



Internet Engineering Task Force (IETF)                         R. Barnes
Request for Comments: 9420                                         Cisco
Category: Standards Track                                  B. Beurdouche
ISSN: 2070-1721                                          Inria & Mozilla
                                                               R. Robert
                                                             Phoenix R&D
                                                             J. Millican
                                                          Meta Platforms
                                                                E. Omara
                                                                        
                                                          K. Cohn-Gordon
                                                    University of Oxford
                                                               July 2023


              The Messaging Layer Security (MLS) Protocol

Abstract

   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 (FS) and post-compromise security (PCS) for groups in size
   ranging from two to thousands.

Status of This Memo

   This is an Internet Standards Track document.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It represents the consensus of the IETF community.  It has
   received public review and has been approved for publication by the
   Internet Engineering Steering Group (IESG).  Further information on
   Internet Standards is available in Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   https://www.rfc-editor.org/info/rfc9420.

Copyright Notice

   Copyright (c) 2023 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (https://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Revised BSD License text as described in Section 4.e of the
   Trust Legal Provisions and are provided without warranty as described
   in the Revised BSD License.

Table of Contents

   1.  Introduction
   2.  Terminology
     2.1.  Presentation Language
       2.1.1.  Optional Value
       2.1.2.  Variable-Size Vector Length Headers
   3.  Protocol Overview
     3.1.  Cryptographic State and Evolution
     3.2.  Example Protocol Execution
     3.3.  External Joins
     3.4.  Relationships between Epochs
   4.  Ratchet Tree Concepts
     4.1.  Ratchet Tree Terminology
       4.1.1.  Ratchet Tree Nodes
       4.1.2.  Paths through a Ratchet Tree
     4.2.  Views of a Ratchet Tree
   5.  Cryptographic Objects
     5.1.  Cipher Suites
       5.1.1.  Public Keys
       5.1.2.  Signing
       5.1.3.  Public Key Encryption
     5.2.  Hash-Based Identifiers
     5.3.  Credentials
       5.3.1.  Credential Validation
       5.3.2.  Credential Expiry and Revocation
       5.3.3.  Uniquely Identifying Clients
   6.  Message Framing
     6.1.  Content Authentication
     6.2.  Encoding and Decoding a Public Message
     6.3.  Encoding and Decoding a Private Message
       6.3.1.  Content Encryption
       6.3.2.  Sender Data Encryption
   7.  Ratchet Tree Operations
     7.1.  Parent Node Contents
     7.2.  Leaf Node Contents
     7.3.  Leaf Node Validation
     7.4.  Ratchet Tree Evolution
     7.5.  Synchronizing Views of the Tree
     7.6.  Update Paths
     7.7.  Adding and Removing Leaves
     7.8.  Tree Hashes
     7.9.  Parent Hashes
       7.9.1.  Using Parent Hashes
       7.9.2.  Verifying Parent Hashes
   8.  Key Schedule
     8.1.  Group Context
     8.2.  Transcript Hashes
     8.3.  External Initialization
     8.4.  Pre-Shared Keys
     8.5.  Exporters
     8.6.  Resumption PSK
     8.7.  Epoch Authenticators
   9.  Secret Tree
     9.1.  Encryption Keys
     9.2.  Deletion Schedule
   10. Key Packages
     10.1.  KeyPackage Validation
   11. Group Creation
     11.1.  Required Capabilities
     11.2.  Reinitialization
     11.3.  Subgroup Branching
   12. Group Evolution
     12.1.  Proposals
       12.1.1.  Add
       12.1.2.  Update
       12.1.3.  Remove
       12.1.4.  PreSharedKey
       12.1.5.  ReInit
       12.1.6.  ExternalInit
       12.1.7.  GroupContextExtensions
       12.1.8.  External Proposals
     12.2.  Proposal List Validation
     12.3.  Applying a Proposal List
     12.4.  Commit
       12.4.1.  Creating a Commit
       12.4.2.  Processing a Commit
       12.4.3.  Adding Members to the Group
   13. Extensibility
     13.1.  Additional Cipher Suites
     13.2.  Proposals
     13.3.  Credential Extensibility
     13.4.  Extensions
     13.5.  GREASE
   14. Sequencing of State Changes
   15. Application Messages
     15.1.  Padding
     15.2.  Restrictions
     15.3.  Delayed and Reordered Application Messages
   16. Security Considerations
     16.1.  Transport Security
     16.2.  Confidentiality of Group Secrets
     16.3.  Confidentiality of Sender Data
     16.4.  Confidentiality of Group Metadata
       16.4.1.  GroupID, Epoch, and Message Frequency
       16.4.2.  Group Extensions
       16.4.3.  Group Membership
     16.5.  Authentication
     16.6.  Forward Secrecy and Post-Compromise Security
     16.7.  Uniqueness of Ratchet Tree Key Pairs
     16.8.  KeyPackage Reuse
     16.9.  Delivery Service Compromise
     16.10. Authentication Service Compromise
     16.11. Additional Policy Enforcement
     16.12. Group Fragmentation by Malicious Insiders
   17. IANA Considerations
     17.1.  MLS Cipher Suites
     17.2.  MLS Wire Formats
     17.3.  MLS Extension Types
     17.4.  MLS Proposal Types
     17.5.  MLS Credential Types
     17.6.  MLS Signature Labels
     17.7.  MLS Public Key Encryption Labels
     17.8.  MLS Exporter Labels
     17.9.  MLS Designated Expert Pool
     17.10. The "message/mls" Media Type
   18. References
     18.1.  Normative References
     18.2.  Informative References
   Appendix A.  Protocol Origins of Example Trees
   Appendix B.  Evolution of Parent Hashes
   Appendix C.  Array-Based Trees
   Appendix D.  Link-Based Trees
   Contributors
   Authors' Addresses

1.  Introduction

   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 [DoubleRatchet] [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.

   For a group of size greater than two, a common strategy is to
   distribute symmetric "sender keys" over existing 1:1 secure 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 transmission 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.

   In this document, we describe a protocol based on tree structures
   that enables asynchronous group keying with forward secrecy and post-
   compromise security.  Based on earlier work on "asynchronous
   ratcheting trees" [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.

2.  Terminology

   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 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

   Client:  An agent that uses this protocol to establish shared
      cryptographic state with other clients.  A client is defined by
      the cryptographic keys it holds.

   Group:  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.

   Epoch:  A state of a group in which a specific set of authenticated
      clients hold shared cryptographic state.

   Member:  A client that is included in the shared state of a group and
      hence has access to the group's secrets.

   Key Package:  A signed object describing a client's identity and
      capabilities, including a hybrid public key encryption (HPKE)
      [RFC9180] public key that can be used to encrypt to that client.
      Other clients can use a client's KeyPackage to introduce the
      client to a new group.

   Group Context:  An object that summarizes the shared, public state of
      the group.  The group context is typically distributed in a signed
      GroupInfo message, which is provided to new members to help them
      join a group.

   Signature Key:  A signing key pair used to authenticate the sender of
      a message.

   Proposal:  A message that proposes a change to the group, e.g.,
      adding or removing a member.

   Commit:  A message that implements the changes to the group proposed
      in a set of Proposals.

   PublicMessage:  An MLS protocol message that is signed by its sender
      and authenticated as coming from a member of the group in a
      particular epoch, but not encrypted.

   PrivateMessage:  An MLS protocol message that is signed by its
      sender, authenticated as coming from a member of the group in a
      particular epoch, and encrypted so that it is confidential to the
      members of the group in that epoch.

   Handshake Message:  A PublicMessage or PrivateMessage carrying an MLS
      Proposal or Commit object, as opposed to application data.

   Application Message:  A PrivateMessage carrying application data.

   Terminology specific to tree computations is described in
   Section 4.1.

   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 to derive
   further secret values and "key" to refer to a value that is used with
   an algorithm such as Hashed Message Authentication Code (HMAC) or an
   Authenticated Encryption with Associated Data (AEAD) algorithm.

   The PublicMessage and PrivateMessage formats are defined in
   Section 6.  Security notions such as forward secrecy and post-
   compromise security are defined in Section 16.

   As detailed in Section 13.5, MLS uses the "Generate Random Extensions
   And Sustain Extensibility" (GREASE) approach to maintaining
   extensibility, where senders insert random values into fields in
   which receivers are required to ignore unknown values.  Specific
   "GREASE values" for this purpose are registered in the appropriate
   IANA registries.

2.1.  Presentation Language

   We use the TLS presentation language [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.

2.1.1.  Optional Value

   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.

   struct {
       uint8 present;
       select (present) {
           case 0: struct{};
           case 1: T value;
       };
   } optional<T>;

2.1.2.  Variable-Size Vector Length Headers

   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.

   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 described in Section 16 of [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 V.  For example:

   struct {
       uint32 fixed<0..255>;
       opaque variable<V>;
   } StructWithVectors;

   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, so that the overall value is 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.

   This means that integers are encoded in 1, 2, or 4 bytes and can
   encode 6-, 14-, or 30-bit values, respectively.

          +========+=========+=============+=======+============+
          | Prefix | Length  | Usable Bits | Min   | Max        |
          +========+=========+=============+=======+============+
          | 00     | 1       | 6           | 0     | 63         |
          +--------+---------+-------------+-------+------------+
          | 01     | 2       | 14          | 64    | 16383      |
          +--------+---------+-------------+-------+------------+
          | 10     | 4       | 30          | 16384 | 1073741823 |
          +--------+---------+-------------+-------+------------+
          | 11     | invalid | -           | -     | -          |
          +--------+---------+-------------+-------+------------+

                   Table 1: Summary of Integer Encodings

   Vectors that start with the prefix "11" are invalid and MUST be
   rejected.

   For example:

   *  The four-byte length value 0x9d7f3e7d decodes to 494878333.

   *  The two-byte length value 0x7bbd decodes to 15293.

   *  The single-byte length value 0x25 decodes to 37.

   The following figure adapts the pseudocode provided in [RFC9000] to
   add a check for minimum-length encoding:

   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 if the value would fit in half the provided length.
     if prefix >= 1 && v < (1 << (8*(length/2) - 2)):
       raise Exception('minimum encoding was not used')

     return v

   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.

3.  Protocol Overview

   MLS is designed to operate in the context described in [MLS-ARCH].
   In particular, we assume that the following services are provided:

   *  An Authentication Service (AS) that enables group members to
      authenticate the credentials presented by other group members.

   *  A Delivery Service (DS) that routes MLS messages among the
      participants in the protocol.

   MLS assumes a trusted AS but a largely untrusted DS.  Section 16.10
   describes the impact of compromise or misbehavior of an AS.  MLS is
   designed to protect the confidentiality and integrity of the group
   data even in the face of a compromised DS; in general, the DS is only
   expected to reliably deliver messages.  Section 16.9 describes the
   impact of compromise or misbehavior of a DS.

   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.  That secret can then be used to protect messages
   sent from one participant in the group to the other participants
   using the MLS framing layer or can be exported for use with other
   protocols.  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.

   The core organizing principles of MLS are _groups_ and _epochs_.  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 _members_ agree on an _epoch secret_ 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.

   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.

   *  A _KeyPackage_ object describes a client's capabilities and
      provides keys that can be used to add the client to a group.

   *  A _Proposal_ message proposes a change to be made in the next
      epoch, such as adding or removing a member.

   *  A _Commit_ message initiates a new epoch by instructing members of
      the group to implement a collection of proposals.

   *  A _Welcome_ 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.

   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.  A client publishes a KeyPackage
   via the DS, thus enabling other clients to add it to groups.  When a
   group member wants to add a new member to a group, it uses the new
   member's KeyPackage to add them and constructs a Welcome message with
   which the new member can initialize their local state.

   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 _PublicMessage_ provides sender authentication for
   unencrypted Proposal and Commit messages.  A _PrivateMessage_
   provides encryption and authentication for both Proposal/Commit
   messages as well as any application data.

3.1.  Cryptographic State and Evolution

   The cryptographic state at the core of MLS is divided into three
   areas of responsibility:

                          .-    ...    -.
                         |               |
                         |       |       |
                         |       |       | Key Schedule
                         |       V       |
                         |  epoch_secret |
.                        |       |       |                             .
|\ Ratchet               |       |       |                     Secret /|
| \ Tree                 |       |       |                      Tree / |
|  \                     |       |       |                          /  |
|   \                    |       V       |                         /   |
|    +--> commit_secret --> epoch_secret --> encryption_secret -->+    |
|   /                    |       |       |                         \   |
|  /                     |       |       |                          \  |
| /                      |       |       |                           \ |
|/                       |       |       |                            \|
'                        |       V       |                             '
                         |  epoch_secret |
                         |       |       |
                         |       |       |
                         |       V       |
                         |               |
                          '-    ...    -'

              Figure 1: Overview of MLS Group Evolution

   *  A _ratchet tree_ 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 _key schedule_.

   *  A _key schedule_ that describes the chain of key derivations used
      to progress from epoch to epoch (mainly using the _init_secret_
      and _epoch_secret_), as well as the derivation of a variety of
      other secrets (see Table 4).  For example:

      -  An _encryption secret_ that is used to initialize the secret
         tree for the epoch.

      -  An _exporter secret_ that allows other protocols to leverage
         MLS as a generic authenticated group key exchange.

      -  A _resumption secret_ that members can use to prove their
         membership in the group, e.g., when creating a subgroup or a
         successor group.

   *  A _secret tree_ 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.

   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.

   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 epoch secret is confidential to the members in the current
   epoch.

   For each Commit that adds one or more members to the group, there are
   one or more corresponding Welcome messages.  Each Welcome message
   provides 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.

3.2.  Example Protocol Execution

   There are three major operations in the life of a group:

   *  Adding a member, initiated by a current member;

   *  Updating the keys that represent a member in the tree; and

   *  Removing a member.

   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.

   Before the initialization of a group, clients publish KeyPackages to
   a directory provided by the DS (see Figure 2).

                                                    Delivery Service
                                                            |
                                                  .--------' '--------.
                                                 |                     |
                                                                 Group
  A                B                C            Directory       Channel
  |                |                |                |              |
  | KeyPackageA    |                |                |              |
  +------------------------------------------------->|              |
  |                |                |                |              |
  |                | KeyPackageB    |                |              |
  |                +-------------------------------->|              |
  |                |                |                |              |
  |                |                | KeyPackageC    |              |
  |                |                +--------------->|              |
  |                |                |                |              |

    Figure 2: Clients A, B, and C publish KeyPackages to the directory

   Figure 3 shows how these pre-published KeyPackages are used to create
   a group.  When client A wants to establish a group with clients 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 proposal and a Commit message to add that member and then
   broadcasts the two messages to the group.  Client A also generates a
   Welcome message and sends it 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.

   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.

                                                                  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)       |
   |<---------------------------------------------------------------+
   |              |<------------------------------------------------+
   |              |              |              |                   |

          Figure 3: Client A creates a group with clients B and C

   Subsequent additions of group members proceed in the same way.  Any
   member of the group can download a KeyPackage for a new client,
   broadcast Add and Commit messages that the current group will use to
   update their state, and send a Welcome message that the new client
   can use to initialize its state and join the group.

   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 Figure 4).  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 secrets corresponding
   to the sender's leaf in the tree.  At the end of the scenario shown
   in Figure 4, the group has post-compromise security with respect to
   both A and B.

   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.  Since
   the purpose of sending an Update is to proactively constrain a
   compromise window, the right frequency is usually on the order of
   hours or days, not milliseconds.  For example, an application might
   send an Update each time a member sends an application message after
   receiving any message from another member, or daily if no application
   messages are sent.

   The MLS architecture recommends that MLS be operated over a secure
   transport (see Section 7.1 of [MLS-ARCH]).  Such transport protocols
   will typically provide functions such as congestion control that
   manage the impact of an MLS-using application on other applications
   sharing the same network.  Applications should take care that they do
   not send MLS messages at a rate that will cause problems such as
   network congestion, especially if they are not following the above
   recommendation (e.g., sending MLS directly over UDP instead).

                                                             Group
   A              B     ...      Z          Directory        Channel
   |              |              |              |              |
   |              | Update(B)    |              |              |
   |              +------------------------------------------->|
   |              |              |              | Update(B)    |
   |<----------------------------------------------------------+
   |              |<-------------------------------------------+
   |              |              |<----------------------------+
   |              |              |              |              |
   | Commit(Upd)  |              |              |              |
   +---------------------------------------------------------->|
   |              |              |              | Commit(Upd)  |
   |<----------------------------------------------------------+
   |              |<-------------------------------------------+
   |              |              |<----------------------------+
   |              |              |              |              |

        Figure 4: Client B proposes to update its key, and client A
                            commits the proposal

   Members are removed from the group in a similar way, as shown in
   Figure 5.  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 mechanisms.

                                                             Group
   A              B     ...      Z          Directory       Channel
   |              |              |              |              |
   |              |              | Remove(B)    |              |
   |              |              | Commit(Rem)  |              |
   |              |              +---------------------------->|
   |              |              |              |              |
   |              |              |              | Remove(B)    |
   |              |              |              | Commit(Rem)  |
   |<----------------------------------------------------------+
   |              |<-------------------------------------------+
   |              |              |<----------------------------+
   |              |              |              |              |

             Figure 5: Client Z removes client B from the group

   Note that the flows in this section are examples; applications can
   arrange message flows in other ways.  For example:

   *  Welcome messages don't necessarily need to be sent directly to new
      joiners.  Since they are encrypted to new joiners, they could be
      distributed more broadly, say if the application only had access
      to a broadcast channel for the group.

   *  Proposal messages don't need to be immediately sent to all group
      members.  They need to be available to the committer before
      generating a Commit, and to other members before processing the
      Commit.

   *  The sender of a Commit doesn't necessarily have to wait to receive
      its own Commit back before advancing its state.  It only needs to
      know that its Commit will be the next one applied by the group,
      say based on a promise from an orchestration server.

3.3.  External Joins

   In addition to the Welcome-based flow for adding a new member to the
   group, it is also possible for a new member to join by means of an
   "external Commit".  This mechanism can be used when the existing
   members don't have a KeyPackage for the new member, for example, in
   the case of an "open" group that can be joined by new members without
   asking permission from existing members.

   Figure 6 shows a typical message flow for an external join.  To
   enable a new member to join the group in this way, a member of the
   group (A, B) publishes a GroupInfo object that includes the
   GroupContext for the group as well as a public key that can be used
   to encrypt a secret to the existing members of the group.  When the
   new member Z wishes to join, they download the GroupInfo object and
   use it to form a Commit of a special form that adds Z to the group
   (as detailed in Section 12.4.3.2).  The existing members of the group
   process this external Commit in a similar way to a normal Commit,
   advancing to a new epoch in which Z is now a member of the group.

