Network Working Group                                          R. Barnes
Internet-Draft                                                     Cisco
Intended status: Informational                             B. Beurdouche
Expires: 14 April 2022                                   Inria & Mozilla
                                                               R. Robert

                                                             J. Millican
                                                                Facebook
                                                                E. Omara
                                                                  Google
                                                          K. Cohn-Gordon
                                                    University of Oxford
                                                         11 October 2021


              The Messaging Layer Security (MLS) Protocol
                       draft-ietf-mls-protocol-12

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 and post-compromise security for groups in size ranging from
   two to thousands.

Discussion Venues

   This note is to be removed before publishing as an RFC.

   Source for this draft and an issue tracker can be found at
   https://github.com/mlswg/mls-protocol (https://github.com/mlswg/mls-
   protocol).

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.



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   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on 14 April 2022.

Copyright Notice

   Copyright (c) 2021 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 Simplified BSD License text
   as described in Section 4.e of the Trust Legal Provisions and are
   provided without warranty as described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   4
     1.1.  Change Log  . . . . . . . . . . . . . . . . . . . . . . .   5
   2.  Terminology . . . . . . . . . . . . . . . . . . . . . . . . .  10
   3.  Basic Assumptions . . . . . . . . . . . . . . . . . . . . . .  11
   4.  Protocol Overview . . . . . . . . . . . . . . . . . . . . . .  11
   5.  Ratchet Trees . . . . . . . . . . . . . . . . . . . . . . . .  14
     5.1.  Tree Computation Terminology  . . . . . . . . . . . . . .  15
     5.2.  Ratchet Tree Nodes  . . . . . . . . . . . . . . . . . . .  17
     5.3.  Views of a Ratchet Tree . . . . . . . . . . . . . . . . .  18
     5.4.  Ratchet Tree Evolution  . . . . . . . . . . . . . . . . .  19
     5.5.  Synchronizing Views of the Tree . . . . . . . . . . . . .  21
   6.  Cryptographic Objects . . . . . . . . . . . . . . . . . . . .  22
     6.1.  Ciphersuites  . . . . . . . . . . . . . . . . . . . . . .  22
     6.2.  Credentials . . . . . . . . . . . . . . . . . . . . . . .  23
   7.  Key Packages  . . . . . . . . . . . . . . . . . . . . . . . .  25
     7.1.  Key Package IDs . . . . . . . . . . . . . . . . . . . . .  26
     7.2.  Client Capabilities . . . . . . . . . . . . . . . . . . .  27
     7.3.  Lifetime  . . . . . . . . . . . . . . . . . . . . . . . .  27
     7.4.  KeyPackage Identifiers  . . . . . . . . . . . . . . . . .  27
     7.5.  Parent Hash . . . . . . . . . . . . . . . . . . . . . . .  28
       7.5.1.  Using Parent Hashes . . . . . . . . . . . . . . . . .  28
       7.5.2.  Verifying Parent Hashes . . . . . . . . . . . . . . .  29
     7.6.  Tree Hashes . . . . . . . . . . . . . . . . . . . . . . .  30
     7.7.  Group State . . . . . . . . . . . . . . . . . . . . . . .  31
     7.8.  Update Paths  . . . . . . . . . . . . . . . . . . . . . .  32



