphersuites">
        <name>MLS Ciphersuites</name>
        <t>A ciphersuite is a combination of a protocol version and the set of
cryptographic algorithms that should be used.</t>
        <t>Ciphersuite names follow the naming convention:</t>
        <sourcecode type="pseudocode"><![CDATA[
CipherSuite MLS_LVL_KEM_AEAD_HASH_SIG = VALUE;
]]></sourcecode>
        <t>Where VALUE is represented as a sixteen-bit integer:</t>
        <sourcecode type="tls"><![CDATA[
uint16 CipherSuite;
]]></sourcecode>
        <table>
          <thead>
            <tr>
              <th align="left">Component</th>
              <th align="left">Contents</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">LVL</td>
              <td align="left">The security level (in bits)</td>
            </tr>
            <tr>
              <td align="left">KEM</td>
              <td align="left">The KEM algorithm used for HPKE in ratchet tree operations</td>
            </tr>
            <tr>
              <td align="left">AEAD</td>
              <td align="left">The AEAD algorithm used for HPKE and message protection</td>
            </tr>
            <tr>
              <td align="left">HASH</td>
              <td align="left">The hash algorithm used for HPKE and the MLS transcript hash</td>
            </tr>
            <tr>
              <td align="left">SIG</td>
              <td align="left">The Signature algorithm used for message authentication</td>
            </tr>
          </tbody>
        </table>
        <t>The columns in the registry are as follows:</t>
        <ul spacing="normal">
          <li>Value: The numeric value of the ciphersuite</li>
          <li>Name: The name of the ciphersuite</li>
        </ul>
        <t>[[ RFC EDITOR: This section should be the same as the corresponding text in
draft-ietf-tls-rfc8447bis.  Please align the two documents if they have diverged
in the approval process. ]]</t>
        <ul spacing="normal">
          <li>
            <t>Recommended: Whether support for this ciphersuite is recommended by the IETF
MLS WG.  Valid values are "Y", "N", and "D", as described below.  The default
value of the "Recommended" column is "N".  Setting the Recommended item to "Y"
or "D", or changing a item whose current value is "Y" or "D", requires
Standards Action <xref target="RFC8126"/>.  </t>
            <ul spacing="normal">
              <li>Y: Indicates that the IETF has consensus that the item is RECOMMENDED. This
only means that the associated mechanism is fit for the purpose for which it
was defined. Careful reading of the documentation for the mechanism is
necessary to understand the applicability of that mechanism. The IETF could
recommend mechanisms that have limited applicability, but will provide
applicability statements that describe any limitations of the mechanism or
necessary constraints on its use.</li>
              <li>N: Indicates that the item has not been evaluated by the IETF and that the
IETF has made no statement about the suitability of the associated
mechanism. This does not necessarily mean that the mechanism is flawed, only
that no consensus exists. The IETF might have consensus to leave an items
marked as "N" on the basis of it having limited applicability or usage
constraints.</li>
              <li>D: Indicates that the item is discouraged and SHOULD NOT or MUST NOT be
used. This marking could be used to identify mechanisms that might result in
problems if they are used, such as a weak cryptographic algorithm or a
mechanism that might cause interoperability problems in deployment.</li>
            </ul>
          </li>
          <li>Reference: The document where this ciphersuite is defined</li>
        </ul>
        <t>Initial contents:</t>
        <table>
          <thead>
            <tr>
              <th align="left">Value</th>
              <th align="left">Name</th>
              <th align="left">R</th>
              <th align="left">Ref</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">0x0000</td>
              <td align="left">RESERVED</td>
              <td align="left">-</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0001</td>
              <td align="left">MLS_128_DHKEMX25519_AES128GCM_SHA256_Ed25519</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0002</td>
              <td align="left">MLS_128_DHKEMP256_AES128GCM_SHA256_P256</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0003</td>
              <td align="left">MLS_128_DHKEMX25519_CHACHA20POLY1305_SHA256_Ed25519</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0004</td>
              <td align="left">MLS_256_DHKEMX448_AES256GCM_SHA512_Ed448</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0005</td>
              <td align="left">MLS_256_DHKEMP521_AES256GCM_SHA512_P521</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0006</td>
              <td align="left">MLS_256_DHKEMX448_CHACHA20POLY1305_SHA512_Ed448</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0007</td>
              <td align="left">MLS_256_DHKEMP384_AES256GCM_SHA384_P384.</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0xf000 - 0xffff</td>
              <td align="left">Reserved for Private Use</td>
              <td align="left">-</td>
              <td align="left">RFC XXXX</td>
            </tr>
          </tbody>
        </table>
        <t>All of these ciphersuites use HMAC <xref target="RFC2104"/> as their MAC function, with
different hashes per ciphersuite.  The mapping of ciphersuites to HPKE
primitives, HMAC hash functions, and TLS signature schemes is as follows
<xref target="RFC9180"/> <xref target="RFC8446"/>:</t>
        <table>
          <thead>
            <tr>
              <th align="left">Value</th>
              <th align="left">KEM</th>
              <th align="left">KDF</th>
              <th align="left">AEAD</th>
              <th align="left">Hash</th>
              <th align="left">Signature</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">0x0001</td>
              <td align="left">0x0020</td>
              <td align="left">0x0001</td>
              <td align="left">0x0001</td>
              <td align="left">SHA256</td>
              <td align="left">ed25519</td>
            </tr>
            <tr>
              <td align="left">0x0002</td>
              <td align="left">0x0010</td>
              <td align="left">0x0001</td>
              <td align="left">0x0001</td>
              <td align="left">SHA256</td>
              <td align="left">ecdsa_secp256r1_sha256</td>
            </tr>
            <tr>
              <td align="left">0x0003</td>
              <td align="left">0x0020</td>
              <td align="left">0x0001</td>
              <td align="left">0x0003</td>
              <td align="left">SHA256</td>
              <td align="left">ed25519</td>
            </tr>
            <tr>
              <td align="left">0x0004</td>
              <td align="left">0x0021</td>
              <td align="left">0x0003</td>
              <td align="left">0x0002</td>
              <td align="left">SHA512</td>
              <td align="left">ed448</td>
            </tr>
            <tr>
              <td align="left">0x0005</td>
              <td align="left">0x0012</td>
              <td align="left">0x0003</td>
              <td align="left">0x0002</td>
              <td align="left">SHA512</td>
              <td align="left">ecdsa_secp521r1_sha512</td>
            </tr>
            <tr>
              <td align="left">0x0006</td>
              <td align="left">0x0021</td>
              <td align="left">0x0003</td>
              <td align="left">0x0003</td>
              <td align="left">SHA512</td>
              <td align="left">ed448</td>
            </tr>
            <tr>
              <td align="left">0x0007</td>
              <td align="left">0x0011</td>
              <td align="left">0x0002</td>
              <td align="left">0x0002</td>
              <td align="left">SHA384</td>
              <td align="left">ecdsa_secp384r1_sha384</td>
            </tr>
          </tbody>
        </table>
        <t>The hash used for the MLS transcript hash is the one referenced in the
ciphersuite name.  In the ciphersuites defined above, "SHA256", "SHA384", and "SHA512"
refer to the SHA-256, SHA-384, and SHA-512 functions defined in <xref target="SHS"/>.</t>
        <t>In addition to the general requirements of <xref target="additional-ciphersuites"/>, future
ciphersuites MUST meet the requirements of <xref target="confidentiality-of-sender-data"/>.</t>
        <t>It is advisable to keep the number of ciphersuites low to increase the chances
clients can interoperate in a federated environment, therefore the ciphersuites
only include modern, yet well-established algorithms.  Depending on their
requirements, clients can choose between two security levels (roughly 128-bit
and 256-bit). Within the security levels clients can choose between faster
X25519/X448 curves and FIPS 140-2 compliant curves for Diffie-Hellman key
negotiations. Clients may also choose ChaCha20Poly1305 or AES-GCM, e.g., for
performance reasons. Since ChaCha20Poly1305 is not listed by FIPS 140-2 it is
not paired with FIPS 140-2 compliant curves. The security level of symmetric
encryption algorithms and hash functions is paired with the security level of
the curves.</t>
        <t>The mandatory-to-implement ciphersuite for MLS 1.0 is
<tt>MLS_128_DHKEMX25519_AES128GCM_SHA256_Ed25519</tt> which uses
Curve25519 for key exchange, AES-128-GCM for HPKE, HKDF over SHA2-256, and
Ed25519 for signatures.</t>
        <t>New ciphersuite values are assigned by IANA as described in
<xref target="iana-considerations"/>.</t>
      </section>
      <section anchor="mls-wire-formats">
        <name>MLS Wire Formats</name>
        <t>This registry lists identifiers for the types of messages that can be sent in
MLS.  The wire format field is two bytes wide, so the valid wire format values
are in the range 0x0000 to 0xffff.</t>
        <t>Template:</t>
        <ul spacing="normal">
          <li>Value: The numeric value of the wire format</li>
          <li>Name: The name of the wire format</li>
          <li>Recommended: Same as in <xref target="mls-ciphersuites"/></li>
          <li>Reference: The document where this wire format is defined</li>