                                                             Group
   A              B              Z          Directory        Channel
   |              |              |              |              |
   | GroupInfo    |              |              |              |
   +------------------------------------------->|              |
   |              |              | GroupInfo    |              |
   |              |              |<-------------+              |
   |              |              |              |              |
   |              |              | Commit(ExtZ) |              |
   |              |              +---------------------------->|
   |              |              |              | Commit(ExtZ) |
   |<----------------------------------------------------------+
   |              |<-------------------------------------------+
   |              |              |<----------------------------+
   |              |              |              |              |

       Figure 6: Client A publishes a GroupInfo object, and Client Z
                         uses it to join the group

3.4.  Relationships between Epochs

   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.  A group member that wishes to inject a PSK
   issues a PreSharedKey proposal (Section 12.1.4) describing the PSK to
   be injected.  When this proposal is committed, the corresponding PSK
   will be incorporated into the key schedule as described in
   Section 8.4.

   Linking epochs in this way 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.

   MLS supports two ways to tie a new group to an existing group, which
   are illustrated in Figures 7 and 8.  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.

   epoch_A_[n-1]
        |
        |
        |<-- ReInit
        |
        V
   epoch_A_[n]           epoch_B_[0]
        .                     |
        .  PSK(usage=reinit)  |
        .....................>|
                              |
                              V
                         epoch_B_[1]

                      Figure 7: Reinitializing a Group

   epoch_A_[n]           epoch_B_[0]
        |                     |
        |  PSK(usage=branch)  |
        |....................>|
        |                     |
        V                     V
   epoch_A_[n+1]         epoch_B_[1]

                        Figure 8: Branching a Group

   Applications may also choose to use resumption PSKs to link epochs in
   other ways.  For example, Figure 9 shows a case where a resumption
   PSK from epoch n is injected into epoch n+k.  This demonstrates that
   the members of the group at epoch n+k were also members at epoch n,
   irrespective of any changes to these members' keys due to Updates or
   Commits.

   epoch_A_[n]
        |
        |  PSK(usage=application)
        |.....................
        |                    .
        |                    .
       ...                  ...
        |                    .
        |                    .
        V                    .
   epoch_A_[n+k-1]           .
        |                    .
        |                    .
        |<....................
        |
        V
   epoch_A_[n+k]

            Figure 9: Reinjecting Entropy from an Earlier Epoch

4.  Ratchet Tree Concepts

   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.

   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 to subtrees, 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).

   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.

4.1.  Ratchet Tree Terminology

   Trees consist of _nodes_. A node is a _leaf_ if it has no children;
   otherwise, it is a _parent_. All parents in our trees have precisely
   two children, a _left_ child and a _right_ child.  A node is the
   _root_ of a tree if it has no parent, and _intermediate_ if it has
   both children and a parent.  The _descendants_ of a node are that
   node's children, and the descendants of its children.  We say a tree
   _contains_ 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
   _siblings_ if they share the same parent.

   A _subtree_ of a tree is the tree given by any node (the _head_ of
   the subtree) and its descendants.  The _size_ of a tree or subtree is
   the number of leaf nodes it contains.  For a given parent node, its
   _left subtree_ is the subtree with its left child as head and its
   _right subtree_ is the subtree with its right child as head.

   Every tree used in this protocol is a perfect binary tree, that is, a
   complete balanced binary tree with 2^d leaves all at the same depth
   d.  This structure is unique for a given depth d.

   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.  Appendices C and D 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.

4.1.1.  Ratchet Tree Nodes

   Each leaf node in a ratchet tree is given an _index_ (or _leaf
   index_), starting at 0 from the left to 2^d - 1 at the right (for a
   tree with 2^d leaves).  A tree with 2^d leaves has 2^(d+1) - 1 nodes,
   including parent nodes.

   Each node in a ratchet tree is either _blank_ (containing no value)
   or it holds an HPKE public key with some associated data:

   *  A public key (for the HPKE scheme in use; see Section 5.1)

   *  A credential (only for leaf nodes; see Section 5.3)

   *  An ordered list of "unmerged" leaves (see Section 4.2)

   *  A hash of certain information about the node's parent, as of the
      last time the node was changed (see Section 7.9).

   As described in Section 4.2, different members know different subsets
   of the set of private keys corresponding to the public keys in nodes
   in the tree.  The private key corresponding to a parent node is known
   only to members at leaf nodes that are descendants of that node.  The
   private key corresponding to a leaf node is known only to the member
   at that leaf node.  A leaf node is _unmerged_ relative to one of its
   ancestor nodes if the member at the leaf node does not know the
   private key corresponding to the ancestor node.

   Every node, regardless of whether the node is blank or populated, has
   a corresponding _hash_ that summarizes the contents of the subtree
   below that node.  The rules for computing these hashes are described
   in Section 7.8.

   The _resolution_ of a node is an ordered list of non-blank nodes that
   collectively cover all non-blank descendants of the node.  The
   resolution of the root contains the set of keys that are collectively
   necessary to encrypt to every node in the group.  The resolution of a
   node is effectively a depth-first, left-first enumeration of the
   nearest non-blank nodes below the node:

   *  The resolution of a non-blank node comprises the node itself,
      followed by its list of unmerged leaves, if any.

   *  The resolution of a blank leaf node is the empty list.

   *  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.

   For example, consider the following subtree, where the _ character
   represents a blank node and unmerged leaves are indicated in square
   brackets:

                  ...
                  /
                 _
           ______|______
          /             \
         X[B]            _
       __|__           __|__
      /     \         /     \
     _       _       Y       _
    / \     / \     / \     / \
   A   B   _   D   E   F   _   H

   0   1   2   3   4   5   6   7

             Figure 10: A Tree with Blanks and Unmerged Leaves

   In this tree, we can see all of the above rules in play:

   *  The resolution of node X is the list [X, B].

   *  The resolution of leaf 2 or leaf 6 is the empty list [].

   *  The resolution of top node is the list [X, B, Y, H].

4.1.2.  Paths through a Ratchet Tree

   The _direct path_ of a root is the empty list.  The direct path of
   any other node is the concatenation of that node's parent along with
   the parent's direct path.

   The _copath_ 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.

   The _filtered direct path_ 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.

   For example, consider the following tree (where blank nodes are
   indicated with _, but also assigned a label for reference):

                 W = root
                 |
           .-----+-----.
          /             \
         _=U             Y
         |               |
       .-+-.           .-+-.
      /     \         /     \
     T       _=V     X       _=Z
    / \     / \     / \     / \
   A   B   _   _   E   F   G   _=H

   0   1   2   3   4   5   6   7

       Figure 11: A Complete Tree with Five Members, with Labels for
                             Blank Parent Nodes

   In this tree, the direct paths, copaths, and filtered direct paths
   for the leaf nodes are as follows:

          +======+=============+=========+======================+
          | Node | Direct path | Copath  | Filtered Direct Path |
          +======+=============+=========+======================+
          | A    | T, U, W     | B, V, Y | T, W                 |
          +------+-------------+---------+----------------------+
          | B    | T, U, W     | A, V, Y | T, W                 |
          +------+-------------+---------+----------------------+
          | E    | X, Y, W     | F, Z, U | X, Y, W              |
          +------+-------------+---------+----------------------+
          | F    | X, Y, W     | E, Z, U | X, Y, W              |
          +------+-------------+---------+----------------------+
          | G    | Z, Y, W     | H, X, U | Y, W                 |
          +------+-------------+---------+----------------------+

                                  Table 2

4.2.  Views of a Ratchet Tree

   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.

   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.

   In particular, MLS maintains the members' views of the tree in such a
   way as to maintain the _tree invariant_:

   |  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.

   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.

   The reverse implication is not true: A member may not know the
   private key of an intermediate node above them.  Such a member has an
   _unmerged_ leaf at the intermediate node.  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 with regard to all of its ancestors when it is first
   added, because the process of adding the leaf does not give it access
   to the private keys for all of the nodes above it in the tree.
   Leaves are "merged" as they receive the private keys for nodes, as
   described in Section 7.4.

   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 _ represents a blank
   node, ? represents an unknown private key, and pk(X) represents the
   public key corresponding to the private key X:

            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

   Note how the tree invariant applies: Each member knows only their own
   leaf, the private key AB is known only to A and B, and the private
   key ABCD is known to all four members.  This also illustrates another
   important point: it is possible for there to be "holes" on the path
   from a member's leaf to the root in which the member knows the key
   both above and below a given node, but not for that node, as in the
   case with D.

5.  Cryptographic Objects

5.1.  Cipher Suites

   Each MLS session uses a single cipher suite that specifies the
   following primitives to be used in group key computations:

   *  HPKE parameters:

      -  A Key Encapsulation Mechanism (KEM)

      -  A Key Derivation Function (KDF)

      -  An Authenticated Encryption with Associated Data (AEAD)
         encryption algorithm

   *  A hash algorithm

   *  A Message Authentication Code (MAC) algorithm

   *  A signature algorithm

   MLS uses HPKE for public key encryption [RFC9180].  The DeriveKeyPair
   function associated to the KEM for the cipher suite 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 [RFC5116]), as opposed to a separate ciphertext and
   tag.

   Cipher suites are represented with the CipherSuite type.  The cipher
   suites are defined in Section 17.1.

5.1.1.  Public Keys

   HPKE public keys are opaque values in a format defined by the
   underlying protocol (see Section 4 of [RFC9180] for more
   information).

   opaque HPKEPublicKey<V>;

   Signature public keys are likewise represented as opaque values in a
   format defined by the cipher suite's signature scheme.

   opaque SignaturePublicKey<V>;

   For cipher suites using the Edwards-curve Digital Signature Algorithm
   (EdDSA) signature schemes (Ed25519 or Ed448), the public key is in
   the format specified in [RFC8032].

   For cipher suites using the Elliptic Curve Digital Signature
   Algorithm (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 [RFC8446].

5.1.2.  Signing

   The signature algorithm specified in a group's cipher suite is the
   mandatory algorithm to be used for signing messages within the group.
   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).

   The signatures used in this document are encoded as specified in
   [RFC8446].  In particular, ECDSA signatures are DER encoded, and
   EdDSA signatures are defined as the concatenation of R and S, as
   specified in [RFC8032].

   To disambiguate different signatures used in MLS, each signed value
   is prefixed by a label as shown below:

   SignWithLabel(SignatureKey, Label, Content) =
       Signature.Sign(SignatureKey, SignContent)

   VerifyWithLabel(VerificationKey, Label, Content, SignatureValue) =
       Signature.Verify(VerificationKey, SignContent, SignatureValue)

   Where SignContent is specified as:

   struct {
       opaque label<V>;
       opaque content<V>;
   } SignContent;

   And its fields are set to:

   label = "MLS 1.0 " + Label;
   content = Content;

   The functions Signature.Sign and Signature.Verify are defined by the
   signature algorithm.  If MLS extensions require signatures by group
   members, they should reuse the SignWithLabel construction, using a
   distinct label.  To avoid collisions in these labels, an IANA
   registry is defined in Section 17.6.

5.1.3.  Public Key Encryption

   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:

   EncryptWithLabel(PublicKey, Label, Context, Plaintext) =
     SealBase(PublicKey, EncryptContext, "", Plaintext)

   DecryptWithLabel(PrivateKey, Label, Context, KEMOutput, Ciphertext) =
     OpenBase(KEMOutput, PrivateKey, EncryptContext, "", Ciphertext)

   Where EncryptContext is specified as:

   struct {
     opaque label<V>;
     opaque context<V>;
   } EncryptContext;

   And its fields are set to:

   label = "MLS 1.0 " + Label;
   context = Context;

   The functions SealBase and OpenBase are defined in Section 6.1 of
   [RFC9180] (with "Base" as the MODE), using the HPKE algorithms
   specified by the group's cipher suite.  If MLS extensions require
   HPKE encryption operations, they should reuse the EncryptWithLabel
   construction, using a distinct label.  To avoid collisions in these
   labels, an IANA registry is defined in Section 17.7.

5.2.  Hash-Based Identifiers

   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:

   opaque HashReference<V>;

   HashReference KeyPackageRef;
   HashReference ProposalRef;

   MakeKeyPackageRef(value)
     = RefHash("MLS 1.0 KeyPackage Reference", value)

   MakeProposalRef(value)
     = RefHash("MLS 1.0 Proposal Reference", value)

   RefHash(label, value) = Hash(RefHashInput)

   Where RefHashInput is defined as:

   struct {
     opaque label<V>;
     opaque value<V>;
   } RefHashInput;

   And its fields are set to:

   label = label;
   value = value;

   For a KeyPackageRef, the value input is the encoded KeyPackage, and
   the cipher suite specified in the KeyPackage determines the KDF used.
   For a ProposalRef, the value input is the AuthenticatedContent
   carrying the Proposal.  In the latter two cases, the KDF is
   determined by the group's cipher suite.

5.3.  Credentials

   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.

   It is up to the application to decide which 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 [RFC6125], a credential
   provides "presented identifiers", and it is up to the application to
   supply a "reference identifier" for the authenticated client, if any.

   // See the "MLS Credential Types" IANA registry for 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 certificates<V>;
       };
   } Credential;

   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.

   For an X.509 credential, each entry in the certificates field
   represents a single DER-encoded X.509 certificate.  The chain is
   ordered such that the first entry (certificates[0]) is the end-entity
   certificate.  The public key encoded in the subjectPublicKeyInfo of
   the end-entity certificate MUST be identical to the signature_key in
   the LeafNode containing this credential.  A chain MAY omit any non-
   leaf certificates that supported peers are known to already possess.

5.3.1.  Credential Validation

   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 [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.

   The parts of the system that perform these functions are collectively
   referred to as the Authentication Service (AS) [MLS-ARCH].  A
   member's credential is said to be _validated with the AS_ when the AS
   verifies that the credential's presented identifiers are correctly
   associated with the signature_key field in the member's LeafNode, and
   that those identifiers match the reference identifiers for the
   member.

   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:

   *  When a member receives a KeyPackage that it will use in an Add
      proposal to add a new member to the group

   *  When a member receives a GroupInfo object that it will use to join
      a group, either via a Welcome or via an external Commit

   *  When a member receives an Add proposal adding a member to the
      group

   *  When a member receives an Update proposal whose LeafNode has a new
      credential for the member

   *  When a member receives a Commit with an UpdatePath whose LeafNode
      has a new credential for the committer

   *  When an external_senders extension is added to the group

   *  When an existing external_senders extension is updated

   In cases where a member's credential is being replaced, such as the
   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.

5.3.2.  Credential Expiry and Revocation

   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 notAfter field, expressing a time after which the
   certificate is not valid.

   Expired credentials can cause operational problems in light of the
   validation requirements of Section 5.3.1.  Applications can apply
   some operational practices and adaptations to Authentication Service
   policies to moderate these impacts.

   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.

   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.

   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.

   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.

   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., by removing members with
   revoked credentials while allowing members with expired credentials
   time to update.

5.3.3.  Uniquely Identifying Clients

   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.

   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.

   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.

   If needed, applications may add application-specific identifiers to
   the extensions field of a LeafNode object with the application_id
   extension.

   opaque application_id<V>;

   However, applications MUST NOT rely on the data in an application_id
   extension as if it were authenticated by the Authentication Service,
   and SHOULD gracefully handle cases where the identifier presented is
   not unique.

6.  Message Framing

   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.

   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 Section 6.1).  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 a 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 a PublicMessage or PrivateMessage into an
   AuthenticatedContent object.

   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 they MAY transmit handshake messages encoded
   as PublicMessage objects in cases where it is necessary for the
   Delivery Service to examine such messages.

   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 the "MLS Wire Formats" IANA registry for 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_public_message:
               PublicMessage public_message;
           case mls_private_message:
               PrivateMessage private_message;
           case mls_welcome:
               Welcome welcome;
           case mls_group_info:
               GroupInfo group_info;
           case mls_key_package:
               KeyPackage key_package;
       };
   } MLSMessage;

   Messages from senders that aren't in the group are sent as
   PublicMessage.  See Sections 12.1.8 and 12.4.3.2 for more details.

   The following structure is used to fully describe the data
   transmitted in plaintexts or ciphertexts.

   struct {
       WireFormat wire_format;
       FramedContent content;
       FramedContentAuthData auth;
   } AuthenticatedContent;

   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:

       Proposal        Commit     Application Data
          |              |              |
          +--------------+--------------+
                         |
                         V
                  FramedContent
                      |  |                -.
             +--------+  |                  |
             |           |                  |
             V           |                  +-- Asymmetric
   FramedContentAuthData |                  |   Sign / Verify
             |           |                  |
             +--------+  |                  |
                      |  |                  |
                      V  V                -'
                AuthenticatedContent
                         |                -.
                +--------+--------+         |
                |                 |         +-- Symmetric
                V                 V         |   Protect / Unprotect
          PublicMessage    PrivateMessage -'
                |                 |
                |                 |  Welcome  KeyPackage  GroupInfo
                |                 |     |          |          |
                +-----------------+-----+----------+----------+
                                  |
                                  V
                              MLSMessage

                 Figure 12: Relationships among MLS Objects

6.1.  Content Authentication

   FramedContent is authenticated using the FramedContentAuthData
   structure.

   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;

   The signature is computed using SignWithLabel with label
   "FramedContentTBS" and with a content that covers the message content
   and the wire format that will be used for this message.  If the
   sender's sender_type is member, the content also covers the
   GroupContext for the current epoch so that signatures are specific to
   a given group and epoch.

   The sender MUST use the private key corresponding to the following
   signature key depending on the sender's sender_type:

   *  member: The signature key contained in the LeafNode at the index
      indicated by leaf_index in the ratchet tree.

   *  external: The signature key at the index indicated by sender_index
      in the external_senders group context extension (see
      Section 12.1.8.1).  The content_type of the message MUST be
      proposal and the proposal_type MUST be a value that is allowed for
      external senders.

   *  new_member_commit: The signature key in the LeafNode in the
      Commit's path (see Section 12.4.3.2).  The content_type of the
      message MUST be commit.

   *  new_member_proposal: The signature key in the LeafNode in the
      KeyPackage embedded in an external Add proposal.  The content_type
      of the message MUST be proposal and the proposal_type of the
      Proposal MUST be add.

   Recipients of an MLSMessage MUST verify the signature with the key
   depending on the sender_type of the sender as described above.

   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 signature and confirmation_tag
   fields are valid.

6.2.  Encoding and Decoding a Public Message

   Messages that are authenticated but not encrypted are encoded using
   the PublicMessage structure.