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   8.  Key Schedule  . . . . . . . . . . . . . . . . . . . . . . . .  33
     8.1.  External Initialization . . . . . . . . . . . . . . . . .  36
     8.2.  Pre-Shared Keys . . . . . . . . . . . . . . . . . . . . .  37
     8.3.  Secret Tree . . . . . . . . . . . . . . . . . . . . . . .  40
     8.4.  Encryption Keys . . . . . . . . . . . . . . . . . . . . .  41
     8.5.  Deletion Schedule . . . . . . . . . . . . . . . . . . . .  42
     8.6.  Exporters . . . . . . . . . . . . . . . . . . . . . . . .  43
     8.7.  Resumption Secret . . . . . . . . . . . . . . . . . . . .  44
     8.8.  State Authentication Keys . . . . . . . . . . . . . . . .  44
   9.  Message Framing . . . . . . . . . . . . . . . . . . . . . . .  44
     9.1.  Content Authentication  . . . . . . . . . . . . . . . . .  47
     9.2.  Content Encryption  . . . . . . . . . . . . . . . . . . .  49
     9.3.  Sender Data Encryption  . . . . . . . . . . . . . . . . .  50
   10. Group Creation  . . . . . . . . . . . . . . . . . . . . . . .  51
     10.1.  Required Capabilities  . . . . . . . . . . . . . . . . .  52
     10.2.  Linking a New Group to an Existing Group . . . . . . . .  53
       10.2.1.  Sub-group Branching  . . . . . . . . . . . . . . . .  53
   11. Group Evolution . . . . . . . . . . . . . . . . . . . . . . .  53
     11.1.  Proposals  . . . . . . . . . . . . . . . . . . . . . . .  54
       11.1.1.  Add  . . . . . . . . . . . . . . . . . . . . . . . .  54
       11.1.2.  Update . . . . . . . . . . . . . . . . . . . . . . .  56
       11.1.3.  Remove . . . . . . . . . . . . . . . . . . . . . . .  56
       11.1.4.  PreSharedKey . . . . . . . . . . . . . . . . . . . .  57
       11.1.5.  ReInit . . . . . . . . . . . . . . . . . . . . . . .  57
       11.1.6.  ExternalInit . . . . . . . . . . . . . . . . . . . .  58
       11.1.7.  AppAck . . . . . . . . . . . . . . . . . . . . . . .  58
       11.1.8.  GroupContextExtensions . . . . . . . . . . . . . . .  59
       11.1.9.  External Proposals . . . . . . . . . . . . . . . . .  60
     11.2.  Commit . . . . . . . . . . . . . . . . . . . . . . . . .  61
       11.2.1.  External Commits . . . . . . . . . . . . . . . . . .  68
       11.2.2.  Welcoming New Members  . . . . . . . . . . . . . . .  71
     11.3.  Ratchet Tree Extension . . . . . . . . . . . . . . . . .  74
   12. Extensibility . . . . . . . . . . . . . . . . . . . . . . . .  75
   13. Sequencing of State Changes . . . . . . . . . . . . . . . . .  77
     13.1.  Server-Enforced Ordering . . . . . . . . . . . . . . . .  78
     13.2.  Client-Enforced Ordering . . . . . . . . . . . . . . . .  78
   14. Application Messages  . . . . . . . . . . . . . . . . . . . .  78
     14.1.  Message Encryption and Decryption  . . . . . . . . . . .  79
     14.2.  Restrictions . . . . . . . . . . . . . . . . . . . . . .  80
     14.3.  Delayed and Reordered Application messages . . . . . . .  80
   15. Security Considerations . . . . . . . . . . . . . . . . . . .  80
     15.1.  Confidentiality of the Group Secrets . . . . . . . . . .  80
     15.2.  Authentication . . . . . . . . . . . . . . . . . . . . .  81
     15.3.  Forward Secrecy and Post-Compromise Security . . . . . .  81
     15.4.  InitKey Reuse  . . . . . . . . . . . . . . . . . . . . .  82
     15.5.  Group Fragmentation by Malicious Insiders  . . . . . . .  82
   16. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  83
     16.1.  MLS Ciphersuites . . . . . . . . . . . . . . . . . . . .  83



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     16.2.  MLS Extension Types  . . . . . . . . . . . . . . . . . .  86
     16.3.  MLS Proposal Types . . . . . . . . . . . . . . . . . . .  87
     16.4.  MLS Credential Types . . . . . . . . . . . . . . . . . .  88
     16.5.  MLS Designated Expert Pool . . . . . . . . . . . . . . .  89
   17. Contributors  . . . . . . . . . . . . . . . . . . . . . . . .  90
   18. References  . . . . . . . . . . . . . . . . . . . . . . . . .  91
     18.1.  Normative References . . . . . . . . . . . . . . . . . .  91
     18.2.  Informative References . . . . . . . . . . . . . . . . .  92
   Appendix A.  Tree Math  . . . . . . . . . . . . . . . . . . . . .  93
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  96

1.  Introduction

   DISCLAIMER: This is a work-in-progress draft of MLS and has not yet
   seen significant security analysis.  It should not be used as a basis
   for building production systems.