        </ul>
        <t>Initial contents:</t>
        <table>
          <thead>
            <tr>
              <th align="left">Value</th>
              <th align="left">Name</th>
              <th align="left">Recommended</th>
              <th align="left">Reference</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">0x0000</td>
              <td align="left">RESERVED</td>
              <td align="left">N/A</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0001</td>
              <td align="left">mls_plaintext</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0002</td>
              <td align="left">mls_ciphertext</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0003</td>
              <td align="left">mls_welcome</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0004</td>
              <td align="left">mls_group_info</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0005</td>
              <td align="left">mls_key_package</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0xf000  - 0xffff</td>
              <td align="left">Reserved for Private Use</td>
              <td align="left">N/A</td>
              <td align="left">RFC XXXX</td>
            </tr>
          </tbody>
        </table>
      </section>
      <section anchor="mls-extension-types">
        <name>MLS Extension Types</name>
        <t>This registry lists identifiers for extensions to the MLS protocol.  The
extension type field is two bytes wide, so valid extension type values are in
the range 0x0000 to 0xffff.</t>
        <t>Template:</t>
        <ul spacing="normal">
          <li>Value: The numeric value of the extension type</li>
          <li>Name: The name of the extension type</li>
          <li>
            <t>Message(s): The messages in which the extension may appear, drawn from the following
list:  </t>
            <ul spacing="normal">
              <li>KP: KeyPackage objects</li>
              <li>LN: LeafNode objects</li>
              <li>GC: GroupContext objects</li>
              <li>GI: GroupInfo objects</li>
            </ul>
          </li>
          <li>Recommended: Same as in <xref target="mls-ciphersuites"/></li>
          <li>Reference: The document where this extension is defined</li>
        </ul>
        <t>Initial contents:</t>
        <table>
          <thead>
            <tr>
              <th align="left">Value</th>
              <th align="left">Name</th>
              <th align="left">Message(s)</th>
              <th align="left">Recommended</th>
              <th align="left">Reference</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">0x0000</td>
              <td align="left">RESERVED</td>
              <td align="left">N/A</td>
              <td align="left">N/A</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0001</td>
              <td align="left">application_id</td>
              <td align="left">LN</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0002</td>
              <td align="left">ratchet_tree</td>
              <td align="left">GI</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0003</td>
              <td align="left">required_capabilities</td>
              <td align="left">GC</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0004</td>
              <td align="left">external_pub</td>
              <td align="left">GI</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0005</td>
              <td align="left">external_senders</td>
              <td align="left">GC</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0xf000  - 0xffff</td>
              <td align="left">Reserved for Private Use</td>
              <td align="left">N/A</td>
              <td align="left">N/A</td>
              <td align="left">RFC XXXX</td>
            </tr>
          </tbody>
        </table>
      </section>
      <section anchor="mls-proposal-types">
        <name>MLS Proposal Types</name>
        <t>This registry lists identifiers for types of proposals that can be made for
changes to an MLS group.  The extension type field is two bytes wide, so valid
extension type values are in the range 0x0000 to 0xffff.</t>
        <t>Template:</t>
        <ul spacing="normal">
          <li>Value: The numeric value of the proposal type</li>
          <li>Name: The name of the proposal type</li>
          <li>Recommended: Same as in <xref target="mls-ciphersuites"/></li>
          <li>Path Required: Whether a Commit covering a proposal of this type is required
to have its <tt>path</tt> field populated (see <xref target="commit"/>).</li>
          <li>Reference: The document where this extension is defined</li>
        </ul>
        <t>Initial contents:</t>
        <table>
          <thead>
            <tr>
              <th align="left">Value</th>
              <th align="left">Name</th>
              <th align="left">Recommended</th>
              <th align="left">Path Required</th>
              <th align="left">Reference</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">0x0000</td>
              <td align="left">RESERVED</td>
              <td align="left">N/A</td>
              <td align="left">N/A</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0001</td>
              <td align="left">add</td>
              <td align="left">Y</td>
              <td align="left">N</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0002</td>
              <td align="left">update</td>
              <td align="left">Y</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0003</td>
              <td align="left">remove</td>
              <td align="left">Y</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0004</td>
              <td align="left">psk</td>
              <td align="left">Y</td>
              <td align="left">N</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0005</td>
              <td align="left">reinit</td>
              <td align="left">Y</td>
              <td align="left">N</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0006</td>
              <td align="left">external_init</td>
              <td align="left">Y</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0007</td>
              <td align="left">group_context_extensions</td>
              <td align="left">Y</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0xf000  - 0xffff</td>
              <td align="left">Reserved for Private Use</td>
              <td align="left">N/A</td>
              <td align="left">N/A</td>
              <td align="left">RFC XXXX</td>
            </tr>
          </tbody>
        </table>
      </section>
      <section anchor="mls-credential-types">
        <name>MLS Credential Types</name>
        <t>This registry lists identifiers for types of credentials that can be used for
authentication in the MLS protocol.  The credential type field is two bytes wide,
so valid credential type values are in the range 0x0000 to 0xffff.</t>
        <t>Template:</t>
        <ul spacing="normal">
          <li>Value: The numeric value of the credential type</li>
          <li>Name: The name of the credential type</li>
          <li>Recommended: Same as in <xref target="mls-ciphersuites"/></li>
          <li>Reference: The document where this credential is defined</li>
        </ul>
        <t>Initial contents:</t>
        <table>
          <thead>
            <tr>
              <th align="left">Value</th>
              <th align="left">Name</th>
              <th align="left">Recommended</th>
              <th align="left">Reference</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">0x0000</td>
              <td align="left">RESERVED</td>
              <td align="left">N/A</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0001</td>
              <td align="left">basic</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0x0002</td>
              <td align="left">x509</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">0xf000  - 0xffff</td>
              <td align="left">Reserved for Private Use</td>
              <td align="left">N/A</td>
              <td align="left">RFC XXXX</td>
            </tr>
          </tbody>
        </table>
      </section>
      <section anchor="mls-signature-labels">
        <name>MLS Signature Labels</name>
        <t>The <tt>SignWithLabel</tt> function defined in <xref target="signing"/> avoids the risk of
confusion between signatures in different contexts.  Each context is assigned a
distinct label that is incorporated into the signature.  This registry records
the labels defined in this document, and allows additional labels to be
registered in case extensions add other types of signature using the same
signature keys used elsewhere in MLS.</t>
        <t>Template:</t>
        <ul spacing="normal">
          <li>Label: The string to be used as the <tt>Label</tt> parameter to <tt>SignWithLabel</tt></li>
          <li>Recommended: Same as in <xref target="mls-ciphersuites"/></li>
          <li>Reference: The document where this credential is defined</li>
        </ul>
        <t>Initial contents:</t>
        <table>
          <thead>
            <tr>
              <th align="left">Label</th>
              <th align="left">Recommended</th>
              <th align="left">Reference</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">"FramedContentTBS"</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">"LeafNodeTBS"</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">"KeyPackageTBS"</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">"GroupInfoTBS"</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
          </tbody>
        </table>
      </section>
      <section anchor="mls-public-key-encryption-labels">
        <name>MLS Public Key Encryption Labels</name>
        <t>The <tt>EncryptWithLabel</tt> function defined in <xref target="public-key-encryption"/> avoids the
risk of confusion between ciphertexts produced for different purposes in
different contexts.  Each context is assigned a distinct label that is
incorporated into the signature.  This registry records the labels defined in
this document, and allows additional labels to be registered in case extensions
add other types of public-key encryption using the same HPKE keys used elsewhere
in MLS.</t>
        <t>Template:</t>