   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;

   The membership_tag 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:

   struct {
     FramedContentTBS content_tbs;
     FramedContentAuthData auth;
   } AuthenticatedContentTBM;

   membership_tag = MAC(membership_key, AuthenticatedContentTBM)

   When decoding a PublicMessage into an AuthenticatedContent, the
   application MUST check membership_tag and MUST check that the
   FramedContentAuthData is valid.

6.3.  Encoding and Decoding a Private Message

   Authenticated and encrypted messages are encoded using the
   PrivateMessage structure.

   struct {
       opaque group_id<V>;
       uint64 epoch;
       ContentType content_type;
       opaque authenticated_data<V>;
       opaque encrypted_sender_data<V>;
       opaque ciphertext<V>;
   } PrivateMessage;

   encrypted_sender_data and ciphertext are encrypted using the AEAD
   function specified by the cipher suite in use, using the SenderData
   and PrivateMessageContent structures as input.

6.3.1.  Content Encryption

   Content to be encrypted is encoded in a PrivateMessageContent
   structure.

   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];
   } PrivateMessageContent;

   The padding field is set by the sender, by first encoding the content
   (via the select) and the auth field, and then appending the chosen
   number of zero bytes.  A receiver identifies the padding field in a
   plaintext decoded from PrivateMessage.ciphertext by first decoding
   the content and the auth field; then the padding field comprises any
   remaining octets of plaintext.  The padding field MUST be filled with
   all zero bytes.  A receiver MUST verify that there are no non-zero
   bytes in the padding 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.

   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 ratchet or the application ratchet, depending on
   the content type of the message.  This generation of the ratchet is
   used to derive a provisional nonce and key.

   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.

   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
   reuse_guard 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.

   +-+-+-+-+---------...---+
   |   Key Schedule Nonce  |
   +-+-+-+-+---------...---+
              XOR
   +-+-+-+-+---------...---+
   | Guard |       0       |
   +-+-+-+-+---------...---+
              ===
   +-+-+-+-+---------...---+
   | Encrypt/Decrypt Nonce |
   +-+-+-+-+---------...---+

   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:

   struct {
       opaque group_id<V>;
       uint64 epoch;
       ContentType content_type;
       opaque authenticated_data<V>;
   } PrivateContentAAD;

   When decoding a PrivateMessageContent, the application MUST check
   that the FramedContentAuthData is valid.

   It is up to the application to decide what authenticated_data 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 [CFRG-AEAD-LIMITS].

6.3.2.  Sender Data Encryption

   The "sender data" used to look up the key for content encryption is
   encrypted with the cipher suite's AEAD with a key and nonce derived
   from both the sender_data_secret and a sample of the encrypted
   content.  Before being encrypted, the sender data is encoded as an
   object of the following form:

   struct {
       uint32 leaf_index;
       uint32 generation;
       opaque reuse_guard[4];
   } SenderData;

   When constructing a SenderData object from a Sender object, the
   sender MUST verify Sender.sender_type is member and use
   Sender.leaf_index for SenderData.leaf_index.

   The reuse_guard field contains a fresh random value used to avoid
   nonce reuse in the case of state loss or corruption, as described in
   Section 6.3.1.

   The key and nonce provided to the AEAD are computed as the KDF of the
   first KDF.Nh bytes of the ciphertext generated in the previous
   section.  If the length of the ciphertext is less than KDF.Nh, the
   whole ciphertext is used.  In pseudocode, the key and nonce are
   derived as:

   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)

   The AAD for the SenderData ciphertext is the first three fields of
   PrivateMessage:

   struct {
       opaque group_id<V>;
       uint64 epoch;
       ContentType content_type;
   } SenderDataAAD;

   When parsing a SenderData struct as part of message decryption, the
   recipient MUST verify that the leaf index indicated in the leaf_index
   field identifies a non-blank node.

7.  Ratchet Tree Operations

   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.

7.1.  Parent Node Contents

   As discussed in Section 4.1.1, 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:

   struct {
       HPKEPublicKey encryption_key;
       opaque parent_hash<V>;
       uint32 unmerged_leaves<V>;
   } ParentNode;

   The encryption_key field contains an HPKE public key whose private
   key is held only by the members at the leaves among its descendants.
   The parent_hash field contains a hash of this node's parent node, as
   described in Section 7.9.  The unmerged_leaves 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 unmerged_leaves
   vector MUST be sorted in increasing order.

7.2.  Leaf Node Contents

   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.

   enum {
       reserved(0),
       key_package(1),
       update(2),
       commit(3),
       (255)
   } LeafNodeSource;

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

   struct {
       uint64 not_before;
       uint64 not_after;
   } Lifetime;

   // See the "MLS Extension Types" IANA registry for 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;

   The encryption_key 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 signature_key field contains the member's public signing key.
   The credential field contains information authenticating both the
   member's identity and the provided signing key, as described in
   Section 5.3.

   The capabilities field indicates the protocol features that the
   client supports, including protocol versions, cipher suites,
   credential types, non-default proposal types, and non-default
   extension types.  The following proposal and extension types are
   considered "default" and MUST NOT be listed:

   *  Proposal types:

      -  0x0001 - add

      -  0x0002 - update

      -  0x0003 - remove

      -  0x0004 - psk

      -  0x0005 - reinit

      -  0x0006 - external_init

      -  0x0007 - group_context_extensions

   *  Extension types:

      -  0x0001 - application_id

      -  0x0002 - ratchet_tree

      -  0x0003 - required_capabilities

      -  0x0004 - external_pub

      -  0x0005 - external_senders

   There are no default values for the other fields of a capabilities
   object.  The client MUST list all values for the respective
   parameters that it supports.

   The types of any non-default extensions that appear in the extensions
   field of a LeafNode MUST be included in the extensions field of the
   capabilities field, and the credential type used in the LeafNode MUST
   be included in the credentials field of the capabilities field.

   As discussed in Section 13, unknown values in capabilities MUST be
   ignored, and the creator of a capabilities field SHOULD include some
   random GREASE values to help ensure that other clients correctly
   ignore unknown values.

   The leaf_node_source 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 lifetime or parent_hash,
   and whether the group_id is added as context to the signature.  These
   fields are included selectively because the client creating a
   LeafNode is not always able to compute all of them.  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 group_id.

   In the case where the leaf was added to the tree based on a pre-
   published KeyPackage, the lifetime 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.  In
   order to avoid disagreements about whether a LeafNode has a valid
   lifetime, the clients in a group SHOULD maintain time synchronization
   (e.g., using the Network Time Protocol [RFC5905]).

   In the case where the leaf node was inserted into the tree via a
   Commit message, the parent_hash field contains the parent hash for
   this leaf node (see Section 7.9).

   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.

   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.

7.3.  Leaf Node Validation

   The validity of a LeafNode needs to be verified at the following
   stages:

   *  When a LeafNode is downloaded in a KeyPackage, before it is used
      to add the client to the group

   *  When a LeafNode is received by a group member in an Add, Update,
      or Commit message

   *  When a client validates a ratchet tree, e.g., when joining a group
      or after processing a Commit

   The client verifies the validity of a LeafNode using the following
   steps:

   *  Verify that the credential in the LeafNode is valid, as described
      in Section 5.3.1.

   *  Verify that the signature on the LeafNode is valid using
      signature_key.

   *  Verify that the LeafNode is compatible with the group's
      parameters.  If the GroupContext has a required_capabilities
      extension, then the required extensions, proposals, and credential
      types MUST be listed in the LeafNode's capabilities field.

   *  Verify that the credential type is supported by all members of the
      group, as specified by the capabilities field of each member's
      LeafNode, and that the capabilities field of this LeafNode
      indicates support for all the credential types currently in use by
      other members.

   *  Verify the lifetime field:

      -  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 lifetime field.

      -  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 lifetime field.  (This check is not mandatory because the
         LeafNode might have expired in the time between when the
         message was sent and when it was received.)

   *  Verify that the extensions in the LeafNode are supported by
      checking that the ID for each extension in the extensions field is
      listed in the capabilities.extensions field of the LeafNode.

   *  Verify the leaf_node_source field:

      -  If the LeafNode appears in a KeyPackage, verify that
         leaf_node_source is set to key_package.

      -  If the LeafNode appears in an Update proposal, verify that
         leaf_node_source is set to update and that encryption_key
         represents a different public key than the encryption_key in
         the leaf node being replaced by the Update proposal.

      -  If the LeafNode appears in the leaf_node value of the
         UpdatePath in a Commit, verify that leaf_node_source is set to
         commit.

   *  Verify that the following fields are unique among the members of
      the group:

      -  signature_key

      -  encryption_key

7.4.  Ratchet Tree Evolution

   Whenever a member initiates an epoch change (i.e., commits; see
   Section 12.4), 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.

   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 Section 7.6.

   A member updates the nodes along its direct path as follows:

   *  Blank all the nodes on the direct path from the leaf to the root.

   *  Generate a fresh HPKE key pair for the leaf.

   *  Generate a sequence of path secrets, one for each node on the
      leaf's filtered direct path, as follows.  In this setting,
      path_secret[0] refers to the first parent node in the filtered
      direct path, path_secret[1] to the second parent node, and so on.

   path_secret[0] is sampled at random
   path_secret[n] = DeriveSecret(path_secret[n-1], "path")

   *  Compute the sequence of HPKE key pairs (node_priv,node_pub), one
      for each node on the leaf's direct path, as follows.

   node_secret[n] = DeriveSecret(path_secret[n], "node")
   node_priv[n], node_pub[n] = KEM.DeriveKeyPair(node_secret[n])

   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.

   For example, suppose there is a group with four members, with C an
   unmerged leaf at Z:

         Y
         |
       .-+-.
      /     \
     X       Z[C]
    / \     / \
   A   B   C   D

   0   1   2   3

               Figure 13: A Full Tree with One Unmerged Leaf

   If member B subsequently generates an UpdatePath based on a secret
   "leaf_secret", then it would generate the following sequence of path
   secrets:

   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

       Figure 14: Derivation of Ratchet Tree Keys along a Direct Path

   After applying the UpdatePath, the tree will have the following
   structure:

   node_priv[1] --------> Y'
                          |
                        .-+-.
                       /     \
   node_priv[0] ----> X'      Z[C]
                     / \     / \
                    A   B   C   D
                        ^
   leaf_priv -----------+
                    0   1   2   3

               Figure 15: Placement of Keys in a Ratchet Tree

7.5.  Synchronizing Views of the Tree

   After generating fresh key material and applying it to update their
   local tree state as described in Section 7.4, 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.

   An UpdatePath contains the following information for each node in the
   filtered direct path of the sender's leaf, including the root:

   *  The public key for the node

   *  One or more encrypted copies of the path secret corresponding to
      the node

   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.

   A member of the group _updates their direct path_ by computing new
   values for their leaf node and the nodes along their filtered direct
   path as follows:

   1.  Blank all nodes along the direct path of the sender's leaf.

   2.  Compute updated path secrets and public keys for the nodes on the
       sender's filtered direct path.

       *  Generate a sequence of path secrets of the same length as the
          filtered direct path, as defined in Section 7.4.

       *  For each node in the filtered direct path, replace the node's
          public key with the node_pub[n] value derived from the
          corresponding path secret path_secret[n].

   3.  Compute the new parent hashes for the nodes along the filtered
       direct path and the sender's leaf node.

   4.  Update the leaf node for the sender.

       *  Set the leaf_node_source to commit.

       *  Set the encryption_key to the public key of a freshly sampled
          key pair.

       *  Set the parent hash to the parent hash for the leaf.

       *  Re-sign the leaf node with its new contents.

   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 Update proposals (aside from leaf_node_source).  The application
   MAY specify other changes to the leaf node, e.g., providing a new
   signature key, updated capabilities, or different extensions.

   The member then _encrypts path secrets to the group_.  For each node
   in the member's filtered direct path, the member takes the following
   steps:

   1.  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.

   2.  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 Section 7.6.

   The recipient of an UpdatePath performs the corresponding steps.
   First, the recipient _merges UpdatePath into the tree_:

   1.  Blank all nodes on the direct path of the sender's leaf.

   2.  For all nodes on the filtered direct path of the sender's leaf,

       *  Set the public key to the public key in the UpdatePath.

       *  Set the list of unmerged leaves to the empty list.

   3.  Compute parent hashes for the nodes in the sender's filtered
       direct path, and verify that the parent_hash field of the leaf
       node matches the parent hash for the first node in its filtered
       direct path.

       *  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.

   Second, the recipient _decrypts the path secrets_:

   1.  Identify a node in the filtered direct path for which the
       recipient is in the subtree of the non-updated child.

   2.  Identify a node in the resolution of the copath node for which
       the recipient has a private key.

   3.  Decrypt the path secret for the parent of the copath node using
       the private key from the resolution node.

   4.  Derive path secrets for ancestors of that node in the sender's
       filtered direct path using the algorithm described above.

   5.  Derive the node secrets and node key pairs from the path secrets.

   6.  Verify that the derived public keys are the same as the
       corresponding public keys sent in the UpdatePath.

   7.  Store the derived private keys in the corresponding ratchet tree
       nodes.

   For example, in order to communicate the example update described in
   Section 7.4, the member at node B would transmit the following
   values:

   +=============+====================================================+
   | Public Key  | Ciphertext(s)                                      |
   +=============+====================================================+
   | node_pub[1] | E(pk(Z), path_secret[1]), E(pk(C), path_secret[1]) |
   +-------------+----------------------------------------------------+
   | node_pub[0] | E(pk(A), path_secret[0])                           |
   +-------------+----------------------------------------------------+

                                 Table 3

   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).

   A recipient at node A would decrypt E(pk(A), path_secret\[0\]) to
   obtain path_secret\[0\], then use it to derive path_secret[1] 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.

   Similarly, a recipient at node D would decrypt E(pk(Z),
   path_secret[1]) to obtain path_secret[1], then use it to derive the
   node secret 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.

   After processing the update, each recipient MUST delete outdated key
   material, specifically:

   *  The path secrets and node secrets used to derive each updated node
      key pair.

   *  Each outdated node key pair that was replaced by the update.

7.6.  Update Paths

   As described in Section 12.4, 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.

   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;

   For each UpdatePathNode, the resolution of the corresponding copath
   node MUST exclude all new leaf nodes added as part of the current
   Commit.  The length of the encrypted_path_secret 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.

   The HPKECiphertext values are encrypted and decrypted as follows:

   (kem_output, ciphertext) =
     EncryptWithLabel(node_public_key, "UpdatePathNode",
                      group_context, path_secret)

   path_secret =
     DecryptWithLabel(node_private_key, "UpdatePathNode",
                      group_context, kem_output, ciphertext)

   Here node_public_key is the public key of the node for which the path
   secret is encrypted, group_context is the provisional GroupContext
   object for the group, and the EncryptWithLabel function is as defined
   in Section 5.1.3.

7.7.  Adding and Removing Leaves

   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 Sections 12.1.1
   and 12.1.3).  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 _extending_ and _truncating_ the tree.

   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.

                     _ <-- new blank root                    _
                   __|__                                   __|__
                  /     \                                 /     \
     X    ===>   X       _ <-- new blank subtree ===>    X       _
    / \         / \     / \                             / \     / \
   A   B       A   B   _   _                           A   B   C   _
                                                               ^
                                                               |
                                                  new member --+

       Figure 16: Extending the Tree to Make Room for a Third Member

   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.

                  Y                  Y
                __|__              __|__
               /     \            /     \
              X       _   ===>   X       _   ==>   X <-- new root
             / \     / \        / \     / \       / \
            A   B   C   _      A   B   _   _     A   B
                    ^
                    |
   removed member --+

               Figure 17: Cleaning Up after Removing Member C

   Concrete algorithms for these operations on array-based and link-
   based trees are provided in Appendices C and D.  The concrete
   algorithms are non-normative.  An implementation may use any
   algorithm that produces the correct tree in its internal
   representation.

7.8.  Tree Hashes

   MLS hashes the contents of the tree in two ways to authenticate
   different properties of the tree.  _Tree hashes_ are defined in this
   section, and _parent hashes_ are defined in Section 7.9.

   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.

   P --> th(P)
         ^ ^
        /   \
       /     \
   th(L)     th(R)

                  Figure 18: Composition of the Tree Hash

   The tree hash of an individual node is the hash of the node's
   TreeHashInput object, which may contain either a LeafNodeHashInput or
   a ParentNodeHashInput depending on the type of node.
   LeafNodeHashInput objects contain the leaf_index and the LeafNode (if
   any).  ParentNodeHashInput objects contain the ParentNode (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.

   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;

   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.

7.9.  Parent Hashes

   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.

   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
   Section 7.5), 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.

                        ph(Q)
                        /
                       /
                      V
   P.public_key --> ph(P)
                    / ^
                   /   \
                  V     \
      N.parent_hash     th(S)

                     Figure 19: Inputs to a Parent Hash

   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 Appendix B.

   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"):

            ...
            /
           P
         __|__
        /     \
       D       S
      / \     / \
    ... ... ... ...
    /
   L

           Figure 20: Nodes Involved in a Parent Hash Computation

   The parent hash of P changes whenever an UpdatePath 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 ParentHashInput struct.

   struct {
       HPKEPublicKey encryption_key;
       opaque parent_hash<V>;
       opaque original_sibling_tree_hash<V>;
   } ParentHashInput;

   The field encryption_key contains the HPKE public key of P.  If P is
   the root, then the parent_hash field is set to a zero-length octet
   string.  Otherwise, parent_hash 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.

   Finally, original_sibling_tree_hash is the tree hash of S in the
   ratchet tree modified as follows: For each leaf L in
   P.unmerged_leaves, blank L and remove it from the unmerged_leaves
   sets of all parent nodes.

   Observe that original_sibling_tree_hash does not change between
   updates of P.  This property is crucial for the correctness of the
   protocol.

   Note that original_sibling_tree_hash is the tree hash of S, not the
   parent hash.  The parent_hash field in ParentHashInput captures
   information about the nodes above P. the original_sibling_tree_hash
   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 Section 7.5).

   For example, in the following tree:

                 W [F]
           ______|_____
          /             \
         U               Y [F]
       __|__           __|__
      /     \         /     \
     T       _       _       _
    / \     / \     / \     / \
   A   B   C   D   E   F   G   _

          Figure 21: A Tree Illustrating Parent Hash Computations

   With P = W and S = Y, original_sibling_tree_hash is the tree hash of
   the following tree:

         Y
       __|__
      /     \
     _       _
    / \     / \
   E   _   G   _

   Because W.unmerged_leaves includes F, F is blanked and removed from
   Y.unmerged_leaves.

   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
   P.unmerged_leaves are 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.

   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.