   RFC EDITOR: PLEASE REMOVE THE FOLLOWING PARAGRAPH The source for this
   draft is maintained in GitHub.  Suggested changes should be submitted
   as pull requests at https://github.com/mlswg/mls-protocol.
   Instructions are on that page as well.  Editorial changes can be
   managed in GitHub, but any substantive change should be discussed on
   the MLS mailing list.

   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
   unilaterally broadcast symmetric "sender" keys over existing shared
   symmetric channels, and then for each member to send messages to the
   group encrypted with their own sender key.  Unfortunately, while this
   improves efficiency over pairwise broadcast of individual messages
   and provides forward secrecy (with the addition of a hash ratchet),
   it is difficult to achieve post-compromise security with sender keys.
   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.






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

1.1.  Change Log

   RFC EDITOR PLEASE DELETE THIS SECTION.

   draft-12

   *  Use the GroupContext to derive the joiner_secret (*)

   *  Make PreSharedKeys non optional in GroupSecrets (*)

   *  Update name for this particular key (*)

   *  Truncate tree size on removal (*)

   *  Use HPKE draft-08 (*)

   *  Clarify requirements around identity in MLS groups (*)

   *  Signal the intended wire format for MLS messages (*)

   *  Inject GroupContext as HPKE info instead of AAD (*)

   *  Clarify extension handling and make extension updatable (*)

   *  Improve extensibility of Proposals (*)

   *  Constrain proposal in External Commit (*)

   *  Remove the notion of a 'leaf index' (*)

   *  Add group_context_extensions proposal ID (*)

   *  Add RequiredCapabilities extension (*)

   *  Use cascaded KDF instead of concatenation to consolidate PSKs (*)

   *  Use key package hash to index clients in message structs (*)

   *  Don't require PublicGroupState for external init (*)




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   *  Make ratchet tree section clearer.

   *  Handle non-member sender cases in MLSPlaintextTBS

   *  Clarify encoding of signatures with NIST curves

   *  Remove OPEN ISSUEs and TODOs

   *  Normalize the description of the zero vector

   draft-11

   *  Include subtree keys in parent hash (*)

   *  Pin HPKE to draft-07 (*)

   *  Move joiner secret to the end of the first key schedule epoch (*)

   *  Add an AppAck proposal

   *  Make initializations of transcript hashes consistent

   draft-10

   *  Allow new members to join via an external Commit (*)

   *  Enable proposals to be sent inline in a Commit (*)

   *  Re-enable constant-time Add (*)

   *  Change expiration extension to lifetime extension (*)

   *  Make the tree in the Welcome optional (*)

   *  PSK injection, re-init, sub-group branching (*)

   *  Require the initial init_secret to be a random value (*)

   *  Remove explicit sender data nonce (*)

   *  Do not encrypt to joiners in UpdatePath generation (*)

   *  Move MLSPlaintext signature under the confirmation tag (*)

   *  Explicitly authenticate group membership with MLSPLaintext (*)

   *  Clarify X509Credential structure (*)




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   *  Remove uneeded interim transcript hash from GroupInfo (*)

   *  IANA considerations

   *  Derive an authentication secret

   *  Use Extract/Expand from HPKE KDF

   *  Clarify that application messages MUST be encrypted

   draft-09

   *  Remove blanking of nodes on Add (*)

   *  Change epoch numbers to uint64 (*)

   *  Add PSK inputs (*)

   *  Add key schedule exporter (*)

   *  Sign the updated direct path on Commit, using "parent hashes" and
      one signature per leaf (*)

   *  Use structured types for external senders (*)

   *  Redesign Welcome to include confirmation and use derived keys (*)