        <ul spacing="normal">
          <li>Label: The string to be used as the <tt>Label</tt> parameter to <tt>EncryptWithLabel</tt></li>
          <li>Recommended: Same as in <xref target="mls-ciphersuites"/></li>
          <li>Reference: The document where this credential is defined</li>
        </ul>
        <t>Initial contents:</t>
        <table>
          <thead>
            <tr>
              <th align="left">Label</th>
              <th align="left">Recommended</th>
              <th align="left">Reference</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">"UpdatePathNode"</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
            <tr>
              <td align="left">"Welcome"</td>
              <td align="left">Y</td>
              <td align="left">RFC XXXX</td>
            </tr>
          </tbody>
        </table>
      </section>
      <section anchor="mls-exporter-labels">
        <name>MLS Exporter Labels</name>
        <t>The exporter function defined in <xref target="exporters"/> allows applications to derive key
material from the MLS key schedule.  Like the TLS exporter <xref target="RFC8446"/>, the MLS
exporter uses a label to distinguish between different applications' use of the
exporter.  This registry allows applications to register their usage to avoid
collisions.</t>
        <t>Template:</t>
        <ul spacing="normal">
          <li>Label: The string to be used as the <tt>Label</tt> parameter to <tt>MLS-Exporter</tt></li>
          <li>Recommended: Same as in <xref target="mls-ciphersuites"/></li>
          <li>Reference: The document where this credential is defined</li>
        </ul>
        <t>The registry has no initial contents, since it is intended to be used by
applications, not the core protocol.  The table below is intended only to show
the column layout of the registry.</t>
        <table>
          <thead>
            <tr>
              <th align="left">Label</th>
              <th align="left">Recommended</th>
              <th align="left">Reference</th>
            </tr>
          </thead>
          <tbody>
            <tr>
              <td align="left">(N/A)</td>
              <td align="left">(N/A)</td>
              <td align="left">(N/A)</td>
            </tr>
          </tbody>
        </table>
      </section>
      <section anchor="de">
        <name>MLS Designated Expert Pool</name>
        <t>Specification Required <xref target="RFC8126"/> registry requests are registered
after a three-week review period on the MLS DEs' mailing list:
<eref target="mailto:mls-reg-review@ietf.org">mls-reg-review@ietf.org</eref>, on the advice of one or more of the MLS DEs. However,
to allow for the allocation of values prior to publication, the MLS
DEs may approve registration once they are satisfied that such a
specification will be published.</t>
        <t>Registration requests sent to the MLS DEs mailing list for review
SHOULD use an appropriate subject (e.g., "Request to register value
in MLS Bar registry").</t>
        <t>Within the review period, the MLS DEs will either approve or deny
the registration request, communicating this decision to the MLS DEs
mailing list and IANA. Denials SHOULD include an explanation and, if
applicable, suggestions as to how to make the request successful.
Registration requests that are undetermined for a period longer than
21 days can be brought to the IESG's attention for resolution using
the <eref target="mailto:iesg@ietf.org">iesg@ietf.org</eref> mailing list.</t>
        <t>Criteria that SHOULD be applied by the MLS DEs includes determining
whether the proposed registration duplicates existing functionality,
whether it is likely to be of general applicability or useful only
for a single application, and whether the registration description
is clear. For example, the MLS DEs will apply the ciphersuite-related
advisory found in <xref target="mls-ciphersuites"/>.</t>
        <t>IANA MUST only accept registry updates from the MLS DEs and SHOULD
direct all requests for registration to the MLS DEs' mailing list.</t>
        <t>It is suggested that multiple MLS DEs be appointed who are able to
represent the perspectives of different applications using this
specification, in order to enable broadly informed review of
registration decisions. In cases where a registration decision could
be perceived as creating a conflict of interest for a particular
MLS DE, that MLS DE SHOULD defer to the judgment of the other MLS DEs.</t>
      </section>
      <section anchor="the-messagemls-mime-type">
        <name>The "message/mls" MIME Type</name>
        <t>This document registers the "message/mls" MIME media type in order to allow other
protocols (e.g., HTTP <xref target="RFC7540"/>) to convey MLS messages.</t>
        <dl>
          <dt>Type name:</dt>
          <dd>
            <t>message</t>
          </dd>
          <dt>Subtype name:</dt>
          <dd>
            <t>mls</t>
          </dd>
          <dt>Required parameters:</dt>
          <dd>
            <t>none</t>
          </dd>
          <dt>Optional parameters:</dt>
          <dd>
            <dl>
              <dt>version</dt>
              <dd>
                <t/>
              </dd>
              <dt>  version:</dt>
              <dd>
                <t>The MLS protocol version expressed as a string
  <tt>&lt;major&gt;.&lt;minor&gt;</tt>.  If omitted the version is "1.0", which
  corresponds to MLS ProtocolVersion mls10. If for some reason
  the version number in the MIME type parameter differs from the
  ProtocolVersion embedded in the protocol, the protocol takes
  precedence.</t>
              </dd>
            </dl>
          </dd>
          <dt>Encoding considerations:</dt>
          <dd>
            <t>MLS messages are represented using the TLS
presentation language <xref target="RFC8446"/>. Therefore MLS messages need to be
treated as binary data.</t>
          </dd>
          <dt>Security considerations:</dt>
          <dd>
            <t>MLS is an encrypted messaging layer designed
to be transmitted over arbitrary lower layer protocols. The
security considerations in this document (RFC XXXX) also apply.</t>
          </dd>
          <dt>Interoperability considerations:</dt>
          <dd>
            <t>N/A</t>
          </dd>
          <dt>Published specification:</dt>
          <dd>
            <t>RFC XXXX</t>
          </dd>
          <dt>Applications that use this media type:</dt>
          <dd>
            <t>MLS-based messaging applications</t>
          </dd>
          <dt>Fragment identifier considerations:</dt>
          <dd>
            <t>N/A</t>
          </dd>
        </dl>
        <t>Additional information:</t>
        <ul spacing="normal">
          <li>Deprecated alias names for this type: N/A</li>
          <li>Magic number(s): N/A</li>
          <li>File extension(s): N/A</li>
          <li>Macintosh file type code(s): N/A</li>
        </ul>
        <dl>
          <dt>Person &amp; email address to contact for further information:</dt>
          <dd>
            <t>IETF MLS Working Group <eref target="mailto:mls@ietf.org">mls@ietf.org</eref></t>
          </dd>
          <dt>Intended usage:</dt>
          <dd>
            <t>COMMON</t>
          </dd>
          <dt>Restrictions on usage:</dt>
          <dd>
            <t>N/A</t>
          </dd>
          <dt>Author:</dt>
          <dd>
            <t>IETF MLS Working Group</t>
          </dd>
          <dt>Change controller:</dt>
          <dd>
            <t>IESG</t>
          </dd>
          <dt>Provisional registration? (standards tree only):</dt>
          <dd>
            <t>No</t>
          </dd>
        </dl>
      </section>
    </section>
  </middle>
  <back>
    <references>
      <name>References</name>
      <references>
        <name>Normative References</name>
        <reference anchor="RFC2119">
          <front>
            <title>Key words for use in RFCs to Indicate Requirement Levels</title>
            <author fullname="S. Bradner" initials="S." surname="Bradner">
              <organization/>
            </author>
            <date month="March" year="1997"/>
            <abstract>
              <t>In many standards track documents several words are used to signify the requirements in the specification.  These words are often capitalized. This document defines these words as they should be interpreted in IETF documents.  This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements.</t>
            </abstract>
          </front>
          <seriesInfo name="BCP" value="14"/>
          <seriesInfo name="RFC" value="2119"/>
          <seriesInfo name="DOI" value="10.17487/RFC2119"/>
        </reference>
        <reference anchor="RFC8174">
          <front>
            <title>Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words</title>
            <author fullname="B. Leiba" initials="B." surname="Leiba">
              <organization/>
            </author>
            <date month="May" year="2017"/>
            <abstract>
              <t>RFC 2119 specifies common key words that may be used in protocol  specifications.  This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the  defined special meanings.</t>
            </abstract>
          </front>
          <seriesInfo name="BCP" value="14"/>
          <seriesInfo name="RFC" value="8174"/>
          <seriesInfo name="DOI" value="10.17487/RFC8174"/>
        </reference>
        <reference anchor="RFC9180">
          <front>
            <title>Hybrid Public Key Encryption</title>
            <author fullname="R. Barnes" initials="R." surname="Barnes">
              <organization/>
            </author>
            <author fullname="K. Bhargavan" initials="K." surname="Bhargavan">
              <organization/>
            </author>
            <author fullname="B. Lipp" initials="B." surname="Lipp">
              <organization/>
            </author>
            <author fullname="C. Wood" initials="C." surname="Wood">
              <organization/>
            </author>
            <date month="February" year="2022"/>
            <abstract>