7.9.1.  Using Parent Hashes

   In ParentNode objects and LeafNode objects with leaf_node_source set
   to commit, the value of the parent_hash 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
   Figure 20, the parent_hash 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.

   The parent_hash field of a LeafNode is signed by the member.  The
   signature of such a LeafNode thus attests to which keys the group
   member introduced into the ratchet tree and to whom the corresponding
   secret keys were sent, in addition to the other contents of the
   LeafNode.  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.

7.9.2.  Verifying Parent Hashes

   Parent hashes are verified at two points in the protocol: When
   joining a group and when processing a Commit.

   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 being the other child:

   *  D is a descendant of P in the tree.

   *  The parent_hash field of D is equal to the parent hash of P with
      copath child S.

   *  D is in the resolution of C, and the intersection of P's
      unmerged_leaves with the subtree under C is equal to the
      resolution of C with D removed.

   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.

   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, then 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.

   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.

   When processing a Commit message that includes an UpdatePath, clients
   MUST recompute the expected value of parent_hash for the committer's
   new leaf and verify that it matches the parent_hash value in the
   supplied leaf_node.  After being merged into the tree, the nodes in
   the UpdatePath form a parent-hash chain from the committer's leaf to
   the root.

8.  Key Schedule

   Group keys are derived using the Extract and Expand functions from
   the KDF for the group's cipher suite, as well as the functions
   defined below:

   ExpandWithLabel(Secret, Label, Context, Length) =
       KDF.Expand(Secret, KDFLabel, Length)

   DeriveSecret(Secret, Label) =
       ExpandWithLabel(Secret, Label, "", KDF.Nh)

   Where KDFLabel is specified as:

   struct {
       uint16 length;
       opaque label<V>;
       opaque context<V>;
   } KDFLabel;

   And its fields are set to:

   length = Length;
   label = "MLS 1.0 " + Label;
   context = Context;

   The value KDF.Nh is the size of an output from KDF.Extract, in bytes.
   In the below diagram:

   *  KDF.Extract takes its salt argument from the top and its Input
      Keying Material (IKM) argument from the left.

   *  DeriveSecret takes its Secret argument from the incoming arrow.

   *  0 represents an all-zero byte string of length KDF.Nh.

   When processing a handshake message, a client combines the following
   information to derive new epoch secrets:

   *  The init secret from the previous epoch

   *  The commit secret for the current epoch

   *  The GroupContext object for current epoch

   Given these inputs, the derivation of secrets for an epoch proceeds
   as shown in the following diagram:

                    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]

                   Figure 22: The MLS Key Schedule

   A number of values are derived from the epoch secret for different
   purposes:

    +==================+=====================+=======================+
    | Label            | Secret              | Purpose               |
    +==================+=====================+=======================+
    | "sender data"    | sender_data_secret  | Deriving keys to      |
    |                  |                     | encrypt sender data   |
    +------------------+---------------------+-----------------------+
    | "encryption"     | encryption_secret   | Deriving message      |
    |                  |                     | encryption keys (via  |
    |                  |                     | the secret tree)      |
    +------------------+---------------------+-----------------------+
    | "exporter"       | exporter_secret     | Deriving exported     |
    |                  |                     | secrets               |
    +------------------+---------------------+-----------------------+
    | "external"       | external_secret     | Deriving the external |
    |                  |                     | init key              |
    +------------------+---------------------+-----------------------+
    | "confirm"        | confirmation_key    | Computing the         |
    |                  |                     | confirmation MAC for  |
    |                  |                     | an epoch              |
    +------------------+---------------------+-----------------------+
    | "membership"     | membership_key      | Computing the         |
    |                  |                     | membership MAC for a  |
    |                  |                     | PublicMessage         |
    +------------------+---------------------+-----------------------+
    | "resumption"     | resumption_psk      | Proving membership in |
    |                  |                     | this epoch (via a PSK |
    |                  |                     | injected later)       |
    +------------------+---------------------+-----------------------+
    | "authentication" | epoch_authenticator | Confirming that two   |
    |                  |                     | clients have the same |
    |                  |                     | view of the group     |
    +------------------+---------------------+-----------------------+

                      Table 4: Epoch-Derived Secrets

   The external_secret is used to derive an HPKE key pair whose private
   key is held by the entire group:

   external_priv, external_pub = KEM.DeriveKeyPair(external_secret)

   The public key external_pub can be published as part of the GroupInfo
   struct in order to allow non-members to join the group using an
   external Commit.

8.1.  Group Context

   Each member of the group maintains a GroupContext object that
   summarizes the state of the group:

   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;

   The fields in this state have the following semantics:

   *  The cipher_suite is the cipher suite used by the group.

   *  The group_id field is an application-defined identifier for the
      group.

   *  The epoch field represents the current version of the group.

   *  The tree_hash 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 Section 7.8.

   *  The confirmed_transcript_hash field contains a running hash over
      the messages that led to this state.

   *  The extensions field contains the details of any protocol
      extensions that apply to the group.

   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.

   Different changes to the group will have different effects on the
   group state.  These effects are described in their respective
   subsections of Section 12.1.  The following general rules apply:

   *  The group_id field is constant.

   *  The epoch field increments by one for each Commit message that is
      processed.

   *  The tree_hash is updated to represent the current tree and
      credentials.

   *  The confirmed_transcript_hash field is updated with the data for
      an AuthenticatedContent encoding a Commit message, as described
      below.

   *  The extensions field changes when a GroupContextExtensions
      proposal is committed.

8.2.  Transcript Hashes

   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.  Messages of
   both types are included by hashing the AuthenticatedContent object in
   which they were sent.

   The transcript hash comprises two individual hashes:

   *  A confirmed_transcript_hash that represents a transcript over the
      whole history of Commit messages, up to and including the
      signature of the most recent Commit.

   *  An interim_transcript_hash that covers the confirmed transcript
      hash plus the confirmation_tag of the most recent Commit.

   New members compute the interim transcript hash using the
   confirmation_tag field of the GroupInfo struct, while existing
   members can compute it directly.

   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
   is used to update the interim transcript hash.

   struct {
       WireFormat wire_format;
       FramedContent content; /* with content_type == commit */
       opaque signature<V>;
   } ConfirmedTranscriptHashInput;

   struct {
       MAC confirmation_tag;
   } InterimTranscriptHashInput;

   confirmed_transcript_hash_[0] = ""; /* zero-length octet string */
   interim_transcript_hash_[0] = ""; /* zero-length octet string */

   confirmed_transcript_hash_[epoch] =
       Hash(interim_transcript_hash_[epoch - 1] ||
           ConfirmedTranscriptHashInput_[epoch]);

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

   In this notation, ConfirmedTranscriptHashInput_[epoch] and
   InterimTranscriptHashInput_[epoch] are based on the Commit that
   initiated the epoch with epoch number epoch.  (Note that
   theepochfield in this Commit will be set toepoch - 1`, since it is
   sent within the previous epoch.)

   The transcript hash ConfirmedTranscriptHashInput_[epoch] is used as
   the confirmed_transcript_hash input to the confirmation_tag field for
   this Commit.  Each Commit thus confirms the whole transcript of
   Commits up to that point, except for the latest Commit's confirmation
   tag.

                                                             ...

                                                              |
                                                              |
                                                              V
                                                     +-----------------+
                                                     |  interim_[N-1]  |
                                                     +--------+--------+
                                                              |
     .--------------.         +------------------+            |
    |  Ratchet Tree  |        | wire_format      |            |
    |  Key Schedule  |<-------+ content          |            |
     '-------+------'         |   epoch = N-1    +------------+
             |                |   commit         |            |
             V                | signature        |            V
 +------------------------+   +------------------+   +-----------------+
 |  confirmation_key_[N]  +-->| confirmation_tag |<--+  confirmed_[N]  |
 +------------------------+   +--------+---------+   +--------+--------+
                                       |                      |
                                       |                      V
                                       |             +-----------------+
                                       +------------>|   interim_[N]   |
                                                     +--------+--------+
                                                              |
     .--------------.         +------------------+            |
    |  Ratchet Tree  |        | wire_format      |            |
    |  Key Schedule  |<-------+ content          |            |
     '-------+------'         |   epoch = N      +------------+
             |                |   commit         |            |
             V                | signature        |            V
 +------------------------+   +------------------+   +-----------------+
 | confirmation_key_[N+1] +-->| confirmation_tag |<--+ confirmed_[N+1] |
 +------------------------+   +--------+---------+   +--------+--------+
                                       |                      |
                                       |                      V
                                       |             +-----------------+
                                       +------------>|  interim_[N+1]  |
                                                     +--------+--------+
                                                              |
                                                              V

                                                             ...

   Figure 23: Evolution of the Transcript Hashes through Two Epoch
                               Changes

8.3.  External Initialization

   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 a new member is joining via an external
   commit.

   In this process, the joiner sends a new init_secret value to the
   group using the HPKE export method.  The joiner then uses that
   init_secret with information provided in the GroupInfo and an
   external Commit to initialize their copy of the key schedule for the
   new epoch.

   kem_output, context = SetupBaseS(external_pub, "")
   init_secret = context.export("MLS 1.0 external init secret", KDF.Nh)

   Members of the group receive the kem_output in an ExternalInit
   proposal and perform the corresponding calculation to retrieve the
   init_secret value.

   context = SetupBaseR(kem_output, external_priv, "")
   init_secret = context.export("MLS 1.0 external init secret", KDF.Nh)

8.4.  Pre-Shared Keys

   Groups that already have an out-of-band mechanism to generate shared
   group secrets can inject them into the MLS key schedule to
   incorporate this external entropy in the computation of MLS group
   secrets.

   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.

   Note that, as a PSK may have a different lifetime than an Update, it
   does not necessarily provide the same forward secrecy or post-
   compromise security 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 they should be considered by application designers
   relying on PSKs.

   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.

   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.

   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;

   Each time a client injects a PSK into a group, the psk_nonce of its
   PreSharedKeyID MUST be set to a fresh random value of length KDF.Nh,
   where KDF is the KDF for the cipher suite 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.

   Upon receiving a Commit with a PreSharedKey proposal or a
   GroupSecrets object with the psks field set, the receiving client
   includes them in the key schedule in the order listed in the Commit,
   or in the psks field, respectively.  For resumption PSKs, the PSK is
   defined as the resumption_psk of the group and epoch specified in the
   PreSharedKeyID object.  Specifically, psk_secret is computed as
   follows:

   struct {
       PreSharedKeyID id;
       uint16 index;
       uint16 count;
   } PSKLabel;

   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]

   Here 0 represents the all-zero vector of length KDF.Nh.  The index
   field in PSKLabel corresponds to the index of the PSK in the psk
   array, while the count 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:

                   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]

        Figure 24: Computation of a PSK Secret from a Set of PSKs

   In particular, if there are no PreSharedKey proposals in a given
   Commit, then the resulting psk_secret is psk_secret_[0], the all-zero
   vector.

8.5.  Exporters

   The main MLS key schedule provides an exporter_secret that can be
   used by an application to derive new secrets for use outside of MLS.

   MLS-Exporter(Label, Context, Length) =
          ExpandWithLabel(DeriveSecret(exporter_secret, Label),
                            "exported", Hash(Context), Length)

   Applications SHOULD provide a unique label to MLS-Exporter 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
   Section 17.8.

   The exported values are bound to the group epoch from which the
   exporter_secret is derived, and hence reflect a particular state of
   the group.

   It is RECOMMENDED for the application generating exported values to
   refresh those values after a Commit is processed.

8.6.  Resumption PSK

   The main MLS key schedule provides a resumption_psk 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 Sections 11.2 and 11.3, but it may be used by
   applications for other purposes.

   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 resumption_psk may be stored.

8.7.  Epoch Authenticators

   The main MLS key schedule provides a per-epoch epoch_authenticator.
   If one member of the group is being impersonated by an active
   attacker, the epoch_authenticator computed by their client will
   differ from those computed by the other group members.

   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 redo this confirmation.  The
   state of the group would have changed, possibly introducing an
   attacker.

   More generally, in order for the members of an MLS group to obtain
   concrete authentication protections using the epoch_authenticator,
   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.

9.  Secret Tree

   For the generation of encryption keys and nonces, the key schedule
   begins with the encryption_secret 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.

   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):

   tree_node_[N]_secret
           |
           |
           +--> ExpandWithLabel(., "tree", "left", KDF.Nh)
           |    = tree_node_[left(N)]_secret
           |
           +--> ExpandWithLabel(., "tree", "right", KDF.Nh)
                = tree_node_[right(N)]_secret

     Figure 25: Derivation of Secrets from Parent to Children within a
                                Secret Tree

   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 Section 9.1.  The root of each
   ratchet is computed as:

   tree_node_[N]_secret
           |
           |
           +--> ExpandWithLabel(., "handshake", "", KDF.Nh)
           |    = handshake_ratchet_secret_[N]_[0]
           |
           +--> ExpandWithLabel(., "application", "", KDF.Nh)
                = application_ratchet_secret_[N]_[0]

     Figure 26: Initialization of the Hash Ratchets from the Leaves of
                               a Secret Tree

9.1.  Encryption Keys

   As described in Section 6, MLS encrypts three different types of
   information:

   *  Metadata (sender information)

   *  Handshake messages (Proposal and Commit)

   *  Application messages

   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 sender_data_secret and a sample of the encrypted message
   content.

   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".

   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.

          G
          |
        .-+-.
       /     \
      E       F
     / \     / \
    A   B   C   D
               / \
             HR0  AR0--+--K0
                   |   |
                   |   +--N0
                   |
                  AR1--+--K1
                   |   |
                   |   +--N1
                   |
                  AR2

               Figure 27: Secret Tree for a Four-Member Group

   A sender ratchet starts from a per-sender base secret derived from a
   Secret Tree, as described in Section 9.  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.

   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.

   DeriveTreeSecret(Secret, Label, Generation, Length) =
       ExpandWithLabel(Secret, Label, Generation, Length)

   Where Generation is encoded as a big endian uint32.

   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]

   Here AEAD.Nn and AEAD.Nk denote the lengths in bytes of the nonce and
   key for the AEAD scheme defined by the cipher suite.

9.2.  Deletion Schedule

   It is important to delete all security-sensitive values as soon as
   they are _consumed_. A sensitive value S is said to be _consumed_ if:

   *  S was used to encrypt or (successfully) decrypt a message, or

   *  a key, nonce, or secret derived from S has been consumed.  (This
      goes for values derived via DeriveSecret as well as
      ExpandWithLabel.)

   Here S may be the init_secret, commit_secret, epoch_secret, or
   encryption_secret as well as any secret in a secret tree or one of
   the ratchets.

   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.

   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:

   *  the commit_secret, joiner_secret, epoch_secret, and
      encryption_secret of that epoch n as well as the init_secret of
      the previous epoch n-1,

   *  all node secrets in the secret tree on the path from the root to
      the leaf with node L,

   *  the first j secrets in the application data ratchet of node L, and

   *  application_ratchet_nonce_[L]_[j] and
      application_ratchet_key_[L]_[j].

   Concretely, consider the secret tree shown in Figure 27.  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:

   *  The key K1 and nonce N1 used to decrypt the message

   *  The application ratchet secrets AR1 and AR0

   *  The tree secrets D, F, and G (recall that G is the
      encryption_secret for the epoch)

   *  The epoch_secret, commit_secret, psk_secret, and joiner_secret for
      the current epoch

   Other values may be retained (not consumed):

   *  K0 and N0 for decryption of an out-of-order message with
      generation 0

   *  AR2 for derivation of further message decryption keys and nonces

   *  HR0 for protection of handshake messages from D

   *  E and C for deriving secrets used by senders A, B, and C

10.  Key Packages

   In order to facilitate the asynchronous addition of clients to a
   group, clients can pre-publish KeyPackage objects that provide some
   public information about a user.  A KeyPackage object specifies:

   1.  a protocol version and cipher suite that the client supports,

   2.  a public key that others can use to encrypt a Welcome message to
       this client (an "init key"), and

   3.  the content of the leaf node that should be added to the tree to
       represent this client.

   KeyPackages are intended to be used only once and SHOULD NOT be
   reused except in the case of a "last resort" KeyPackage (see
   Section 16.8).  Clients MAY generate and publish multiple KeyPackages
   to support multiple cipher suites.

   The value for init_key MUST be a public key for the asymmetric
   encryption scheme defined by cipher_suite, and it MUST be unique
   among the set of KeyPackages created by this client.  Likewise, the
   leaf_node field MUST be valid for the cipher suite, including both
   the encryption_key and signature_key fields.  The whole structure is
   signed using the client's signature key.  A KeyPackage object with an
   invalid signature field MUST be considered malformed.

   The signature is computed by the function SignWithLabel with a label
   "KeyPackageTBS" and a Content input comprising all of the fields
   except for the signature field.

   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;

   If a client receives a KeyPackage carried within an MLSMessage
   object, then it MUST verify that the version field of the KeyPackage
   has the same value as the version field of the MLSMessage.  The
   version 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.

   The field leaf_node.capabilities indicates what protocol versions,
   cipher suites, credential types, and non-default proposal/extension
   types are supported by the client.  (As discussed in Section 7.2,
   some proposal and extension types defined in this document are
   considered "default" and thus are not listed.)  This information
   allows MLS session establishment to be safe from downgrade attacks on
   the parameters described (as discussed in Section 11), while still
   only advertising one version and one cipher suite per KeyPackage.

   The field leaf_node.leaf_node_source of the LeafNode in a KeyPackage
   MUST be set to key_package.

   Extensions included in the extensions or leaf_node.extensions fields
   MUST be included in the leaf_node.capabilities field.  As discussed
   in Section 13, unknown extensions in KeyPackage.extensions MUST be
   ignored, and the creator of a KeyPackage object SHOULD include some
   random GREASE extensions to help ensure that other clients correctly
   ignore unknown extensions.

10.1.  KeyPackage Validation

   The validity of a KeyPackage needs to be verified at a few stages:

   *  When a KeyPackage is downloaded by a group member, before it is
      used to add the client to the group

   *  When a KeyPackage is received by a group member in an Add message

   The client verifies the validity of a KeyPackage using the following
   steps:

   *  Verify that the cipher suite and protocol version of the
      KeyPackage match those in the GroupContext.

   *  Verify that the leaf_node of the KeyPackage is valid for a
      KeyPackage according to Section 7.3.

   *  Verify that the signature on the KeyPackage is valid using the
      public key in leaf_node.credential.

   *  Verify that the value of leaf_node.encryption_key is different
      from the value of the init_key field.

11.  Group Creation

   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.