   *  Remove ignored proposals (*)

   *  Always include an Update with a Commit (*)

   *  Add per-message entropy to guard against nonce reuse (*)

   *  Use the same hash ratchet construct for both application and
      handshake keys (*)

   *  Add more ciphersuites

   *  Use HKDF to derive key pairs (*)

   *  Mandate expiration of ClientInitKeys (*)

   *  Add extensions to GroupContext and flesh out the extensibility
      story (*)

   *  Rename ClientInitKey to KeyPackage

   draft-08



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   *  Change ClientInitKeys so that they only refer to one ciphersuite
      (*)

   *  Decompose group operations into Proposals and Commits (*)

   *  Enable Add and Remove proposals from outside the group (*)

   *  Replace Init messages with multi-recipient Welcome message (*)

   *  Add extensions to ClientInitKeys for expiration and downgrade
      resistance (*)

   *  Allow multiple Proposals and a single Commit in one MLSPlaintext
      (*)

   draft-07

   *  Initial version of the Tree based Application Key Schedule (*)

   *  Initial definition of the Init message for group creation (*)

   *  Fix issue with the transcript used for newcomers (*)

   *  Clarifications on message framing and HPKE contexts (*)

   draft-06

   *  Reorder blanking and update in the Remove operation (*)

   *  Rename the GroupState structure to GroupContext (*)

   *  Rename UserInitKey to ClientInitKey

   *  Resolve the circular dependency that draft-05 introduced in the
      confirmation MAC calculation (*)

   *  Cover the entire MLSPlaintext in the transcript hash (*)

   draft-05

   *  Common framing for handshake and application messages (*)

   *  Handshake message encryption (*)

   *  Convert from literal state to a commitment via the "tree hash" (*)

   *  Add credentials to the tree and remove the "roster" concept (*)




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   *  Remove the secret field from tree node values

   draft-04

   *  Updating the language to be similar to the Architecture document

   *  ECIES is now renamed in favor of HPKE (*)

   *  Using a KDF instead of a Hash in TreeKEM (*)

   draft-03

   *  Added ciphersuites and signature schemes (*)

   *  Re-ordered fields in UserInitKey to make parsing easier (*)

   *  Fixed inconsistencies between Welcome and GroupState (*)

   *  Added encryption of the Welcome message (*)

   draft-02

   *  Removed ART (*)

   *  Allowed partial trees to avoid double-joins (*)

   *  Added explicit key confirmation (*)

   draft-01

   *  Initial description of the Message Protection mechanism. (*)

   *  Initial specification proposal for the Application Key Schedule
      using the per-participant chaining of the Application Secret
      design. (*)

   *  Initial specification proposal for an encryption mechanism to
      protect Application Messages using an AEAD scheme. (*)

   *  Initial specification proposal for an authentication mechanism of
      Application Messages using signatures. (*)

   *  Initial specification proposal for a padding mechanism to
      improving protection of Application Messages against traffic
      analysis. (*)






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   *  Inversion of the Group Init Add and Application Secret derivations
      in the Handshake Key Schedule to be ease chaining in case we
      switch design. (*)

   *  Removal of the UserAdd construct and split of GroupAdd into Add
      and Welcome messages (*)

   *  Initial proposal for authenticating handshake messages by signing
      over group state and including group state in the key schedule (*)

   *  Added an appendix with example code for tree math

   *  Changed the ECIES mechanism used by TreeKEM so that it uses nonces
      generated from the shared secret

   draft-00

   *  Initial adoption of draft-barnes-mls-protocol-01 as a WG item.

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 collection of clients with shared cryptographic state.

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

   Key Package:  A signed object describing a client's identity and
      capabilities, and including a hybrid public-key encryption (HPKE
      [I-D.irtf-cfrg-hpke]) public key that can be used to encrypt to
      that client.

   Initialization Key (InitKey):  A key package that is prepublished by
      a client, which other clients can use to introduce the client to a
      new group.

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




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   Terminology specific to tree computations is described in Section 5.