              <t>This document describes a scheme for hybrid public key encryption (HPKE). This scheme provides a variant of public key encryption of arbitrary-sized plaintexts for a recipient public key. It also includes three authenticated variants, including one that authenticates possession of a pre-shared key and two optional ones that authenticate possession of a key encapsulation mechanism (KEM) private key. HPKE works for any combination of an asymmetric KEM, key derivation function (KDF), and authenticated encryption with additional data (AEAD) encryption function. Some authenticated variants may not be supported by all KEMs. We provide instantiations of the scheme using widely used and efficient primitives, such as Elliptic Curve Diffie-Hellman (ECDH) key agreement, HMAC-based key derivation function (HKDF), and SHA2.</t>
              <t>This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF.</t>
            </abstract>
          </front>
          <seriesInfo name="RFC" value="9180"/>
          <seriesInfo name="DOI" value="10.17487/RFC9180"/>
        </reference>
        <reference anchor="RFC8446">
          <front>
            <title>The Transport Layer Security (TLS) Protocol Version 1.3</title>
            <author fullname="E. Rescorla" initials="E." surname="Rescorla">
              <organization/>
            </author>
            <date month="August" year="2018"/>
            <abstract>
              <t>This document specifies version 1.3 of the Transport Layer Security (TLS) protocol.  TLS allows client/server applications to communicate over the Internet in a way that is designed to prevent eavesdropping, tampering, and message forgery.</t>
              <t>This document updates RFCs 5705 and 6066, and obsoletes RFCs 5077, 5246, and 6961.  This document also specifies new requirements for TLS 1.2 implementations.</t>
            </abstract>
          </front>
          <seriesInfo name="RFC" value="8446"/>
          <seriesInfo name="DOI" value="10.17487/RFC8446"/>
        </reference>
        <reference anchor="RFC8126">
          <front>
            <title>Guidelines for Writing an IANA Considerations Section in RFCs</title>
            <author fullname="M. Cotton" initials="M." surname="Cotton">
              <organization/>
            </author>
            <author fullname="B. Leiba" initials="B." surname="Leiba">
              <organization/>
            </author>
            <author fullname="T. Narten" initials="T." surname="Narten">
              <organization/>
            </author>
            <date month="June" year="2017"/>
            <abstract>
              <t>Many protocols make use of points of extensibility that use constants to identify various protocol parameters.  To ensure that the values in these fields do not have conflicting uses and to promote interoperability, their allocations are often coordinated by a central record keeper.  For IETF protocols, that role is filled by the Internet Assigned Numbers Authority (IANA).</t>
              <t>To make assignments in a given registry prudently, guidance describing the conditions under which new values should be assigned, as well as when and how modifications to existing values can be made, is needed.  This document defines a framework for the documentation of these guidelines by specification authors, in order to assure that the provided guidance for the IANA Considerations is clear and addresses the various issues that are likely in the operation of a registry.</t>
              <t>This is the third edition of this document; it obsoletes RFC 5226.</t>
            </abstract>
          </front>
          <seriesInfo name="BCP" value="26"/>
          <seriesInfo name="RFC" value="8126"/>
          <seriesInfo name="DOI" value="10.17487/RFC8126"/>
        </reference>
        <reference anchor="RFC2104">
          <front>
            <title>HMAC: Keyed-Hashing for Message Authentication</title>
            <author fullname="H. Krawczyk" initials="H." surname="Krawczyk">
              <organization/>
            </author>
            <author fullname="M. Bellare" initials="M." surname="Bellare">
              <organization/>
            </author>
            <author fullname="R. Canetti" initials="R." surname="Canetti">
              <organization/>
            </author>
            <date month="February" year="1997"/>
            <abstract>
              <t>This document describes HMAC, a mechanism for message authentication using cryptographic hash functions. HMAC can be used with any iterative cryptographic hash function, e.g., MD5, SHA-1, in combination with a secret shared key.  The cryptographic strength of HMAC depends on the properties of the underlying hash function.  This memo provides information for the Internet community.  This memo does not specify an Internet standard of any kind</t>
            </abstract>
          </front>
          <seriesInfo name="RFC" value="2104"/>
          <seriesInfo name="DOI" value="10.17487/RFC2104"/>
        </reference>
      </references>
      <references>
        <name>Informative References</name>
        <reference anchor="ART" target="https://eprint.iacr.org/2017/666.pdf">
          <front>
            <title>On Ends-to-Ends Encryption: Asynchronous Group Messaging with Strong Security Guarantees</title>
            <author initials="K." surname="Cohn-Gordon" fullname="Katriel Cohn-Gordon">
              <organization/>
            </author>
            <author initials="C." surname="Cremers" fullname="Cas Cremers">
              <organization/>
            </author>
            <author initials="L." surname="Garratt" fullname="Luke Garratt">
              <organization/>
            </author>
            <author initials="J." surname="Millican" fullname="Jon Millican">
              <organization/>
            </author>
            <author initials="K." surname="Milner" fullname="Kevin Milner">
              <organization/>
            </author>
            <date year="2018" month="January" day="18"/>
          </front>
        </reference>
        <reference anchor="DoubleRatchet">
          <front>
            <title>A Formal Security Analysis of the Signal Messaging Protocol</title>
            <author fullname="Katriel Cohn-Gordon" initials="K." surname="Cohn-Gordon">
              <organization/>
            </author>
            <author fullname="Cas Cremers" initials="C." surname="Cremers">
              <organization/>
            </author>
            <author fullname="Benjamin Dowling" initials="B." surname="Dowling">
              <organization/>
            </author>
            <author fullname="Luke Garratt" initials="L." surname="Garratt">
              <organization/>
            </author>
            <author fullname="Douglas Stebila" initials="D." surname="Stebila">
              <organization/>
            </author>
            <date month="April" year="2017"/>
          </front>
          <seriesInfo name="2017 IEEE European Symposium on Security and Privacy" value="(EuroS&amp;P)"/>
          <seriesInfo name="DOI" value="10.1109/eurosp.2017.27"/>
        </reference>
        <reference anchor="Signal" target="https://www.signal.org/docs/specifications/doubleratchet/">
          <front>
            <title>The Double Ratchet Algorithm</title>
            <author initials="T." surname="Perrin(ed)" fullname="Trevor Perrin(ed)">
              <organization/>
            </author>
            <author initials="M." surname="Marlinspike" fullname="Moxie Marlinspike">
              <organization/>
            </author>
            <date year="2016" month="November" day="20"/>
          </front>
        </reference>
        <reference anchor="SHS">
          <front>
            <title>Secure Hash Standard</title>
            <author fullname="Quynh H. Dang" initials="Q." surname="Dang">
              <organization/>
            </author>
            <date month="July" year="2015"/>
          </front>
          <seriesInfo name="National Institute of Standards and Technology" value="report"/>
          <seriesInfo name="DOI" value="10.6028/nist.fips.180-4"/>
        </reference>
        <reference anchor="NAN">
          <front>
            <title>Nonces Are Noticed: AEAD Revisited</title>
            <author fullname="Mihir Bellare" initials="M." surname="Bellare">
              <organization/>
            </author>
            <author fullname="Ruth Ng" initials="R." surname="Ng">
              <organization/>
            </author>
            <author fullname="Björn Tackmann" initials="B." surname="Tackmann">
              <organization/>
            </author>
            <date year="2019"/>
          </front>
          <seriesInfo name="Advances in Cryptology - CRYPTO 2019" value="pp. 235-265"/>
          <seriesInfo name="DOI" value="10.1007/978-3-030-26948-7_9"/>
        </reference>
        <reference anchor="I-D.ietf-mls-architecture">
          <front>
            <title>The Messaging Layer Security (MLS) Architecture</title>
            <author fullname="Benjamin Beurdouche" initials="B." surname="Beurdouche">
              <organization>Inria &amp; Mozilla</organization>
            </author>
            <author fullname="Eric Rescorla" initials="E." surname="Rescorla">
              <organization>Mozilla</organization>
            </author>
            <author fullname="Emad Omara" initials="E." surname="Omara">
              <organization>Google</organization>
            </author>
            <author fullname="Srinivas Inguva" initials="S." surname="Inguva">
              <organization>Twitter</organization>
            </author>
            <author fullname="Alan Duric" initials="A." surname="Duric">
              <organization>Wire</organization>
            </author>
            <date day="16" month="December" year="2022"/>
            <abstract>
              <t>   The Messaging Layer Security (MLS) protocol (I-D.ietf-mls-protocol)
   specification has the role of defining a Group Key Agreement
   protocol, including all the cryptographic operations and
   serialization/deserialization functions necessary for scalable and
   secure group messaging.  The MLS protocol is meant to protect against
   eavesdropping, tampering, message forgery, and provide further
   properties such as Forward Secrecy (FS) and Post-Compromise Security
   (PCS) in the case of past or future device compromises.