   The creator of a group is responsible for setting the group ID,
   cipher suite, 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 cipher
   suite and extensions according to the capabilities of the members.
   To protect against downgrade attacks, the creator MUST use the
   capabilities information in these KeyPackages to verify that the
   chosen version and cipher suite is the best option supported by all
   members.

   Group IDs SHOULD be constructed in such a way that there is an
   overwhelmingly low probability of honest group creators generating
   the same group ID, even without assistance from the Delivery Service.
   This can be done, for example, by making the group ID a freshly
   generated random value of size KDF.Nh.  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.

   To initialize a group, the creator of the group MUST take the
   following steps:

   *  Initialize a one-member group with the following initial values:

      -  Ratchet tree: A tree with a single node, a leaf node containing
         an HPKE public key and credential for the creator

      -  Group ID: A value set by the creator

      -  Epoch: 0

      -  Tree hash: The root hash of the above ratchet tree

      -  Confirmed transcript hash: The zero-length octet string

      -  Epoch secret: A fresh random value of size KDF.Nh

      -  Extensions: Any values of the creator's choosing

   *  Calculate the interim transcript hash:

      -  Derive the confirmation_key for the epoch as described in
         Section 8.

      -  Compute a confirmation_tag over the empty
         confirmed_transcript_hash using the confirmation_key as
         described in Section 6.1.

      -  Compute the updated interim_transcript_hash from the
         confirmed_transcript_hash and the confirmation_tag as described
         in Section 8.2.

   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.

   Members other than the creator join either by being sent a Welcome
   message (as described in Section 12.4.3.1) or by sending an external
   Commit (see Section 12.4.3.2).

   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.

11.1.  Required Capabilities

   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 cipher suite and protocol version in use.  Additional
   requirements can be imposed by including a required_capabilities
   extension in the GroupContext.

   struct {
       ExtensionType extension_types<V>;
       ProposalType proposal_types<V>;
       CredentialType credential_types<V>;
   } RequiredCapabilities;

   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.

   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 required_capabilities extension that requires non-
   default capabilities not supported by all current members.

11.2.  Reinitialization

   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:

   1.  A member of the old group sends a ReInit proposal (see
       Section 12.1.5).

   2.  A member of the old group sends a Commit covering the ReInit
       proposal.

   3.  A member of the old group creates an initial Commit that sets up
       a new group that matches the ReInit and sends a Welcome message:

       *  The version, cipher_suite, group_id, and extensions fields of
          the GroupContext object in the Welcome message MUST be the
          same as the corresponding fields in the ReInit proposal.  The
          epoch in the Welcome message MUST be 1.

       *  The Welcome message MUST specify a PreSharedKeyID of type
          resumption with usage reinit, where the group_id field matches
          the old group and the epoch field indicates the epoch after
          the Commit covering the ReInit.

   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.

   Resumption PSKs with usage reinit MUST NOT be used in other contexts.
   A PreSharedKey proposal with type resumption and usage reinit MUST be
   considered invalid.

11.3.  Subgroup Branching

   A new group can be formed from a subset of an existing group's
   members, using the same parameters as the old group.

   A member can create a subgroup by performing the following steps:

   1.  Fetch a new KeyPackage for each group member that should be
       included in the subgroup.

   2.  Create an initial Commit message that sets up the new group and
       contains a PreSharedKey proposal of type resumption with usage
       branch.  To avoid key reuse, the psk_nonce included in the
       PreSharedKeyID object MUST be a randomly sampled nonce of length
       KDF.Nh.

   3.  Send the corresponding Welcome message to the subgroup members.

   A client receiving a Welcome message including a PreSharedKey of type
   resumption with usage branch MUST verify that the new group reflects
   a subgroup branched from the referenced group by checking that:

   *  The version and cipher_suite values in the Welcome message are the
      same as those used by the old group.

   *  The epoch in the Welcome message MUST be 1.

   *  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.

   Resumption PSKs with usage branch MUST NOT be used in other contexts.
   A PreSharedKey proposal with type resumption and usage branch MUST be
   considered invalid.

12.  Group Evolution

   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:

   1.  A proposal to make the change is broadcast to the group in a
       Proposal message.

   2.  A member of the group or a new member broadcasts a Commit message
       that causes one or more proposed changes to enter into effect.

   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.

   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.

12.1.  Proposals

   Proposals are included in a FramedContent by way of a Proposal
   structure that indicates their type:

   // See the "MLS Proposal Types" IANA registry for values
   uint16 ProposalType;

   struct {
       ProposalType proposal_type;
       select (Proposal.proposal_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;

   On receiving a FramedContent containing a Proposal, a client MUST
   verify the signature inside FramedContentAuthData and that the epoch
   field of the enclosing FramedContent is equal to the epoch 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.

12.1.1.  Add

   An Add proposal requests that a client with a specified KeyPackage be
   added to the group.

   struct {
       KeyPackage key_package;
   } Add;

   An Add proposal is invalid if the KeyPackage is invalid according to
   Section 10.1.

   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.

   *  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 as described in Section 7.7, and L is
      assigned the leftmost new blank leaf.

   *  For each non-blank intermediate node along the path from the leaf
      L to the root, add L's leaf index to the unmerged_leaves list for
      the node.

   *  Set the leaf node L to a new node containing the LeafNode object
      carried in the leaf_node field of the KeyPackage in the Add.

12.1.2.  Update

   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.

   struct {
       LeafNode leaf_node;
   } Update;

   An Update proposal is invalid if the LeafNode is invalid for an
   Update proposal according to Section 7.3.

   A member of the group applies an Update message by taking the
   following steps:

   *  Replace the sender's LeafNode with the one contained in the Update
      proposal.

   *  Blank the intermediate nodes along the path from the sender's leaf
      to the root.

12.1.3.  Remove

   A Remove proposal requests that the member with the leaf index
   removed be removed from the group.

   struct {
       uint32 removed;
   } Remove;

   A Remove proposal is invalid if the removed field does not identify a
   non-blank leaf node.

   A member of the group applies a Remove message by taking the
   following steps:

   *  Identify the leaf node matching removed.  Let L be this leaf node.

   *  Replace the leaf node L with a blank node.

   *  Blank the intermediate nodes along the path from L to the root.

   *  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 2^d leaves, where d is the smallest value such that
      2^d > L.

12.1.4.  PreSharedKey

   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.

   struct {
       PreSharedKeyID psk;
   } PreSharedKey;

   A PreSharedKey proposal is invalid if any of the following is true:

   *  The PreSharedKey proposal is not being processed as part of a
      reinitialization of the group (see Section 11.2), and the
      PreSharedKeyID has psktype set to resumption and usage set to
      reinit.

   *  The PreSharedKey proposal is not being processed as part of a
      subgroup branching operation (see Section 11.3), and the
      PreSharedKeyID has psktype set to resumption and usage set to
      branch.

   *  The psk_nonce is not of length KDF.Nh.

   The psk_nonce MUST be randomly sampled.  When processing a Commit
   message that includes one or more PreSharedKey proposals, group
   members derive psk_secret as described in Section 8.4, where the
   order of the PSKs corresponds to the order of the PreSharedKey
   proposals in the Commit.

12.1.5.  ReInit

   A ReInit proposal represents a request to reinitialize the group with
   different parameters, for example, to increase the version number or
   to change the cipher suite.  The reinitialization is done by creating
   a completely new group and shutting down the old one.

   struct {
       opaque group_id<V>;
       ProtocolVersion version;
       CipherSuite cipher_suite;
       Extension extensions<V>;
   } ReInit;

   A ReInit proposal is invalid if the version field is less than the
   version for the current group.

   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 Section 11.2.

12.1.6.  ExternalInit

   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.

   struct {
     opaque kem_output<V>;
   } ExternalInit;

   A member of the group applies an ExternalInit message by initializing
   the next epoch using an init secret computed as described in
   Section 8.3.  The kem_output field contains the required KEM output.

12.1.7.  GroupContextExtensions

   A GroupContextExtensions proposal is used to update the list of
   extensions in the GroupContext for the group.

   struct {
     Extension extensions<V>;
   } GroupContextExtensions;

   A GroupContextExtensions proposal is invalid if it includes a
   required_capabilities 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).

   A member of the group applies a GroupContextExtensions proposal with
   the following steps:

   *  Remove all of the existing extensions from the GroupContext object
      for the group and replace 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.)

   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.

12.1.8.  External Proposals

   Proposals can be constructed and sent to the group by a party that is
   outside the group in two cases.  One case, indicated by the external
   SenderType, allows an entity outside the group to submit proposals to
   the group.  For example, an automated service might propose removing
   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.  An external sender might send a ReInit proposal to
   enforce a changed policy regarding MLS versions or cipher suites.

   The external SenderType requires that signers are pre-provisioned to
   the clients within a group and can only be used if the
   external_senders extension is present in the group's GroupContext.

   The other case, indicated by the new_member_proposal SenderType, is
   useful when existing members of the group can independently verify
   that an Add proposal sent by the new joiner itself (not an existing
   member) is authorized.  External proposals that are not authorized
   are considered invalid.

   An external proposal MUST be sent as a PublicMessage object, since
   the sender will not have the keys necessary to construct a
   PrivateMessage object.

   Proposals of some types cannot be sent by an external sender.  Among
   the proposal types defined in this document, only the following types
   may be sent by an external sender:

   *  add

   *  remove

   *  psk

   *  reinit

   *  group_context_extensions

   Messages from external senders containing proposal types other than
   the above MUST be rejected as malformed.  New proposal types defined
   in the future MUST define whether they may be sent by external
   senders.  The "Ext" column in the "MLS Proposal Types" registry
   (Section 17.4) reflects this property.

12.1.8.1.  External Senders Extension

   The external_senders 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.

   struct {
     SignaturePublicKey signature_key;
     Credential credential;
   } ExternalSender;

   ExternalSender external_senders<V>;

12.2.  Proposal List Validation

   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.  If the list of proposals is invalid, then
   the Commit message MUST be rejected as invalid.

   For a regular, i.e., not external, Commit, the list is invalid if any
   of the following occurs:

   *  It contains an individual proposal that is invalid as specified in
      Section 12.1.

   *  It contains an Update proposal generated by the committer.

   *  It contains a Remove proposal that removes the committer.

   *  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.

   *  It contains multiple Add proposals that contain KeyPackages that
      represent the same client according to the application (for
      example, identical signature keys).

   *  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.

   *  It contains multiple PreSharedKey proposals that reference the
      same PreSharedKeyID.

   *  It contains multiple GroupContextExtensions proposals.

   *  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.

   *  It contains an ExternalInit proposal.

   *  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).

   *  After processing the Commit the ratchet tree is invalid, in
      particular, if it contains any leaf node that is invalid according
      to Section 7.3.

   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.

   For an external Commit, the list is valid if it contains only the
   following proposals (not necessarily in this order):

   *  Exactly one ExternalInit

   *  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 path field of the external Commit MUST meet the
      same criteria as would the LeafNode in an Update for the removed
      leaf (see Section 12.1.2).  In particular, the credential in the
      LeafNode MUST present a set of identifiers that is acceptable to
      the application for the removed participant.

   *  Zero or more PreSharedKey proposals

   *  No other proposals

   Proposal types defined in the future may make updates to the above
   validation logic to incorporate considerations related to proposals
   of the new type.

12.3.  Applying a Proposal List

   The sections above defining each proposal type describe how each
   individual proposal 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:

   *  If there is a GroupContextExtensions proposal, replace the
      extensions field of the GroupContext for the group with the
      contents of the proposal.  The new extensions MUST be used when
      evaluating other proposals in this list.  For example, if a
      GroupContextExtensions proposal adds a required_capabilities
      extension, then any Add proposals need to indicate support for
      those capabilities.

   *  Apply any Update proposals to the ratchet tree, in any order.

   *  Apply any Remove proposals to the ratchet tree, in any order.

   *  Apply any Add proposals to the ratchet tree, in the order they
      appear in the list.

   *  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.

   *  If there is an ExternalInit proposal, use it to derive the
      init_secret for use later in Commit processing.

   *  If there is a ReInit proposal, note its parameters for application
      later in Commit processing.

   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.

12.4.  Commit

   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.

   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
   Section 5.2).

   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;

   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.

   A sender and a receiver of a Commit MUST verify that the committed
   list of proposals is valid as specified in Section 12.2.  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.

   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.

   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.

   A member of the group MAY send a Commit that references no proposals
   at all, which would thus have an empty proposals 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.

   By default, the path field of a Commit MUST be populated.  The path
   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:

   *  add

   *  psk

   *  reinit

   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 "MLS Proposal Types" registry
   defined in Section 17.4.

   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.

   In pseudocode, the logic for validating the path field of a Commit is
   as follows:

   pathRequiredTypes = [
       update,
       remove,
       external_init,
       group_context_extensions
   ]

   pathRequired = false

   for proposal in commit.proposals:
       pathRequired = pathRequired ||
                      (proposal.msg_type in pathRequiredTypes)

   if len(commit.proposals) == 0 || pathRequired:
       assert(commit.path != null)

   To summarize, a Commit can have three different configurations, with
   different uses:

   1.  An "empty" Commit that references no proposals, which updates the
       committer's contribution to the group and provides PCS with
       regard to the committer.

   2.  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.

   3.  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.

12.4.1.  Creating a Commit

   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.

   A member of the group creates a Commit message and the corresponding
   Welcome message at the same time, by taking the following steps:

   *  Verify that the list of proposals to be committed is valid as
      specified in Section 12.2.

   *  Construct an initial Commit object with the proposals field
      populated from Proposals received during the current epoch, and
      with the path field empty.

   *  Create the new ratchet tree and GroupContext by applying the list
      of proposals to the old ratchet tree and GroupContext, as defined
      in Section 12.3.

   *  Decide whether to populate the path field: If the path 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 path field at its discretion.

   *  If populating the path field:

      -  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, expand the tree to the
         right as defined in Section 7.7 and assign the leftmost new
         blank leaf to the sender.

      -  Update the sender's direct path in the ratchet tree as
         described in Section 7.5.  Define commit_secret as the value
         path_secret[n+1] derived from the last path secret value
         (path_secret[n]) derived for the UpdatePath.

      -  Construct a provisional GroupContext object containing the
         following values:

         o  group_id: Same as the old GroupContext

         o  epoch: The epoch number for the new epoch

         o  tree_hash: The tree hash of the new ratchet tree

         o  confirmed_transcript_hash: Same as the old GroupContext

         o  extensions: The new GroupContext extensions (possibly
            updated by a GroupContextExtensions proposal)

      -  Encrypt the path secrets resulting from the tree update to the
         group as described in Section 7.5, using the provisional group
         context as the context for HPKE encryption.

      -  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
         path field in the Commit.

   *  If not populating the path field: Set the path field in the Commit
      to the null optional.  Define commit_secret as the all-zero vector
      of length KDF.Nh (the same length as a path_secret value would
      be).

   *  Derive the psk_secret as specified in Section 8.4, where the order
      of PSKs in the derivation corresponds to the order of PreSharedKey
      proposals in the proposals vector.

   *  Construct a FramedContent object containing the Commit object.
      Sign the FramedContent using the old GroupContext as context.

      -  Use the FramedContent to update the confirmed transcript hash
         and update the new GroupContext.

      -  Use the init_secret from the previous epoch, the commit_secret
         and psk_secret defined in the previous steps, and the new
         GroupContext to compute the new joiner_secret, welcome_secret,
         epoch_secret, and derived secrets for the new epoch.

      -  Use the confirmation_key for the new epoch to compute the
         confirmation_tag value.

      -  Calculate the interim transcript hash using the new confirmed
         transcript hash and the confirmation_tag from the
         FramedContentAuthData.

   *  Protect the AuthenticatedContent object using keys from the old
      epoch:

      -  If encoding as PublicMessage, compute the membership_tag value
         using the membership_key.

      -  If encoding as a PrivateMessage, encrypt the message using the
         sender_data_secret and the next (key, nonce) pair from the
         sender's handshake ratchet.

   *  Construct a GroupInfo reflecting the new state:

      -  Set the group_id, epoch, tree, confirmed_transcript_hash,
         interim_transcript_hash, and group_context_extensions fields to
         reflect the new state.

      -  Set the confirmation_tag field to the value of the
         corresponding field in the FramedContentAuthData object.

      -  Add any other extensions as defined by the application.

      -  Optionally derive an external key pair as described in
         Section 8. (required for external Commits, see
         Section 12.4.3.2).

      -  Sign the GroupInfo using the member's private signing key.

      -  Encrypt the GroupInfo using the key and nonce derived from the
         joiner_secret. for the new epoch (see Section 12.4.3.1).

   *  For each new member in the group:

      -  Identify the lowest common ancestor in the tree of the new
         member's leaf node and the member sending the Commit.

      -  If the path field was populated above: Compute the path secret
         corresponding to the common ancestor node.

      -  Compute an EncryptedGroupSecrets object that encapsulates the
         init_secret for the current epoch and the path secret (if
         present).

   *  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
      psks MUST be the same as the order of PreSharedKey proposals in
      the proposals vector.  As discussed in Section 12.4.3.1, 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.

   *  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 PreSharedKeyID with the following
      parameters:

      -  psktype: resumption

      -  usage: reinit

      -  group_id: The group ID for the current group

      -  epoch: The epoch that the group will be in after this Commit

12.4.2.  Processing a Commit

   A member of the group applies a Commit message by taking the
   following steps:

   *  Verify that the epoch field of the enclosing FramedContent is
      equal to the epoch field of the current GroupContext object.

   *  Unprotect the Commit using the keys from the current epoch:

      -  If the message is encoded as PublicMessage, verify the
         membership MAC using the membership_key.

      -  If the message is encoded as PrivateMessage, decrypt the
         message using the sender_data_secret and the (key, nonce) pair
         from the step on the sender's hash ratchet indicated by the
         generation field.

   *  Verify the signature on the FramedContent message as described in
      Section 6.1.

   *  Verify that the proposals vector is valid according to the rules
      in Section 12.2.

   *  Verify that all PreSharedKey proposals in the proposals vector are
      available.

   *  Create the new ratchet tree and GroupContext by applying the list
      of proposals to the old ratchet tree and GroupContext, as defined
      in Section 12.3.

   *  Verify that the path value is populated if the proposals vector
      contains any Update or Remove proposals, or if it's empty.
      Otherwise, the path value MAY be omitted.

   *  If the path value is populated, validate it and apply it to the
      tree:

      -  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.

      -  Validate the LeafNode as specified in Section 7.3.  The
         leaf_node_source field MUST be set to commit.

      -  Verify that the encryption_key value in the LeafNode is
         different from the committer's current leaf node.

      -  Verify that none of the public keys in the UpdatePath appear in
         any node of the new ratchet tree.

      -  Merge the UpdatePath into the new ratchet tree, as described in
         Section 7.5.

      -  Construct a provisional GroupContext object containing the
         following values:

         o  group_id: Same as the old GroupContext

         o  epoch: The epoch number for the new epoch

         o  tree_hash: The tree hash of the new ratchet tree

         o  confirmed_transcript_hash: Same as the old GroupContext

         o  extensions: The new GroupContext extensions (possibly
            updated by a GroupContextExtensions proposal)

      -  Decrypt the path secrets for UpdatePath as described in
         Section 7.5, using the provisional GroupContext as the context
         for HPKE decryption.

      -  Define commit_secret as the value path_secret[n+1] derived from
         the last path secret value (path_secret[n]) derived for the
         UpdatePath.

   *  If the path value is not populated, define commit_secret as the
      all-zero vector of length KDF.Nh (the same length as a path_secret
      value would be).

   *  Update the confirmed and interim transcript hashes using the new
      Commit, and generate the new GroupContext.

   *  Derive the psk_secret as specified in Section 8.4, where the order
      of PSKs in the derivation corresponds to the order of PreSharedKey
      proposals in the proposals vector.

   *  Use the init_secret from the previous epoch, the commit_secret and
      psk_secret defined in the previous steps, and the new GroupContext
      to compute the new joiner_secret, welcome_secret, epoch_secret,
      and derived secrets for the new epoch.

   *  Use the confirmation_key for the new epoch to compute the
      confirmation tag for this message, as described below, and verify
      that it is the same as the confirmation_tag field in the
      FramedContentAuthData object.

   *  If the above checks are successful, consider the new GroupContext
      object as the current state of the group.

   *  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
      Section 11.2.

   Note that clients need to be prepared to receive a valid Commit
   message that 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.)

12.4.3.  Adding Members to the Group

   New members can join the group in two ways: 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.

   struct {
       GroupContext group_context;
       Extension extensions<V>;
       MAC confirmation_tag;
       uint32 signer;
       /* SignWithLabel(., "GroupInfoTBS", GroupInfoTBS) */
       opaque signature<V>;
   } GroupInfo;

   The group_context field represents the current state of the group.
   The extensions field allows the sender to provide additional data
   that might be useful to new joiners.  The confirmation_tag 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 Section 11).  (In either case, the creator of a
   GroupInfo may recompute the confirmation tag as MAC(confirmation_key,
   confirmed_transcript_hash).)

   As discussed in Section 13, unknown extensions in
   GroupInfo.extensions MUST be ignored, and the creator of a GroupInfo
   object SHOULD include some random GREASE extensions to help ensure
   that other clients correctly ignore unknown extensions.  Extensions
   in GroupInfo.group_context.extensions, however, MUST be supported by
   the new joiner.

   New members MUST verify that group_id is unique among the groups they
   are currently participating in.

   New members also MUST verify the signature using the public key taken
   from the leaf node of the ratchet tree with leaf index signer.  The
   signature covers the following structure, comprising all the fields
   in the GroupInfo above signature:

   struct {
       GroupContext group_context;
       Extension extensions<V>;
       MAC confirmation_tag;
       uint32 signer;
   } GroupInfoTBS;

12.4.3.1.  Joining via Welcome Message

   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.

   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
   they will have the secrets they need to participate in the epoch
   initiated by the Commit message.

   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 joiner_secret for the new
   epoch.  The joiner_secret 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 that 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.

   If the sender of the Welcome message wants the receiving member to
   include a PSK in the derivation of the epoch_secret, they can
   populate the psks field indicating which PSK to use.

   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;

   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 ratchet_tree.  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.

   On receiving a Welcome message, a client processes it using the
   following steps:

   *  Identify an entry in the secrets array where the new_member value
      corresponds to one of this client's KeyPackages, using the hash
      indicated by the cipher_suite field.  If no such field exists, or
      if the cipher suite indicated in the KeyPackage does not match the
      one in the Welcome message, return an error.

   *  Decrypt the encrypted_group_secrets value with the algorithms
      indicated by the cipher suite and the private key init_key_priv
      corresponding to init_key in the referenced KeyPackage.

   encrypted_group_secrets =
     EncryptWithLabel(init_key, "Welcome",
                      encrypted_group_info, group_secrets)

   group_secrets =
     DecryptWithLabel(init_key_priv, "Welcome",
                      encrypted_group_info, kem_output, ciphertext)

   *  If a PreSharedKeyID is part of the GroupSecrets and the client is
      not in possession of the corresponding PSK, return an error.
      Additionally, if a PreSharedKeyID has type resumption with usage
      reinit or branch, verify that it is the only such PSK.

   *  From the joiner_secret in the decrypted GroupSecrets object and
      the PSKs specified in the GroupSecrets, derive the welcome_secret
      and then the welcome_key and welcome_nonce.  Use the key and nonce
      to decrypt the encrypted_group_info field.

   welcome_nonce = ExpandWithLabel(welcome_secret, "nonce", "", AEAD.Nn)
   welcome_key = ExpandWithLabel(welcome_secret, "key", "", AEAD.Nk)

   *  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 signer.  If the node is blank or if
      signature verification fails, return an error.

   *  Verify that the group_id is unique among the groups that the
      client is currently participating in.

   *  Verify that the cipher_suite in the GroupInfo matches the
      cipher_suite in the KeyPackage.

   *  Verify the integrity of the ratchet tree.

      -  Verify that the tree hash of the ratchet tree matches the
         tree_hash field in GroupInfo.

      -  For each non-empty parent node, verify that it is "parent-hash
         valid", as described in Section 7.9.2.

      -  For each non-empty leaf node, validate the LeafNode as
         described in Section 7.3.

      -  For each non-empty parent node and each entry in the node's
         unmerged_leaves field:

         o  Verify that the entry represents a non-blank leaf node that
            is a descendant of the parent node.

         o  Verify that every non-blank intermediate node between the
            leaf node and the parent node also has an entry for the leaf
            node in its unmerged_leaves.

         o  Verify that the encryption key in the parent node does not
            appear in any other node of the tree.

   *  Identify a leaf whose LeafNode is identical to the one in the
      KeyPackage.  If no such field exists, return an error.  Let
      my_leaf represent this leaf in the tree.

   *  Construct a new group state using the information in the GroupInfo
      object.

      -  Initialize the GroupContext for the group from the
         group_context field from the GroupInfo object.

      -  Update the leaf my_leaf with the private key corresponding to
         the public key in the node, where my_leaf is the new member's
         leaf node in the ratchet tree, as defined above.

      -  If the path_secret value is set in the GroupSecrets object:
         Identify the lowest common ancestor of the leaf node my_leaf
         and of the node of the member with leaf index GroupInfo.signer.
         Set the private key for this node to the private key derived
         from the path_secret.

      -  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.

   *  Use the joiner_secret from the GroupSecrets object to generate the
      epoch secret and other derived secrets for the current epoch.

   *  Set the confirmed transcript hash in the new state to the value of
      the confirmed_transcript_hash in the GroupInfo.

   *  Verify the confirmation tag in the GroupInfo using the derived
      confirmation key and the confirmed_transcript_hash from the
      GroupInfo.

   *  Use the confirmed transcript hash and confirmation tag to compute
      the interim transcript hash in the new state.

   *  If a PreSharedKeyID was used that has type resumption with usage
      reinit or branch, verify that the epoch field in the GroupInfo is
      equal to 1.

      -  For usage reinit, verify that the last Commit to the referenced
         group contains a ReInit proposal and that the group_id,
         version, cipher_suite, and group_context.extensions 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.

      -  For usage branch, verify that the version and cipher_suite 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.

12.4.3.2.  Joining via External Commits

   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.

   Whether existing members of the group will accept or reject an
   external Commit follows the same rules that are applied to other
   handshake messages.

   New members can create and issue an external Commit if they have
   access to the following information for the group's current epoch:

   *  group ID

   *  epoch ID

   *  cipher suite

   *  public tree hash

   *  confirmed transcript hash

   *  confirmation tag of the most recent Commit

   *  group extensions

   *  external public key

   In other words, to join a group via an external Commit, a new member
   needs a GroupInfo with an external_pub extension present in its
   extensions field.

   struct {
       HPKEPublicKey external_pub;
   } ExternalPub;

   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.

   Note that the tree_hash field is used the same way as in the Welcome
   message.  The full tree can be included via the ratchet_tree
   extension (see Section 12.4.3.3).

   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.

   In principle, external Commits work like regular Commits.  However,
   their content has to meet a specific set of requirements:

   *  External Commits MUST contain a path 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.

   *  The Commit MUST NOT include any proposals by reference, since an
      external joiner cannot determine the validity of proposals sent
      within the group.

   *  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 leaf_node of the
      path field.

   *  When processing a Commit, both existing and new members MUST use
      the external init secret as described in Section 8.3.

   *  The sender type for the AuthenticatedContent encapsulating the
      external Commit MUST be new_member_commit.

   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.

   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 it 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.

12.4.3.3.  Ratchet Tree Extension

   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 the tree.

   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 ratchet_tree, containing a
   ratchet_tree object of the following form:

   struct {
       NodeType node_type;
       select (Node.node_type) {
           case leaf:   LeafNode leaf_node;
           case parent: ParentNode parent_node;
       };
   } Node;

   optional<Node> ratchet_tree<V>;

   Each entry in the ratchet_tree vector provides the value for a node
   in the tree, or the null optional for a blank node.

   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 Appendix C.)

   If the tree has 2^d leaves, then it has 2^(d+1) - 1 nodes.  The
   ratchet_tree vector logically has this number of entries, but the
   sender MUST NOT include blank nodes after the last non-blank node.
   The receiver MUST check that the last node in ratchet_tree is non-
   blank, and then extend the tree to the right until it has a length of
   the form 2^(d+1) - 1, 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.)

   The leaves of the tree are stored in even-numbered entries in the
   array (the leaf with index L in array position 2*L).  The root node
   of the tree is at position 2^d - 1 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:

   # 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

   (Note that this is the same ordering of nodes as in the array-based
   tree representation described in Appendix C.  The algorithms in that
   section may be used to simplify decoding this extension into other
   representations.)

   For example, the following tree with six non-blank leaves would be
   represented as an array of eleven elements, [A, W, B, X, C, _, D, Y,
   E, Z, F].  The above decoding procedure would identify the subtree
   roots as follows (using R to represent a subtree root):

                 Y
                 |
           .-----+-----.
          /             \
         X               _
         |               |
       .-+-.           .-+-.
      /     \         /     \
     W       _       Z       _
    / \     / \     / \     / \
   A   B   C   D   E   F   _   _

                       1
   0 1 2 3 4 5 6 7 8 9 0
   <-----------> R <----------->
   <---> R <--->   <---> R <--->
   - R -   - R -   - R -   - R -

      Figure 28: Left-to-Right In-Order Traversal of a Six-Member Tree

   The presence of a ratchet_tree 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.

   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.

   Regardless of how the client obtains the tree, the client MUST verify
   that the root hash of the ratchet tree matches the tree_hash of the
   GroupContext before using the tree for MLS operations.

13.  Extensibility

   The base MLS protocol can be extended in a few ways.  New cipher
   suites 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.

13.1.  Additional Cipher Suites

   As discussed in Section 5.1, 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 [RFC7696].  It also creates a risk of
   interoperability failure due to clients not supporting a common
   cipher suite.

   The cipher suite registry defined in Section 17.1 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.  On the other hand, 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 cipher suites are
   considered.

   MLS cipher suites are defined independent of MLS versions, so that in
   principle, the same cipher suite 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
   cipher suites, or whether the new version should rule out some cipher
   suites.  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 [RFC9113]).

13.2.  Proposals

   Commit messages do not have an extension field because the set of
   proposals is extensible.  As discussed in Section 12.4, 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.

13.3.  Credential Extensibility

   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.

   The only types of credential that may be used in a group are those
   that all members of the group support, as specified by the
   capabilities field of each LeafNode in the ratchet tree.  An
   application can introduce new credential types by choosing an
   unallocated identifier from the registry in Section 17.5 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
   required_capabilities extension to the group's GroupContext, which
   would prevent any member from being added to the group that doesn't
   support them.

   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.

13.4.  Extensions

   This protocol includes a mechanism for negotiating extension
   parameters similar to the one in TLS [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:

   *  In KeyPackages, to describe additional information related to the
      client

   *  In LeafNodes, to describe additional information about the client
      or its participation in the group (once in the ratchet tree)

   *  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

   *  In the GroupContext object, to ensure that all members of the
      group have the same view of the parameters in use

   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 capabilities
   field of their LeafNode.  New members of a group are informed of the
   group's GroupContext extensions via the extensions field in the
   group_context field of the GroupInfo object.  The extensions field in
   a GroupInfo object (outside of the group_context field) can be used
   to provide additional parameters to new joiners that are used to join
   the group.

   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:

   *  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.

   *  A client processing a KeyPackage object MUST ignore all
      unrecognized values in the capabilities field of the LeafNode and
      all unknown extensions in the extensions and leaf_node.extensions
      fields.  Otherwise, it could fail to interoperate with newer
      clients.

   *  A client processing a GroupInfo object MUST ignore all
      unrecognized extensions in the extensions field.

   *  Any field containing a list of extensions MUST NOT have more than
      one extension of any given type.

   *  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 capabilities field MUST indicate support for each
      extension in the GroupContext.

   *  A client joining a group MUST verify that it supports every
      extension in the GroupContext for the group.  Otherwise, it MUST
      treat the enclosing GroupInfo message as invalid and not join the
      group.

   Note that the latter two requirements mean that all MLS GroupContext
   extensions are mandatory, in the sense that an extension in use by
   the group MUST be supported by all members of the group.

   The parameters of a group may be changed by sending a
   GroupContextExtensions proposal to enable additional extensions
   (Section 12.1.7), or by reinitializing the group (Section 11.2).

13.5.  GREASE

   As described in Section 13.4, clients are required to ignore unknown
   values for certain parameters.  To help ensure that other clients
   implement this behavior, a client can follow the "Generate Random
   Extensions And Sustain Extensibility" or GREASE approach described in
   [RFC8701].  In the context of MLS, this means that a client
   generating a KeyPackage, LeafNode, or GroupInfo object includes
   random values in certain fields which would be ignored by a correctly
   implemented client processing the message.  A client that incorrectly
   rejects unknown code points will fail to process such a message,
   providing a signal to its implementer that the client needs to be
   fixed.

   When generating the following fields, an MLS client SHOULD include a
   random selection of values chosen from these GREASE values:

   *  LeafNode.capabilities.cipher_suites

   *  LeafNode.capabilities.extensions

   *  LeafNode.capabilities.proposals

   *  LeafNode.capabilities.credentials

   *  LeafNode.extensions

   *  KeyPackage.extensions

   *  GroupInfo.extensions

   For the KeyPackage and GroupInfo extensions, the extension_data for
   GREASE extensions MAY have any contents selected by the sender, since
   they will be ignored by a correctly implemented receiver.  For
   example, a sender might populate these extensions with a randomly
   sized amount of random data.

   Note that any GREASE values added to LeafNode.extensions need to be
   reflected in LeafNode.capabilities.extensions, since the LeafNode
   validation process described in Section 7.3 requires that these two
   fields be consistent.

   GREASE values MUST NOT be sent in the following fields, because an
   unsupported value in one these fields (including a GREASE value) will
   cause the enclosing message to be rejected:

   *  Proposal.proposal_type

   *  Credential.credential_type

   *  GroupContext.extensions

   *  GroupContextExtensions.extensions

   Values reserved for GREASE have been registered in the various
   registries in Section 17.  This prevents conflict between GREASE and
   real future values.  The following values are reserved in each
   registry: 0x0A0A, 0x1A1A, 0x2A2A, 0x3A3A, 0x4A4A, 0x5A5A, 0x6A6A,
   0x7A7A, 0x8A8A, 0x9A9A, 0xAAAA, 0xBABA, 0xCACA, 0xDADA, and 0xEAEA.
   (The value 0xFAFA falls within the private use range.)  These values
   MUST only appear in the fields listed above, and not, for example, in
   the proposal_type field of a Proposal.  Clients MUST NOT implement
   any special processing rules for how to handle these values when
   receiving them, since this negates their utility for detecting
   extensibility failures.

   GREASE values MUST be handled using normal logic for processing
   unsupported values.  When comparing lists of capabilities to identify
   mutually supported capabilities, clients MUST represent their own
   capabilities with a list containing only the capabilities actually
   supported, without any GREASE values.  In other words, lists
   including GREASE values are only sent to other clients;
   representations of a client's own capabilities MUST NOT contain
   GREASE values.

14.  Sequencing of State Changes

   Each Commit message is premised on a given starting state, indicated
   by the epoch 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.

   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.

   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.

   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.

   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.

15.  Application Messages

   The primary purpose of handshake messages is to provide an
   authenticated group key exchange to clients.  In order to protect
   application messages sent among the members of a group, the
   encryption_secret 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 Section 9, along with a new set of
   symmetric ratchets of nonces and keys for each member.

   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.

   The group identifier and epoch allow a recipient to know which group
   secrets should be used and from which epoch_secret to start computing
   other secrets.  The sender identifier and content type are used to
   identify which symmetric ratchet to use from the secret tree.  The
   generation counter determines how far into the ratchet to iterate in
   order to produce the required nonce and key for encryption or
   decryption.

15.1.  Padding

   Application messages MAY be padded to provide some resistance against
   traffic analysis techniques over encrypted traffic [CLINIC] [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.

   The length of the padding field in PrivateMessageContent 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.

15.2.  Restrictions

   During each epoch, senders MUST NOT encrypt more data than permitted
   by the security bounds of the AEAD scheme used [CFRG-AEAD-LIMITS].

   Note that each change to the group through a handshake message will
   also set a new encryption_secret.  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.

15.3.  Delayed and Reordered Application Messages

   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 that were delayed or
   reordered.

   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 Section 9.2.  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 is 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 generation =
   0xffffffff at the beginning of a new epoch, forcing recipients to
   perform billions of key derivations unless they apply limits of the
   type discussed above.

16.  Security Considerations

   The security goals of MLS are described in [MLS-ARCH].  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 [MLS-ARCH] provides some
   citations to detailed security analyses.

16.1.  Transport Security

   Because MLS messages are protected at the message level, the
   confidentiality and integrity of the group state do not depend on
   those messages being protected in transit.  However, an attacker who
   can observe those messages in transit will be able to learn about the
   group state, including potentially the group membership (see
   Section 16.4.3 below).  Such an attacker might also be able to mount
   denial-of-service attacks on the group or exclude new members by
   selectively removing messages in transit.  In order to prevent this
   form of attack, it is RECOMMENDED that all MLS messages be carried
   over a secure transport such as TLS [RFC8446] or QUIC [RFC9000].