   This document describes a general secure group messaging
   infrastructure and its security goals.  It provides guidance on
   building a group messaging system and discusses security and privacy
   tradeoffs offered by multiple security mechanisms that are part of
   the MLS protocol (e.g., frequency of public encryption key rotation).

   The document also provides guidance for parts of the infrastructure
   that are not standardized by the MLS Protocol document and left to
   the application or the infrastructure architects to design.

   While the recommendations of this document are not mandatory to
   follow in order to interoperate at the protocol level, they affect
   the overall security guarantees that are achieved by a messaging
   application.  This is especially true in case of active adversaries
   that are able to compromise clients, the delivery service, or the
   authentication service.

              </t>
            </abstract>
          </front>
          <seriesInfo name="Internet-Draft" value="draft-ietf-mls-architecture-10"/>
        </reference>
        <reference anchor="RFC9000">
          <front>
            <title>QUIC: A UDP-Based Multiplexed and Secure Transport</title>
            <author fullname="J. Iyengar" initials="J." role="editor" surname="Iyengar">
              <organization/>
            </author>
            <author fullname="M. Thomson" initials="M." role="editor" surname="Thomson">
              <organization/>
            </author>
            <date month="May" year="2021"/>
            <abstract>
              <t>This document defines the core of the QUIC transport protocol.  QUIC provides applications with flow-controlled streams for structured communication, low-latency connection establishment, and network path migration. QUIC includes security measures that ensure confidentiality, integrity, and availability in a range of deployment circumstances.  Accompanying documents describe the integration of TLS for key negotiation, loss detection, and an exemplary congestion control algorithm.</t>
            </abstract>
          </front>
          <seriesInfo name="RFC" value="9000"/>
          <seriesInfo name="DOI" value="10.17487/RFC9000"/>
        </reference>
        <reference anchor="RFC5116">
          <front>
            <title>An Interface and Algorithms for Authenticated Encryption</title>
            <author fullname="D. McGrew" initials="D." surname="McGrew">
              <organization/>
            </author>
            <date month="January" year="2008"/>
            <abstract>
              <t>This document defines algorithms for Authenticated Encryption with Associated Data (AEAD), and defines a uniform interface and a registry for such algorithms.  The interface and registry can be used as an application-independent set of cryptoalgorithm suites.  This approach provides advantages in efficiency and security, and promotes the reuse of crypto implementations.  [STANDARDS-TRACK]</t>
            </abstract>
          </front>
          <seriesInfo name="RFC" value="5116"/>
          <seriesInfo name="DOI" value="10.17487/RFC5116"/>
        </reference>
        <reference anchor="RFC8032">
          <front>
            <title>Edwards-Curve Digital Signature Algorithm (EdDSA)</title>
            <author fullname="S. Josefsson" initials="S." surname="Josefsson">
              <organization/>
            </author>
            <author fullname="I. Liusvaara" initials="I." surname="Liusvaara">
              <organization/>
            </author>
            <date month="January" year="2017"/>
            <abstract>
              <t>This document describes elliptic curve signature scheme Edwards-curve Digital Signature Algorithm (EdDSA).  The algorithm is instantiated with recommended parameters for the edwards25519 and edwards448 curves.  An example implementation and test vectors are provided.</t>
            </abstract>
          </front>
          <seriesInfo name="RFC" value="8032"/>
          <seriesInfo name="DOI" value="10.17487/RFC8032"/>
        </reference>
        <reference anchor="RFC6125">
          <front>
            <title>Representation and Verification of Domain-Based Application Service Identity within Internet Public Key Infrastructure Using X.509 (PKIX) Certificates in the Context of Transport Layer Security (TLS)</title>
            <author fullname="P. Saint-Andre" initials="P." surname="Saint-Andre">
              <organization/>
            </author>
            <author fullname="J. Hodges" initials="J." surname="Hodges">
              <organization/>
            </author>
            <date month="March" year="2011"/>
            <abstract>
              <t>Many application technologies enable secure communication between two entities by means of Internet Public Key Infrastructure Using X.509 (PKIX) certificates in the context of Transport Layer Security (TLS). This document specifies procedures for representing and verifying the identity of application services in such interactions.   [STANDARDS-TRACK]</t>
            </abstract>
          </front>
          <seriesInfo name="RFC" value="6125"/>
          <seriesInfo name="DOI" value="10.17487/RFC6125"/>
        </reference>
        <reference anchor="RFC7696">
          <front>
            <title>Guidelines for Cryptographic Algorithm Agility and Selecting Mandatory-to-Implement Algorithms</title>
            <author fullname="R. Housley" initials="R." surname="Housley">
              <organization/>
            </author>
            <date month="November" year="2015"/>
            <abstract>
              <t>Many IETF protocols use cryptographic algorithms to provide confidentiality, integrity, authentication, or digital signature.  Communicating peers must support a common set of cryptographic algorithms for these mechanisms to work properly.  This memo provides guidelines to ensure that protocols have the ability to migrate from one mandatory-to-implement algorithm suite to another over time.</t>
            </abstract>
          </front>
          <seriesInfo name="BCP" value="201"/>
          <seriesInfo name="RFC" value="7696"/>
          <seriesInfo name="DOI" value="10.17487/RFC7696"/>
        </reference>
        <reference anchor="RFC7540">
          <front>
            <title>Hypertext Transfer Protocol Version 2 (HTTP/2)</title>
            <author fullname="M. Belshe" initials="M." surname="Belshe">
              <organization/>
            </author>
            <author fullname="R. Peon" initials="R." surname="Peon">
              <organization/>
            </author>
            <author fullname="M. Thomson" initials="M." role="editor" surname="Thomson">
              <organization/>
            </author>
            <date month="May" year="2015"/>
            <abstract>
              <t>This specification describes an optimized expression of the semantics of the Hypertext Transfer Protocol (HTTP), referred to as HTTP version 2 (HTTP/2).  HTTP/2 enables a more efficient use of network resources and a reduced perception of latency by introducing header field compression and allowing multiple concurrent exchanges on the same connection.  It also introduces unsolicited push of representations from servers to clients.</t>
              <t>This specification is an alternative to, but does not obsolete, the HTTP/1.1 message syntax.  HTTP's existing semantics remain unchanged.</t>
            </abstract>
          </front>
          <seriesInfo name="RFC" value="7540"/>
          <seriesInfo name="DOI" value="10.17487/RFC7540"/>
        </reference>
        <reference anchor="CLINIC">
          <front>
            <title>I Know Why You Went to the Clinic: Risks and Realization of HTTPS Traffic Analysis</title>
            <author fullname="Brad Miller" initials="B." surname="Miller">
              <organization/>
            </author>
            <author fullname="Ling Huang" initials="L." surname="Huang">
              <organization/>
            </author>
            <author fullname="A. D. Joseph" initials="A." surname="Joseph">
              <organization/>
            </author>
            <author fullname="J. D. Tygar" initials="J." surname="Tygar">
              <organization/>
            </author>
            <date year="2014"/>
          </front>
          <seriesInfo name="Privacy Enhancing Technologies" value="pp. 143-163"/>
          <seriesInfo name="DOI" value="10.1007/978-3-319-08506-7_8"/>
        </reference>
        <reference anchor="HCJ16">
          <front>
            <title>HTTPS traffic analysis and client identification using passive SSL/TLS fingerprinting</title>
            <author fullname="Martin Husák" initials="M." surname="Husák">
              <organization/>
            </author>
            <author fullname="Milan Čermák" initials="M." surname="Čermák">
              <organization/>
            </author>
            <author fullname="Tomáš Jirsík" initials="T." surname="Jirsík">
              <organization/>
            </author>
            <author fullname="Pavel Čeleda" initials="P." surname="Čeleda">
              <organization/>
            </author>
            <date month="February" year="2016"/>
          </front>
          <seriesInfo name="EURASIP Journal on Information Security" value="vol. 2016, no. 1"/>
          <seriesInfo name="DOI" value="10.1186/s13635-016-0030-7"/>
        </reference>
        <reference anchor="I-D.irtf-cfrg-aead-limits">
          <front>
            <title>Usage Limits on AEAD Algorithms</title>
            <author fullname="Felix Günther" initials="F." surname="Günther">
              <organization>ETH Zurich</organization>
            </author>
            <author fullname="Martin Thomson" initials="M." surname="Thomson">
              <organization>Mozilla</organization>
            </author>
            <author fullname="Christopher A. Wood" initials="C. A." surname="Wood">
              <organization>Cloudflare</organization>
            </author>
            <date day="11" month="July" year="2022"/>
            <abstract>
              <t>   An Authenticated Encryption with Associated Data (AEAD) algorithm
   provides confidentiality and integrity.  Excessive use of the same
   key can give an attacker advantages in breaking these properties.
   This document provides simple guidance for users of common AEAD
   functions about how to limit the use of keys in order to bound the
   advantage given to an attacker.  It considers limits in both single-
   and multi-key settings.

              </t>
            </abstract>
          </front>
          <seriesInfo name="Internet-Draft" value="draft-irtf-cfrg-aead-limits-05"/>
        </reference>
        <reference anchor="RFC9001">
          <front>
            <title>Using TLS to Secure QUIC</title>
            <author fullname="M. Thomson" initials="M." role="editor" surname="Thomson">
              <organization/>
            </author>
            <author fullname="S. Turner" initials="S." role="editor" surname="Turner">
              <organization/>
            </author>
            <date month="May" year="2021"/>
            <abstract>
              <t>This document describes how Transport Layer Security (TLS) is used to secure QUIC.</t>
            </abstract>
          </front>
          <seriesInfo name="RFC" value="9001"/>
          <seriesInfo name="DOI" value="10.17487/RFC9001"/>
        </reference>
      </references>
    </references>
    <section anchor="protocol-origins-of-example-trees">
      <name>Protocol Origins of Example Trees</name>
      <t>Protocol operations in MLS give rise to specific forms of ratchet tree,
typically affecting a whole direct path at once.  In this section, we describe
the protocol operations that could have given rise to the various example trees
in this document.</t>
      <t>To construct the tree in <xref target="full-tree"/>:</t>
      <ul spacing="normal">
        <li>A creates a group with B, ..., G</li>
        <li>F sends an empty Commit, setting X, Y, W</li>
        <li>G removes C and D, blanking V, U, and setting Y, W</li>
        <li>B sends an empty Commit, setting T and W</li>
      </ul>
      <t>To construct the tree in <xref target="resolution-tree"/>:</t>
      <ul spacing="normal">
        <li>A creates a group with B, ..., H, as well as some members outside this subtree</li>
        <li>F sends an empty Commit, setting Y and its ancestors</li>
        <li>
          <t>D removes B and C, with the following effects:
          </t>
          <ul spacing="normal">
            <li>Blank the direct paths of B and C</li>
            <li>Set X, the top node, and any further nodes in the direct path of D</li>
          </ul>
        </li>
        <li>Someone outside this subtree removes G, blanking the direct path of G</li>
        <li>A adds a new member at B with a partial Commit, adding B as unmerged at X</li>
      </ul>
      <t>To construct the tree in <xref target="evolution-tree"/>:</t>
      <ul spacing="normal">
        <li>A creates a group with B, C, D</li>
        <li>B sends a full Commit, setting X and Y</li>
        <li>D removes C, setting Z and Y</li>
        <li>
          <t>B adds a new member at C with a full Commit
          </t>
          <ul spacing="normal">
            <li>The Add proposal adds C as unmerged at Z and Y</li>
            <li>The path in the Commit resets X and Y, clearing Y's unmerged leaves</li>
          </ul>
        </li>
      </ul>
      <t>To construct the tree in <xref target="parent-hash-tree"/>:</t>
      <ul spacing="normal">
        <li>A creates a group with B, ..., G</li>
        <li>A removes F in a full Commit, setting T, U, and W</li>
        <li>E sends an empty Commit, setting Y and W</li>
        <li>A adds a new member at F in a partial Commit, adding F as unmerged at Y and W</li>
      </ul>
    </section>
    <section anchor="ph-evolution">
      <name>Evolution of Parent Hashes</name>
      <t>To better understand how parent hashes are maintained, let's look in detail at
how they evolve in a small group.  Consider the following sequence of
operations:</t>
      <ol spacing="normal" type="1"><li>A initializes a new group</li>
        <li>A adds B to the group with a full Commit</li>
        <li>B adds C and D to the group with a full Commit</li>
        <li>C sends an empty Commit.</li>
      </ol>
      <artset>
        <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="144" width="432" viewBox="0 0 432 144" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
            <path d="M 216,48 L 216,64" fill="none" stroke="black"/>
            <path d="M 376,48 L 376,64" fill="none" stroke="black"/>
            <path d="M 200,64 L 232,64" fill="none" stroke="black"/>
            <path d="M 360,64 L 392,64" fill="none" stroke="black"/>
            <path d="M 32,78 L 48,78" fill="none" stroke="black"/>
            <path d="M 32,82 L 48,82" fill="none" stroke="black"/>
            <path d="M 128,78 L 144,78" fill="none" stroke="black"/>
            <path d="M 128,82 L 144,82" fill="none" stroke="black"/>
            <path d="M 288,78 L 304,78" fill="none" stroke="black"/>
            <path d="M 288,82 L 304,82" fill="none" stroke="black"/>
            <path d="M 232,64 L 240,80" fill="none" stroke="black"/>
            <path d="M 252,104 L 256,112" fill="none" stroke="black"/>
            <path d="M 392,64 L 400,80" fill="none" stroke="black"/>
            <path d="M 192,80 L 200,64" fill="none" stroke="black"/>
            <path d="M 240,112 L 244,104" fill="none" stroke="black"/>
            <path d="M 352,80 L 360,64" fill="none" stroke="black"/>
            <polygon class="arrowhead" points="312,80 300,74.4 300,85.6" fill="black" transform="rotate(0,304,80)"/>
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            <g class="text">
              <text x="216" y="36">Y</text>
              <text x="380" y="36">Y'</text>
              <text x="88" y="100">X</text>
              <text x="188" y="100">X'</text>
              <text x="256" y="100">_=Z</text>
              <text x="348" y="100">X'</text>
              <text x="412" y="100">Z'</text>
              <text x="80" y="116">/</text>
              <text x="96" y="116">\</text>
              <text x="176" y="116">/</text>
              <text x="192" y="116">\</text>
              <text x="336" y="116">/</text>
              <text x="352" y="116">\</text>
              <text x="400" y="116">/</text>
              <text x="416" y="116">\</text>
              <text x="8" y="132">A</text>
              <text x="72" y="132">A</text>
              <text x="104" y="132">B</text>
              <text x="168" y="132">A</text>
              <text x="200" y="132">B</text>
              <text x="232" y="132">C</text>
              <text x="264" y="132">D</text>
              <text x="328" y="132">A</text>
              <text x="360" y="132">B</text>
              <text x="392" y="132">C</text>
              <text x="424" y="132">D</text>
            </g>
          </svg>
        </artwork>
        <artwork type="ascii-art"><![CDATA[
                          Y                   Y'
                          |                   |
                        .-+-.               .-+-.
   ==>         ==>     /     \     ==>     /     \
          X           X'      _=Z         X'      Z'
         / \         / \     / \         / \     / \
A       A   B       A   B   C   D       A   B   C   D
]]></artwork>
      </artset>
      <t>Then the parent hashes associated to the nodes will be updated as follows (where
we use the shorthand <tt>ph</tt> for parent hash, <tt>th</tt> for tree hash, and <tt>osth</tt> for
original sibling tree hash):</t>
      <ol spacing="normal" type="1"><li>
          <t>A adds B: set X  </t>
          <ul spacing="normal">
            <li>
              <tt>A.parent_hash = ph(X) = H(X, ph="", osth=th(B))</tt></li>
          </ul>
        </li>
        <li>
          <t>B adds C, D: set B', X', Y  </t>
          <ul spacing="normal">
            <li>
              <tt>X'.parent_hash = ph(Y)  = H(Y, ph="", osth=th(Z))</tt>,
where <tt>th(Z)</tt> covers <tt>(C, _, D)</tt></li>
            <li>
              <tt>B'.parent_hash = ph(X') = H(X', ph=X'.parent_hash, osth=th(A))</tt></li>
          </ul>
        </li>
        <li>
          <t>C sends empty Commit: set C', Z', Y'  </t>
          <ul spacing="normal">
            <li>
              <tt>Z'.parent_hash = ph(Y') = H(Y', ph="", osth=th(X'))</tt>, where
<tt>th(X')</tt> covers <tt>(A, X', B')</tt></li>
            <li>
              <tt>C'.parent_hash = ph(Z') = H(Z', ph=Z'.parent_hash, osth=th(D))</tt></li>
          </ul>
        </li>
      </ol>
      <t>When a new member joins, they will receive a tree that has the following parent
hash values, and compute the indicated parent-hash validity relationships:</t>
      <table>
        <thead>
          <tr>
            <th align="left">Node</th>
            <th align="left">Parent hash value</th>
            <th align="left">Valid?</th>
          </tr>
        </thead>
        <tbody>
          <tr>
            <td align="left">A</td>
            <td align="left">H(X, ph="", osth=th(B))</td>
            <td align="left">No, B changed</td>
          </tr>
          <tr>
            <td align="left">B'</td>
            <td align="left">H(X', ph=X'.parent_hash, osth=th(A))</td>
            <td align="left">Yes</td>
          </tr>
          <tr>
            <td align="left">C'</td>
            <td align="left">H(Z', ph=Z'.parent_hash, osth=th(D))</td>
            <td align="left">Yes</td>
          </tr>
          <tr>
            <td align="left">D</td>
            <td align="left">(none, never sent an UpdatePath)</td>
            <td align="left">N/A</td>
          </tr>
          <tr>
            <td align="left">X'</td>
            <td align="left">H(Y, ph="", osth=th(Z))</td>
            <td align="left">No, Y and Z changed</td>
          </tr>
          <tr>
            <td align="left">Z'</td>
            <td align="left">H(Y', ph="", osth=th(X'))</td>
            <td align="left">Yes</td>
          </tr>
        </tbody>
      </table>
      <t>In other words, the joiner will find the following path-hash links in the tree:</t>
      <artset>
        <artwork type="svg"><svg xmlns="http://www.w3.org/2000/svg" version="1.1" height="160" width="112" viewBox="0 0 112 160" class="diagram" text-anchor="middle" font-family="monospace" font-size="13px">
            <path d="M 56,48 L 56,64" fill="none" stroke="black"/>
            <path d="M 56,64 L 72,64" fill="none" stroke="black"/>
            <path d="M 72,64 L 80,80" fill="none" stroke="black"/>
            <g class="text">
              <text x="60" y="36">Y'</text>
              <text x="28" y="100">X'</text>
              <text x="92" y="100">Z'</text>
              <text x="32" y="116">\</text>
              <text x="80" y="116">/</text>
              <text x="8" y="132">A</text>
              <text x="44" y="132">B'</text>
              <text x="76" y="132">C'</text>
              <text x="104" y="132">D</text>
            </g>
          </svg>
        </artwork>
        <artwork type="ascii-art"><![CDATA[
       Y'
       |
       +-.
          \
   X'      Z'
    \     /
 A   B'  C'  D
]]></artwork>
      </artset>
      <t>Since these chains collectively cover all non-blank parent nodes in the tree,
the tree is parent-hash valid.</t>
      <t>Note that this tree, though valid, contains invalid parent-hash links. If a
client were checking parent hashes top-down from Y', for example, they would
find that X' has an invalid parent hash relative to Y', but that Z' has valid
parent hash.  Likewise, if the client were checking bottom-up, they would find
that the chain from B' ends in an invalid link from X' to Y'.  These invalid
links are the natural result of multiple clients having committed.</t>
      <t>Note also the way the tree hash and the parent hash interact.  The parent hash
of node C' includes the tree hash of node D.  The parent hash of node Z'
includes the tree hash of X', which covers nodes A and B' (including the parent
hash of B').  Although the tree hash and the parent hash depend on each other,
the dependency relationships are structured so that there's never a circular
dependency.</t>
      <t>In the particular case where a new member first receives the tree for a group
(e.g., in a ratchet tree GroupInfo extension <xref target="ratchet-tree-extension"/>), the
parent hashes will be expressed in the tree representation, but the tree hash
need not be.  Instead, the new member will recompute the tree hashes for all the
nodes in the tree, verifying that this matches the tree hash in the GroupInfo
object.  Then, if the tree is valid, then the subtree hashes computed in this
way will align with the inputs needed for parent hash validation (except where
recomputation is needed to account for unmerged leaves).</t>
    </section>
    <section anchor="array-based-trees">
      <name>Array-Based Trees</name>
      <t>One benefit of using complete balanced trees is that they admit a simple
flat array representation.  In this representation, leaf nodes are
even-numbered nodes, with the <tt>n</tt>-th leaf at <tt>2*n</tt>.  Intermediate nodes
are held in odd-numbered nodes.  For example, the tree with 8 leaves has
the following structure:</t>
      <artset>
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        </artwork>
        <artwork type="ascii-art"><![CDATA[
                           X
                           |
                 .---------+---------.
                /                     \
               X                       X
               |                       |
           .---+---.               .---+---.
          /         \             /         \
         X           X           X           X
        / \         / \         / \         / \
       /   \       /   \       /   \       /   \
      X     X     X     X     X     X     X     X