16.2.  Confidentiality of Group Secrets

   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 _tree
   invariant_, 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.

   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 key pair such that the old private key can no longer
   be used to decrypt new messages.

16.3.  Confidentiality of Sender Data

   The PrivateMessage framing encrypts "sender data" that identifies
   which group member sent an encrypted message, as described in
   Section 6.3.2.  As with the QUIC header protection scheme [RFC9001],
   Section 5.4, this scheme is a variant of the HN1 construction
   analyzed in [NAN].  A sample of the ciphertext is combined with a
   sender_data_secret to derive a key and nonce that are used for AEAD
   encryption of the sender data.

   (key, nonce) = PRF(sender_data_secret, sample)
   encrypted_sender_data =
     AEAD.Seal(key, nonce, sender_data_aad, sender_data)

   The only differences between this construction and HN1 as described
   in [NAN] are that it (1) uses authenticated encryption instead of
   unauthenticated encryption and (2) protects information used to
   derive a nonce instead of the nonce itself.

   Since the sender_data_secret is distinct from the content encryption
   key, it follows that the sender data encryption scheme achieves AE2
   security as defined in [NAN], and therefore guarantees the
   confidentiality of the sender data.

   Use of the same sender_data_secret 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 [NAN]),
   the odds of two ciphertext samples being identical is roughly
   2^(-L/2), i.e., the birthday bound.

   The AEAD algorithms for cipher suites defined in this document all
   provide this property.  The size of the sample depends on the cipher
   suite's hash function, but in all cases, the probability of collision
   is no more than 2^-128.  Any future cipher suite MUST use an
   AE1-secure AEAD algorithm.

16.4.  Confidentiality of Group Metadata

   MLS does not provide confidentiality protection to some messages and
   fields within messages:

   *  KeyPackage messages

   *  GroupInfo messages

   *  The unencrypted portion of a Welcome message

   *  Any Proposal or Commit messages sent as PublicMessage messages

   *  The unencrypted header fields in PrivateMessage messages

   *  The lengths of encrypted Welcome and PrivateMessage messages

   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 ratchet_tree extension.  If an application distributes
   the tree in some other way, its security will depend on that
   application mechanism.

   A party observing these fields might be able to infer certain
   properties of the group:

   *  Group ID

   *  Current epoch and frequency of epoch changes

   *  Frequency of messages within an epoch

   *  Group extensions

   *  Group membership

   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:

   *  How KeyPackages are distributed

   *  How the ratchet tree is distributed

   *  How prospective external joiners get a GroupInfo object for the
      group

   *  Whether Proposal and Commit messages are sent as PublicMessage or
      PrivateMessage

   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.

16.4.1.  GroupID, Epoch, and Message Frequency

   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.
   However, any modifications to these will cause decryption failure.

16.4.2.  Group Extensions

   A group's extensions are first set by the group's creator and then
   updated by GroupContextExtensions proposals.  A
   GroupContextExtensions proposal sent as a PublicMessage leaks the
   group's extensions.

   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.

16.4.3.  Group Membership

   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.

   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.

   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.

   Note that these information leaks reveal the group's membership only
   to the degree 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.

16.5.  Authentication

   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
   membership_tag, which constitutes a MAC over the message, under a key
   derived from the group secrets.

   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.

   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.

   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.

16.6.  Forward Secrecy and Post-Compromise Security

   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.

                      Compromise
                          |
                          |
                     |    V    |
   ------------------|---------|------------------------->
                     |         |                     Time
   <-----------------|         |---------------->
     Forward Secrecy |         | Post-Compromise
                     |         |   Security

          Figure 29: Forward Secrecy and Post-Compromise Security

   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.
   Note that sending an Update proposal does not achieve PCS until
   another member includes it in a Commit.  Members can achieve
   immediate PCS by sending their own Commit and populating the path
   field, as described in Section 12.4.  To be clear, in all these
   cases, the PCS guarantees come into effect when the members of the
   group process the relevant Commit, not when the sender creates it.

   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 _within_ an epoch is
   provided by deleting message encryption keys once they've been used
   to encrypt or decrypt a message.  Note that group secrets and message
   encryption keys are shared by the group.  There is thus a risk to
   forward secrecy as long as any member has not deleted these keys.
   This is a particular risk if a member is offline for a long period of
   time.  Applications SHOULD have mechanisms for evicting group members
   that are offline for too long (i.e., have not changed their key
   within some period).

   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.

16.7.  Uniqueness of Ratchet Tree Key Pairs

   The encryption and signature keys stored in the encryption_key and
   signature_key fields of ratchet tree nodes MUST be distinct from one
   another.  If two members' leaf nodes have the same signature key, for
   example, then the data origin authentication properties afforded by
   signatures within the group are degraded.

   Uniqueness of keys in leaf nodes is assured by explicitly checking
   each leaf node as it is added to the tree, whether in an Add
   proposal, in an Update proposal, or in the path field of a Commit.
   Details can be found in Sections 7.3, 12.2, and 12.4.2.  Uniqueness
   of encryption keys in parent nodes is assured by checking that the
   keys in an UpdatePath are not found elsewhere in the tree (see
   Section 12.4.2).

16.8.  KeyPackage Reuse

   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.

   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 from 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.

16.9.  Delivery Service Compromise

   MLS is designed to protect the confidentiality and integrity of the
   group data even in the face of a compromised DS.  However, a
   compromised DS can still mount some attacks.  While it cannot forge
   messages, it can selectively delay or remove them.  In some cases,
   this can be observed by detecting gaps in the per-sender generation
   counter, though it may not always be possible to distinguish an
   attack from message loss.  In addition, the DS can permanently block
   messages to and from a group member.  This will not always be
   detectable by other members.  If an application uses the DS to
   resolve conflicts between simultaneous Commits (see Section 14), it
   is also possible for the DS to influence which Commit is applied,
   even to the point of preventing a member from ever having its Commits
   applied.

   When put together, these abilities potentially allow a DS to collude
   with an attacker who has compromised a member's state to defeat PCS
   by suppressing the valid Update and Commit messages from the member
   that would lock out the attacker and update the member's leaf to a
   new, uncompromised state.  Aside from the SenderData.generation
   value, MLS leaves loss detection up to the application.

16.10.  Authentication Service Compromise

   Authentication Service compromise is much more serious than
   compromise of the Delivery Service.  A compromised AS can assert a
   binding for a signature key and identity pair of its choice, thus
   allowing impersonation of a given user.  This ability is sufficient
   to allow the AS to join new groups as if it were that user.
   Depending on the application architecture, it may also be sufficient
   to allow the compromised AS to join the group as an existing user,
   for instance, as if it were a new device associated with the same
   user.  If the application uses a transparency mechanism such as
   CONIKS [CONIKS] or Key Transparency [KT], then it may be possible for
   end users to detect this kind of misbehavior by the AS.  It is also
   possible to construct schemes in which the various clients owned by a
   user vouch for each other, e.g., by signing each others' keys.

16.11.  Additional Policy Enforcement

   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 credentials are
   admitted.  MLS provides no inherent protection against denial of
   service; a DS could also enforce rate limits in order to mitigate
   these risks.

16.12.  Group Fragmentation by Malicious Insiders

   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 Section 7.4, 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.

   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.

   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 will possibly be 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 need to either add themselves back with an
   external Commit or reinitialize the group from scratch.

   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.  MLS does
   not provide a built-in mechanism for such acknowledgements, but they
   can be added at the application layer.

17.  IANA Considerations

   IANA has created the following registries:

   *  MLS Cipher Suites (Section 17.1)

   *  MLS Wire Formats (Section 17.2)

   *  MLS Extension Types (Section 17.3)

   *  MLS Proposal Types (Section 17.4)

   *  MLS Credential Types (Section 17.5)

   *  MLS Signature Labels (Section 17.6)

   *  MLS Public Key Encryption Labels (Section 17.7)

   *  MLS Exporter Labels (Section 17.8)

   All of these registries are under the "Messaging Layer Security"
   group registry heading, and assignments are made via the
   Specification Required policy [RFC8126].  See Section 17.9 for
   additional information about the MLS Designated Experts (DEs).

17.1.  MLS Cipher Suites

   A cipher suite is a combination of a protocol version and the set of
   cryptographic algorithms that should be used.

   Cipher suite names follow the naming convention:

   CipherSuite MLS_LVL_KEM_AEAD_HASH_SIG = VALUE;

   Where VALUE is represented as a 16-bit integer:

   uint16 CipherSuite;

             +===========+==================================+
             | Component | Contents                         |
             +===========+==================================+
             | LVL       | The security level (in bits)     |
             +-----------+----------------------------------+
             | KEM       | The KEM algorithm used for HPKE  |
             |           | in ratchet tree operations       |
             +-----------+----------------------------------+
             | AEAD      | The AEAD algorithm used for HPKE |
             |           | and message protection           |
             +-----------+----------------------------------+
             | HASH      | The hash algorithm used for HPKE |
             |           | and the MLS transcript hash      |
             +-----------+----------------------------------+
             | SIG       | The signature algorithm used for |
             |           | message authentication           |
             +-----------+----------------------------------+

                                 Table 5

   The columns in the registry are as follows:

   *  Value: The numeric value of the cipher suite

   *  Name: The name of the cipher suite

   *  Recommended: Whether support for this cipher suite is recommended
      by the IETF.  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 an item
      whose current value is "Y" or "D", requires Standards Action
      [RFC8126].

      -  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 it
         will provide applicability statements that describe any
         limitations of the mechanism or necessary constraints on its
         use.

      -  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 item marked as "N" on
         the basis of it having limited applicability or usage
         constraints.

      -  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.

   *  Reference: The document where this cipher suite is defined

   Initial contents:

   +========+===================================================+=+====+
   | Value  |Name                                               |R|Ref |
   +========+===================================================+=+====+
   | 0x0000 |RESERVED                                           |-|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x0001 |MLS_128_DHKEMX25519_AES128GCM_SHA256_Ed25519       |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x0002 |MLS_128_DHKEMP256_AES128GCM_SHA256_P256            |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x0003 |MLS_128_DHKEMX25519_CHACHA20POLY1305_SHA256_Ed25519|Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x0004 |MLS_256_DHKEMX448_AES256GCM_SHA512_Ed448           |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x0005 |MLS_256_DHKEMP521_AES256GCM_SHA512_P521            |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x0006 |MLS_256_DHKEMX448_CHACHA20POLY1305_SHA512_Ed448    |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x0007 |MLS_256_DHKEMP384_AES256GCM_SHA384_P384            |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x0A0A |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x1A1A |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x2A2A |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x3A3A |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x4A4A |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x5A5A |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x6A6A |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x7A7A |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x8A8A |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0x9A9A |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0xAAAA |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0xBABA |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0xCACA |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0xDADA |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0xEAEA |GREASE                                             |Y|RFC |
   |        |                                                   | |9420|
   +--------+---------------------------------------------------+-+----+
   | 0xF000 |Reserved for Private Use                           |-|RFC |
   | -      |                                                   | |9420|
   | 0xFFFF |                                                   | |    |
   +--------+---------------------------------------------------+-+----+

                   Table 6: MLS Extension Types Registry

   All of the non-GREASE cipher suites use HMAC [RFC2104] as their MAC
   function, with different hashes per cipher suite.  The mapping of
   cipher suites to HPKE primitives [RFC9180], HMAC hash functions, and
   TLS signature schemes [RFC8446] is as follows:

    +======+======+========+========+========+========================+
    |Value |KEM   | KDF    | AEAD   | Hash   | Signature              |
    +======+======+========+========+========+========================+
    |0x0001|0x0020| 0x0001 | 0x0001 | SHA256 | ed25519                |
    +------+------+--------+--------+--------+------------------------+
    |0x0002|0x0010| 0x0001 | 0x0001 | SHA256 | ecdsa_secp256r1_sha256 |
    +------+------+--------+--------+--------+------------------------+
    |0x0003|0x0020| 0x0001 | 0x0003 | SHA256 | ed25519                |
    +------+------+--------+--------+--------+------------------------+
    |0x0004|0x0021| 0x0003 | 0x0002 | SHA512 | ed448                  |
    +------+------+--------+--------+--------+------------------------+
    |0x0005|0x0012| 0x0003 | 0x0002 | SHA512 | ecdsa_secp521r1_sha512 |
    +------+------+--------+--------+--------+------------------------+
    |0x0006|0x0021| 0x0003 | 0x0003 | SHA512 | ed448                  |
    +------+------+--------+--------+--------+------------------------+
    |0x0007|0x0011| 0x0002 | 0x0002 | SHA384 | ecdsa_secp384r1_sha384 |
    +------+------+--------+--------+--------+------------------------+

                                  Table 7

   The hash used for the MLS transcript hash is the one referenced in
   the cipher suite name.  In the cipher suites defined above, "SHA256",
   "SHA384", and "SHA512" refer, respectively, to the SHA-256, SHA-384,
   and SHA-512 functions defined in [SHS].

   In addition to the general requirements of Section 13.1, future
   cipher suites MUST meet the requirements of Section 16.3.

   It is advisable to keep the number of cipher suites low to increase
   the likelihood that clients can interoperate in a federated
   environment.  The cipher suites therefore include only 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 curves compliant with FIPS 140-2 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
   curves compliant with FIPS 140-2.  The security level of symmetric
   encryption algorithms and hash functions is paired with the security
   level of the curves.

   The mandatory-to-implement cipher suite for MLS 1.0 is
   MLS_128_DHKEMX25519_AES128GCM_SHA256_Ed25519, which uses Curve25519
   for key exchange, AES-128-GCM for HPKE, HKDF over SHA2-256, and
   Ed25519 for signatures.  MLS clients MUST implement this cipher
   suite.

17.2.  MLS Wire Formats

   The "MLS Wire Formats" 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.

   Template:

   *  Value: The numeric value of the wire format

   *  Name: The name of the wire format

   *  Recommended: Same as in Section 17.1

   *  Reference: The document where this wire format is defined

   Initial contents:

       +=================+==========================+===+==========+
       | Value           | Name                     | R | Ref      |
       +=================+==========================+===+==========+
       | 0x0000          | RESERVED                 | - | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x0001          | mls_public_message       | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x0002          | mls_private_message      | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x0003          | mls_welcome              | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x0004          | mls_group_info           | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x0005          | mls_key_package          | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0xF000 - 0xFFFF | Reserved for Private Use | - | RFC 9420 |
       +-----------------+--------------------------+---+----------+

                     Table 8: MLS Wire Formats Registry

17.3.  MLS Extension Types

   The "MLS Extension Types" 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.

   Template:

   *  Value: The numeric value of the extension type

   *  Name: The name of the extension type

   *  Message(s): The messages in which the extension may appear, drawn
      from the following list:

      -  KP: KeyPackage objects

      -  LN: LeafNode objects

      -  GC: GroupContext objects

      -  GI: GroupInfo objects

   *  Recommended: Same as in Section 17.1

   *  Reference: The document where this extension is defined

   Initial contents:

     +==========+=======================+============+===+==========+
     | Value    | Name                  | Message(s) | R | Ref      |
     +==========+=======================+============+===+==========+
     | 0x0000   | RESERVED              | N/A        | - | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x0001   | application_id        | LN         | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x0002   | ratchet_tree          | GI         | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x0003   | required_capabilities | GC         | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x0004   | external_pub          | GI         | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x0005   | external_senders      | GC         | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x0A0A   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x1A1A   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x2A2A   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x3A3A   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x4A4A   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x5A5A   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x6A6A   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x7A7A   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x8A8A   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0x9A9A   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0xAAAA   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0xBABA   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0xCACA   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0xDADA   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0xEAEA   | GREASE                | KP, GI, LN | Y | RFC 9420 |
     +----------+-----------------------+------------+---+----------+
     | 0xF000 - | Reserved for Private  | N/A        | - | RFC 9420 |
     | 0xFFFF   | Use                   |            |   |          |
     +----------+-----------------------+------------+---+----------+

                  Table 9: MLS Extension Types Registry

17.4.  MLS Proposal Types

   The "MLS Proposal Types" 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.

   Template:

   *  Value: The numeric value of the proposal type

   *  Name: The name of the proposal type

   *  Recommended: Same as in Section 17.1

   *  External: Whether a proposal of this type may be sent by an
      external sender (see Section 12.1.8)

   *  Path Required: Whether a Commit covering a proposal of this type
      is required to have its path field populated (see Section 12.4)

   *  Reference: The document where this extension is defined

   Initial contents:

    +==========+==========================+===+=====+======+==========+
    | Value    | Name                     | R | Ext | Path | Ref      |
    +==========+==========================+===+=====+======+==========+
    | 0x0000   | RESERVED                 | - | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x0001   | add                      | Y | Y   | N    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x0002   | update                   | Y | N   | Y    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x0003   | remove                   | Y | Y   | Y    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x0004   | psk                      | Y | Y   | N    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x0005   | reinit                   | Y | Y   | N    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x0006   | external_init            | Y | N   | Y    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x0007   | group_context_extensions | Y | Y   | Y    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x0A0A   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x1A1A   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x2A2A   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x3A3A   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x4A4A   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x5A5A   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x6A6A   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x7A7A   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x8A8A   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0x9A9A   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0xAAAA   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0xBABA   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0xCACA   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0xDADA   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0xEAEA   | GREASE                   | Y | -   | -    | RFC 9420 |
    +----------+--------------------------+---+-----+------+----------+
    | 0xF000 - | Reserved for Private Use | - | -   | -    | RFC 9420 |
    | 0xFFFF   |                          |   |     |      |          |
    +----------+--------------------------+---+-----+------+----------+

                   Table 10: MLS Proposal Types Registry

17.5.  MLS Credential Types

   The "MLS Credential Types" 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.

   Template:

   *  Value: The numeric value of the credential type

   *  Name: The name of the credential type

   *  Recommended: Same as in Section 17.1

   *  Reference: The document where this credential is defined

   Initial contents:

       +=================+==========================+===+==========+
       | Value           | Name                     | R | Ref      |
       +=================+==========================+===+==========+
       | 0x0000          | RESERVED                 | - | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x0001          | basic                    | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x0002          | x509                     | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x0A0A          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x1A1A          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x2A2A          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x3A3A          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x4A4A          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x5A5A          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x6A6A          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x7A7A          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x8A8A          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0x9A9A          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0xAAAA          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0xBABA          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0xCACA          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0xDADA          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0xEAEA          | GREASE                   | Y | RFC 9420 |
       +-----------------+--------------------------+---+----------+
       | 0xF000 - 0xFFFF | Reserved for Private Use | - | RFC 9420 |
       +-----------------+--------------------------+---+----------+

                  Table 11: MLS Credential Types Registry

17.6.  MLS Signature Labels

   The SignWithLabel function defined in Section 5.1.2 avoids the risk
   of confusion between signatures in different contexts.  Each context
   is assigned a distinct label that is incorporated into the signature.
   The "MLS Signature Labels" registry records the labels defined in
   this document and allows additional labels to be registered in case
   extensions add other types of signatures using the same signature
   keys used elsewhere in MLS.