Node: 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14

Leaf: 0     1     2     3     4     5     6     7
]]></artwork>
      </artset>
      <t>This allows us to compute relationships between tree nodes simply by
manipulating indices, rather than having to maintain complicated structures in
memory. The basic rule is that the high-order bits of parent and child nodes
indices have the following relation (where <tt>x</tt> is an arbitrary bit string):</t>
      <sourcecode type="pseudocode"><![CDATA[
parent=01x => left=00x, right=10x
]]></sourcecode>
      <t>Since node relationships are implicit, the algorithms for adding and removing
nodes at the right edge of the tree are quite simple.  If there are <tt>N</tt> nodes in
the array:</t>
      <ul spacing="normal">
        <li>Add: Append <tt>N + 1</tt> blank values to the end of the array.</li>
        <li>Remove: Truncate the array to its first <tt>(N-1) / 2</tt> entries.</li>
      </ul>
      <t>The following python code demonstrates the tree computations necessary to use an
array-based tree for MLS.</t>
      <sourcecode type="python"><![CDATA[
# The exponent of the largest power of 2 less than x. Equivalent to:
#   int(math.floor(math.log(x, 2)))
def log2(x):
    if x == 0:
        return 0

    k = 0
    while (x >> k) > 0:
        k += 1
    return k-1

# The level of a node in the tree. Leaves are level 0, their parents
# are level 1, etc. If a node's children are at different levels,
# then its level is the max level of its children plus one.
def level(x):
    if x & 0x01 == 0:
        return 0

    k = 0
    while ((x >> k) & 0x01) == 1:
        k += 1
    return k

# The number of nodes needed to represent a tree with n leaves.
def node_width(n):
    if n == 0:
        return 0
    else:
        return 2*(n - 1) + 1

# The index of the root node of a tree with n leaves.
def root(n):
    w = node_width(n)
    return (1 << log2(w)) - 1

# The left child of an intermediate node.
def left(x):
    k = level(x)
    if k == 0:
        raise Exception('leaf node has no children')

    return x ^ (0x01 << (k - 1))

# The right child of an intermediate node.
def right(x):
    k = level(x)
    if k == 0:
        raise Exception('leaf node has no children')

    return x ^ (0x03 << (k - 1))

# The parent of a node.
def parent(x, n):
    if x == root(n):
        raise Exception('root node has no parent')

    k = level(x)
    b = (x >> (k + 1)) & 0x01
    return (x | (1 << k)) ^ (b << (k + 1))

# The other child of the node's parent.
def sibling(x, n):
    p = parent(x, n)
    if x < p:
        return right(p)
    else:
        return left(p)

# The direct path of a node, ordered from leaf to root.
def direct_path(x, n):
    r = root(n)
    if x == r:
        return []

    d = []
    while x != r:
        x = parent(x, n)
        d.append(x)
    return d

# The copath of a node, ordered from leaf to root.
def copath(x, n):
    if x == root(n):
        return []

    d = direct_path(x, n)
    d.insert(0, x)
    d.pop()
    return [sibling(y, n) for y in d]

# The common ancestor of two nodes is the lowest node that is in the
# direct paths of both leaves.
def common_ancestor_semantic(x, y, n):
    dx = set([x]) | set(direct_path(x, n))
    dy = set([y]) | set(direct_path(y, n))
    dxy = dx & dy
    if len(dxy) == 0:
        raise Exception('failed to find common ancestor')

    return min(dxy, key=level)

# The common ancestor of two nodes is the lowest node that is in the
# direct paths of both leaves.
def common_ancestor_direct(x, y, _):
    # Handle cases where one is an ancestor of the other
    lx, ly = level(x)+1, level(y)+1
    if (lx <= ly) and (x>>ly == y>>ly):
      return y
    elif (ly <= lx) and (x>>lx == y>>lx):
      return x

    # Handle other cases
    xn, yn = x, y
    k = 0
    while xn != yn:
       xn, yn = xn >> 1, yn >> 1
       k += 1
    return (xn << k) + (1 << (k-1)) - 1
]]></sourcecode>
    </section>
    <section anchor="link-based-trees">
      <name>Link-Based Trees</name>
      <t>An implementation may choose to store ratchet trees in a "link-based"
representation, where each node stores references to its parents and/or
children.   (As opposed to the array-based representation suggested above, where
these relationships are computed from relationships between nodes' indices in
the array.)  Such an implementation needs to update these links to maintain the
balanced structure of the tree as the tree is extended to add new members,
or truncated when members are removed.</t>
      <t>The following code snippet shows how these algorithms could be implemented in
Python.</t>
      <sourcecode type="python"><![CDATA[
class Node:
    def __init__(self, value, left=None, right=None):
        self.value = value    # Value of the node
        self.left = left      # Left child node
        self.right = right    # Right child node

    @staticmethod
    def blank_subtree(depth):
        if depth == 1:
            return Node(None)

        L = Node.blank_subtree(depth-1)
        R = Node.blank_subtree(depth-1)
        return Node(None, left=L, right=R)

    def empty(self):
        L_empty = (self.left == None) or self.left.empty()
        R_empty = (self.left == None) or self.left.empty()
        return (self.value == None) and L_empty and R_empty

class Tree:
    def __init__(self):
        self.depth = 0    # Depth of the tree
        self.root = None  # Root node of the tree, initially empty

    # Add a blank subtree to the right
    def extend(self):
        if self.depth == 0:
            self.depth = 1
            self.root = Node(None)

        L = self.root
        R = Node.blank_subtree(self.depth)
        self.root = Node(None, left=self.root, right=R)
        self.depth += 1

    # Truncate the right subtree
    def truncate(self):
        if self.root == None or self.root.right == None:
            raise Exception("Cannot truncate a tree with 0 or 1 nodes")

        if not self.root.right.empty():
            raise Exception("Cannot truncate non-blank subtree")

        self.depth -= 1
        self.root = self.root.left
]]></sourcecode>
    </section>
    <section anchor="contributors" numbered="false" toc="include" removeInRFC="false">
      <name>Contributors</name>
      <contact initials="J." surname="Alwen" fullname="Joel Alwen">
        <organization>Amazon</organization>
        <address>
          <email>alwenjo@amazon.com</email>
        </address>
      </contact>
      <contact initials="K." surname="Bhargavan" fullname="Karthikeyan Bhargavan">
        <organization>Inria</organization>
        <address>
          <email>karthikeyan.bhargavan@inria.fr</email>
        </address>
      </contact>
      <contact initials="C." surname="Cremers" fullname="Cas Cremers">
        <organization>CISPA</organization>
        <address>
          <email>cremers@cispa.de</email>
        </address>
      </contact>
      <contact initials="A." surname="Duric" fullname="Alan Duric">
        <organization>Wire</organization>
        <address>
          <email>alan@wire.com</email>
        </address>
      </contact>
      <contact initials="B." surname="Hale" fullname="Britta Hale">
        <organization>Naval Postgraduate School</organization>
        <address>
          <email>britta.hale@nps.edu</email>
        </address>
      </contact>
      <contact initials="S." surname="Inguva" fullname="Srinivas Inguva">
        <organization>Twitter</organization>
        <address>
          <email>singuva@twitter.com</email>
        </address>
      </contact>
      <contact initials="K." surname="Kohbrok" fullname="Konrad Kohbrok">
        <organization>Phoenix R&amp;D</organization>
        <address>
          <email>konrad.kohbrok@datashrine.de</email>
        </address>
      </contact>
      <contact initials="A." surname="Kwon" fullname="Albert Kwon">
        <organization>MIT</organization>
        <address>
          <email>kwonal@mit.edu</email>
        </address>
      </contact>
      <contact initials="T." surname="Leavy" fullname="Tom Leavy">
        <organization>Amazon</organization>
        <address>
          <email>tomleavy@amazon.com</email>
        </address>
      </contact>
      <contact initials="B." surname="McMillion" fullname="Brendan McMillion">
        <organization/>
        <address>
          <email>brendanmcmillion@gmail.com</email>
        </address>
      </contact>
      <contact initials="M." surname="Mularczyk" fullname="Marta Mularczyk">
        <organization>Amazon</organization>
        <address>
          <email>mulmarta@amazon.com</email>
        </address>
      </contact>
      <contact initials="E." surname="Rescorla" fullname="Eric Rescorla">
        <organization>Mozilla</organization>
        <address>
          <email>ekr@rtfm.com</email>
        </address>
      </contact>
      <contact initials="M." surname="Rosenberg" fullname="Michael Rosenberg">
        <organization>Trail of Bits</organization>
        <address>
          <email>michael.rosenberg@trailofbits.com</email>
        </address>
      </contact>
      <contact initials="T." surname="Wallez" fullname="Théophile Wallez">
        <organization>Inria</organization>
        <address>
          <email>theophile.wallez@inria.fr</email>
        </address>
      </contact>
      <contact initials="T. van der" surname="Merwe" fullname="Thyla van der Merwe">
        <organization>Royal Holloway, University of London</organization>
        <address>
          <email>thyla.van.der@merwe.tech</email>
        </address>
      </contact>
    </section>
  </back>
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