   Template:

   *  Label: The string to be used as the Label parameter to
      SignWithLabel

   *  Recommended: Same as in Section 17.1

   *  Reference: The document where this label is defined

   Initial contents:

                   +====================+===+==========+
                   | Label              | R | Ref      |
                   +====================+===+==========+
                   | "FramedContentTBS" | Y | RFC 9420 |
                   +--------------------+---+----------+
                   | "LeafNodeTBS"      | Y | RFC 9420 |
                   +--------------------+---+----------+
                   | "KeyPackageTBS"    | Y | RFC 9420 |
                   +--------------------+---+----------+
                   | "GroupInfoTBS"     | Y | RFC 9420 |
                   +--------------------+---+----------+

                       Table 12: MLS Signature Labels
                                  Registry

17.7.  MLS Public Key Encryption Labels

   The EncryptWithLabel function defined in Section 5.1.3 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.  The "MLS Public Key
   Encryption Labels" 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.

   Template:

   *  Label: The string to be used as the Label parameter to
      EncryptWithLabel

   *  Recommended: Same as in Section 17.1

   *  Reference: The document where this label is defined

   Initial contents:

                    +==================+===+==========+
                    | Label            | R | Ref      |
                    +==================+===+==========+
                    | "UpdatePathNode" | Y | RFC 9420 |
                    +------------------+---+----------+
                    | "Welcome"        | Y | RFC 9420 |
                    +------------------+---+----------+

                          Table 13: MLS Public Key
                         Encryption Labels Registry

17.8.  MLS Exporter Labels

   The exporter function defined in Section 8.5 allows applications to
   derive key material from the MLS key schedule.  Like the TLS exporter
   [RFC8446], the MLS exporter uses a label to distinguish between
   different applications' use of the exporter.  The "MLS Exporter
   Labels" registry allows applications to register their usage to avoid
   collisions.

   Template:

   *  Label: The string to be used as the Label parameter to MLS-
      Exporter

   *  Recommended: Same as in Section 17.1

   *  Reference: The document where this label is defined

   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.

                    +=======+=============+===========+
                    | Label | Recommended | Reference |
                    +=======+=============+===========+
                    | (N/A) | (N/A)       | (N/A)     |
                    +-------+-------------+-----------+

                       Table 14: MLS Exporter Labels
                                  Registry

17.9.  MLS Designated Expert Pool

   Specification Required [RFC8126] registry requests are registered
   after a three-week review period on the MLS Designated Expert (DE)
   mailing list <mailto:mls-reg-review@ietf.org> 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.

   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").

   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 <mailto:iesg@ietf.org> mailing list.

   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, for cipher suite registrations, the MLS DEs will
   apply the advisory found in Section 17.1.

   IANA MUST only accept registry updates from the MLS DEs and SHOULD
   direct all requests for registration to the MLS DEs' mailing list.

   It is suggested that multiple MLS DEs who are able to represent the
   perspectives of different applications using this specification be
   appointed, in order to enable a 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.

17.10.  The "message/mls" Media Type

   This document registers the "message/mls" media type in the "message"
   registry in order to allow other protocols (e.g., HTTP [RFC9113]) to
   convey MLS messages.

   Type name:  message

   Subtype name:  mls

   Required parameters:  none

   Optional parameters:  version

                         version:  The MLS protocol version expressed as
         a string <major>.<minor>.  If omitted, the version is "1.0",
         which corresponds to MLS ProtocolVersion mls10.  If for some
         reason the version number in the media type parameter differs
         from the ProtocolVersion embedded in the protocol, the protocol
         takes precedence.

   Encoding considerations:  MLS messages are represented using the TLS
      presentation language [RFC8446].  Therefore, MLS messages need to
      be treated as binary data.

   Security considerations:  MLS is an encrypted messaging layer
      designed to be transmitted over arbitrary lower-layer protocols.
      The security considerations in this document (RFC 9420) also
      apply.

   Interoperability considerations:  N/A

   Published specification:  RFC 9420

   Applications that use this media type:  MLS-based messaging
      applications

   Fragment identifier considerations:  N/A

   Additional information:

      Deprecated alias names for this type:  N/A
      Magic number(s):  N/A
      File extension(s):  N/A
      Macintosh file type code(s):  N/A

   Person & email address to contact for further information:  IETF MLS
      Working Group <mailto:mls@ietf.org>

   Intended usage:  COMMON

   Restrictions on usage:  N/A

   Author:  IETF MLS Working Group

   Change controller:  IETF

18.  References

18.1.  Normative References

   [RFC2104]  Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
              Hashing for Message Authentication", RFC 2104,
              DOI 10.17487/RFC2104, February 1997,
              <https://www.rfc-editor.org/info/rfc2104>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC8126]  Cotton, M., Leiba, B., and T. Narten, "Guidelines for
              Writing an IANA Considerations Section in RFCs", BCP 26,
              RFC 8126, DOI 10.17487/RFC8126, June 2017,
              <https://www.rfc-editor.org/info/rfc8126>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

   [RFC8446]  Rescorla, E., "The Transport Layer Security (TLS) Protocol
              Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
              <https://www.rfc-editor.org/info/rfc8446>.

   [RFC9180]  Barnes, R., Bhargavan, K., Lipp, B., and C. Wood, "Hybrid
              Public Key Encryption", RFC 9180, DOI 10.17487/RFC9180,
              February 2022, <https://www.rfc-editor.org/info/rfc9180>.

18.2.  Informative References

   [ART]      Cohn-Gordon, K., Cremers, C., Garratt, L., Millican, J.,
              and K. Milner, "On Ends-to-Ends Encryption: Asynchronous
              Group Messaging with Strong Security Guarantees", Version
              2.3, DOI 10.1145/3243734.3243747, March 2020,
              <https://eprint.iacr.org/2017/666.pdf>.

   [CFRG-AEAD-LIMITS]
              Günther, F., Thomson, M., and C. A. Wood, "Usage Limits on
              AEAD Algorithms", Work in Progress, Internet-Draft, draft-
              irtf-cfrg-aead-limits-07, 31 May 2023,
              <https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-
              aead-limits-07>.

   [CLINIC]   Miller, B., Huang, L., Joseph, A., and J. Tygar, "I Know
              Why You Went to the Clinic: Risks and Realization of HTTPS
              Traffic Analysis", Privacy Enhancing Technologies, pp.
              143-163, DOI 10.1007/978-3-319-08506-7_8, 2014,
              <https://doi.org/10.1007/978-3-319-08506-7_8>.

   [CONIKS]   Melara, M. S., Blankstein, A., Bonneau, J., Felten, E. W.,
              and M. J. Freedman, "CONIKS: Bringing Key Transparency to
              End Users", Proceedings of the 24th USENIX Security
              Symposium, ISBN 978-1-939133-11-3, August 2015,
              <https://www.usenix.org/system/files/conference/
              usenixsecurity15/sec15-paper-melara.pdf>.

   [DoubleRatchet]
              Cohn-Gordon, K., Cremers, C., Dowling, B., Garratt, L.,
              and D. Stebila, "A Formal Security Analysis of the Signal
              Messaging Protocol", 2017 IEEE European Symposium on
              Security and Privacy (EuroS&P),
              DOI 10.1109/eurosp.2017.27, April 2017,
              <https://doi.org/10.1109/eurosp.2017.27>.

   [HCJ16]    Husák, M., Čermák, M., Jirsík, T., and P. Čeleda, "HTTPS
              traffic analysis and client identification using passive
              SSL/TLS fingerprinting", EURASIP Journal on Information
              Security, Vol. 2016, Issue 1,
              DOI 10.1186/s13635-016-0030-7, February 2016,
              <https://doi.org/10.1186/s13635-016-0030-7>.

   [KT]       "Key Transparency Design Doc", commit fb0f87f, June 2020,
              <https://github.com/google/keytransparency/blob/master/
              docs/design.md>.

   [MLS-ARCH] Beurdouche, B., Rescorla, E., Omara, E., Inguva, S., and
              A. Duric, "The Messaging Layer Security (MLS)
              Architecture", Work in Progress, Internet-Draft, draft-
              ietf-mls-architecture-10, 16 December 2022,
              <https://datatracker.ietf.org/doc/html/draft-ietf-mls-
              architecture-10>.

   [NAN]      Bellare, M., Ng, R., and B. Tackmann, "Nonces Are Noticed:
              AEAD Revisited", Advances in Cryptology - CRYPTO 2019, pp.
              235-265, DOI 10.1007/978-3-030-26948-7_9, August 2019,
              <https://doi.org/10.1007/978-3-030-26948-7_9>.

   [RFC5116]  McGrew, D., "An Interface and Algorithms for Authenticated
              Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008,
              <https://www.rfc-editor.org/info/rfc5116>.

   [RFC5905]  Mills, D., Martin, J., Ed., Burbank, J., and W. Kasch,
              "Network Time Protocol Version 4: Protocol and Algorithms
              Specification", RFC 5905, DOI 10.17487/RFC5905, June 2010,
              <https://www.rfc-editor.org/info/rfc5905>.

   [RFC6125]  Saint-Andre, P. and J. Hodges, "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)", RFC 6125, DOI 10.17487/RFC6125, March
              2011, <https://www.rfc-editor.org/info/rfc6125>.

   [RFC7696]  Housley, R., "Guidelines for Cryptographic Algorithm
              Agility and Selecting Mandatory-to-Implement Algorithms",
              BCP 201, RFC 7696, DOI 10.17487/RFC7696, November 2015,
              <https://www.rfc-editor.org/info/rfc7696>.

   [RFC8032]  Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
              Signature Algorithm (EdDSA)", RFC 8032,
              DOI 10.17487/RFC8032, January 2017,
              <https://www.rfc-editor.org/info/rfc8032>.

   [RFC8701]  Benjamin, D., "Applying Generate Random Extensions And
              Sustain Extensibility (GREASE) to TLS Extensibility",
              RFC 8701, DOI 10.17487/RFC8701, January 2020,
              <https://www.rfc-editor.org/info/rfc8701>.

   [RFC9000]  Iyengar, J., Ed. and M. Thomson, Ed., "QUIC: A UDP-Based
              Multiplexed and Secure Transport", RFC 9000,
              DOI 10.17487/RFC9000, May 2021,
              <https://www.rfc-editor.org/info/rfc9000>.

   [RFC9001]  Thomson, M., Ed. and S. Turner, Ed., "Using TLS to Secure
              QUIC", RFC 9001, DOI 10.17487/RFC9001, May 2021,
              <https://www.rfc-editor.org/info/rfc9001>.

   [RFC9113]  Thomson, M., Ed. and C. Benfield, Ed., "HTTP/2", RFC 9113,
              DOI 10.17487/RFC9113, June 2022,
              <https://www.rfc-editor.org/info/rfc9113>.

   [SHS]      National Institute of Standards and Technology (NIST),
              "Secure Hash Standard (SHS)", FIPS PUB 180-4,
              DOI 10.6028/NIST.FIPS.180-4, August 2015,
              <https://doi.org/10.6028/NIST.FIPS.180-4>.

   [Signal]   Perrin(ed), T. and M. Marlinspike, "The Double Ratchet
              Algorithm", Revision 1, November 2016,
              <https://www.signal.org/docs/specifications/
              doubleratchet/>.

Appendix A.  Protocol Origins of Example Trees

   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.

   To construct the tree in Figure 11:

   *  A creates a group with B, ..., G

   *  F sends an empty Commit, setting X, Y, and W

   *  G removes C and D, blanking V, U, and setting Y and W

   *  B sends an empty Commit, setting T and W

   To construct the tree in Figure 10:

   *  A creates a group with B, ..., H, as well as some members outside
      this subtree

   *  F sends an empty Commit, setting Y and its ancestors

   *  D removes B and C, with the following effects:

      -  Blank the direct paths of B and C

      -  Set X, the top node, and any further nodes in the direct path
         of D

   *  Someone outside this subtree removes G, blanking the direct path
      of G

   *  A adds a new member at B with a partial Commit, adding B as
      unmerged at X

   To construct the tree in Figure 13:

   *  A creates a group with B, C, and D

   *  B sends a full Commit, setting X and Y

   *  D removes C, setting Z and Y

   *  B adds a new member at C with a full Commit

      -  The Add proposal adds C as unmerged at Z and Y

      -  The path in the Commit resets X and Y, clearing Y's unmerged
         leaves

   To construct the tree in Figure 21:

   *  A creates a group with B, ..., G

   *  A removes F in a full Commit, setting T, U, and W

   *  E sends an empty Commit, setting Y and W

   *  A adds a new member at F in a partial Commit, adding F as unmerged
      at Y and W

Appendix B.  Evolution of Parent Hashes

   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:

   1.  A initializes a new group

   2.  A adds B to the group with a full Commit

   3.  B adds C and D to the group with a full Commit

   4.  C sends an empty Commit

                             Y                   Y'
                             |                   |
                           .-+-.               .-+-.
      ==>         ==>     /     \     ==>     /     \
             X           X'      _=Z         X'      Z'
            / \         / \     / \         / \     / \
   A       A   B       A   B   C   D       A   B   C   D

     Figure 30: Building a Four-Member Tree to Illustrate Parent Hashes

   Then the parent hashes associated to the nodes will be updated as
   follows (where we use the shorthand ph for parent hash, th for tree
   hash, and osth for original sibling tree hash):

   1.  A adds B: set X

       *  A.parent_hash = ph(X) = H(X, ph="", osth=th(B))

   2.  B adds C, D: set B', X', and Y

       *  X'.parent_hash = ph(Y) = H(Y, ph="", osth=th(Z)), where th(Z)
          covers (C, _, D)

       *  B'.parent_hash = ph(X') = H(X', ph=X'.parent_hash, osth=th(A))

   3.  C sends empty Commit: set C', Z', Y'

       *  Z'.parent_hash = ph(Y') = H(Y', ph="", osth=th(X')), where
          th(X') covers (A, X', B')

       *  C'.parent_hash = ph(Z') = H(Z', ph=Z'.parent_hash, osth=th(D))

   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:

   +======+======================================+=====================+
   | Node | Parent Hash Value                    | Valid?              |
   +======+======================================+=====================+
   | A    | H(X, ph="", osth=th(B))              | No, B changed       |
   +------+--------------------------------------+---------------------+
   | B'   | H(X', ph=X'.parent_hash, osth=th(A)) | Yes                 |
   +------+--------------------------------------+---------------------+
   | C'   | H(Z', ph=Z'.parent_hash, osth=th(D)) | Yes                 |
   +------+--------------------------------------+---------------------+
   | D    | (none, never sent an UpdatePath)     | N/A                 |
   +------+--------------------------------------+---------------------+
   | X'   | H(Y, ph="", osth=th(Z))              | No, Y and Z         |
   |      |                                      | changed             |
   +------+--------------------------------------+---------------------+
   | Z'   | H(Y', ph="", osth=th(X'))            | Yes                 |
   +------+--------------------------------------+---------------------+

                                  Table 15

   In other words, the joiner will find the following path-hash links in
   the tree:

          Y'
          |
          +-.
             \
      X'      Z'
       \     /
    A   B'  C'  D

      Figure 31: Parent-hash links connect all non-empty parent nodes
                                 to leaves

   Since these chains collectively cover all non-blank parent nodes in
   the tree, the tree is parent-hash valid.

   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 a 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.

   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 is never a circular dependency.

   In the particular case where a new member first receives the tree for
   a group (e.g., in a ratchet tree GroupInfo extension
   Section 12.4.3.3), 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.
   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).

Appendix C.  Array-Based Trees

   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 n-th leaf at 2*n.  Intermediate
   nodes are held in odd-numbered nodes.  For example, the tree with 8
   leaves has the following structure:

                              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

          Figure 32: An Eight-Member Tree Represented as an Array

   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 x
   is an arbitrary bit string):

   parent=01x => left=00x, right=10x

   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 N nodes in the array:

   *  Add: Append N + 1 blank values to the end of the array.

   *  Remove: Truncate the array to its first (N-1) / 2 entries.

   The following python code demonstrates the tree computations
   necessary to use an array-based tree for MLS.

   # 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

Appendix D.  Link-Based Trees

   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.

   The following code snippet shows how these algorithms could be
   implemented in Python.

   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.right == None) or self.right.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=L, right=R)
           self.depth += 1

       # Truncate the right subtree
       def truncate(self):
           if self.root == None:
               return

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

           self.depth -= 1
           self.root = self.root.left

Contributors

   Joel Alwen
   Amazon
   Email: alwenjo@amazon.com


   Karthikeyan Bhargavan
   Inria
   Email: karthikeyan.bhargavan@inria.fr


   Cas Cremers
   CISPA
   Email: cremers@cispa.de


   Alan Duric
   Wire
   Email: alan@wire.com


   Britta Hale
   Naval Postgraduate School
   Email: britta.hale@nps.edu


   Srinivas Inguva
   Email: singuva@yahoo.com


   Konrad Kohbrok
   Phoenix R&D
   Email: konrad.kohbrok@datashrine.de


   Albert Kwon
   MIT
   Email: kwonal@mit.edu


   Tom Leavy
   Amazon
   Email: tomleavy@amazon.com


   Brendan McMillion
   Email: brendanmcmillion@gmail.com


   Marta Mularczyk
   Amazon
   Email: mulmarta@amazon.com


   Eric Rescorla
   Mozilla
   Email: ekr@rtfm.com


   Michael Rosenberg
   Trail of Bits
   Email: michael.rosenberg@trailofbits.com


   Théophile Wallez
   Inria
   Email: theophile.wallez@inria.fr


   Thyla van der Merwe
   Royal Holloway, University of London
   Email: tjvdmerwe@gmail.com


Authors' Addresses

   Richard Barnes
   Cisco
   Email: rlb@ipv.sx


   Benjamin Beurdouche
   Inria & Mozilla
   Email: ietf@beurdouche.com


   Raphael Robert
   Phoenix R&D
   Email: ietf@raphaelrobert.com


   Jon Millican
   Meta Platforms
   Email: jmillican@meta.com


   Emad Omara
   Email: emad.omara@gmail.com


   Katriel Cohn-Gordon
   University of Oxford
   Email: me@katriel.co.uk