   We use the TLS presentation language [RFC8446] to describe the
   structure of protocol messages.

3.  Basic Assumptions

   This protocol is designed to execute in the context of a Service
   Provider (SP) as described in [I-D.ietf-mls-architecture].  In
   particular, we assume the SP provides the following services:

   *  A signature key provider which allows clients to authenticate
      protocol messages in a group.

   *  A broadcast channel, for each group, which will relay a message to
      all members of a group.  For the most part, we assume that this
      channel delivers messages in the same order to all participants.
      (See Section 13 for further considerations.)

   *  A directory to which clients can publish key packages and download
      key packages for other participants.

4.  Protocol Overview

   The goal of this protocol is to allow a group of clients to exchange
   confidential and authenticated messages.  It does so by deriving a
   sequence of secrets and keys known only to members.  Those should be
   secret against an active network adversary and should have both
   forward secrecy and post-compromise security with respect to
   compromise of any members.

   We describe the information stored by each client as _state_, which
   includes both public and private data.  An initial state is set up by
   a group creator, which is a group containing only itself.  The
   creator then sends _Add_ proposals for each client in the initial set
   of members, followed by a _Commit_ message which incorporates all of
   the _Adds_ into the group state.  Finally, the group creator
   generates a _Welcome_ message corresponding to the Commit and sends
   this directly to all the new members, who can use the information it
   contains to set up their own group state and derive a shared secret.
   Members exchange Commit messages for post-compromise security, to add
   new members, and to remove existing members.  These messages produce
   new shared secrets which are causally linked to their predecessors,
   forming a logical Directed Acyclic Graph (DAG) of states.

   The protocol algorithms we specify here follow.  Each algorithm
   specifies both (i) how a client performs the operation and (ii) how
   other clients update their state based on it.



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

   *  Adding a member, initiated by a current member;

   *  Updating the leaf secret of a member;

   *  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.

   Before the initialization of a group, clients publish InitKeys (as
   KeyPackage objects) to a directory provided by the Service Provider.

                                                                 Group
  A                B                C            Directory       Channel
  |                |                |                |              |
  | KeyPackageA    |                |                |              |
  |------------------------------------------------->|              |
  |                |                |                |              |
  |                | KeyPackageB    |                |              |
  |                |-------------------------------->|              |
  |                |                |                |              |
  |                |                | KeyPackageC    |              |
  |                |                |--------------->|              |
  |                |                |                |              |

   When a client A wants to establish a group with B and C, it first
   initializes a group state containing only itself and downloads
   KeyPackages for B and C.  For each member, A generates an Add and
   Commit message adding that member, and broadcasts them to the group.
   It also generates a Welcome message and sends this directly to the
   new member (there's no need to send it to the group).  Only after A
   has received its Commit message back from the server does it update
   its state to reflect the new member's addition.

   Upon receiving the Welcome message, the new member will be able to
   read and send new messages to the group.  Messages received before
   the client has joined the group are ignored.







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                                                                  Group
   A              B              C          Directory            Channel
   |              |              |              |                   |
   |         KeyPackageB, KeyPackageC           |                   |
   |<-------------------------------------------|                   |
   |state.init()  |              |              |                   |
   |              |              |              |                   |
   |              |              |              | Add(A->AB)        |
   |              |              |              | Commit(Add)       |
   |--------------------------------------------------------------->|
   |              |              |              |                   |
   |  Welcome(B)  |              |              |                   |
   |------------->|state.join()  |              |                   |
   |              |              |              |                   |
   |              |              |              | Add(A->AB)        |
   |              |              |              | Commit(Add)       |
   |<---------------------------------------------------------------|
   |state.add(B)  |              |              |                   |
   |              |              |              |                   |
   |              |              |              |                   |
   |              |              |              | Add(AB->ABC)      |
   |              |              |              | Commit(Add)       |
   |--------------------------------------------------------------->|
   |              |              |              |                   |
   |              |  Welcome(C)  |              |                   |
   |---------------------------->|state.join()  |                   |
   |              |              |              |                   |
   |              |              |              | Add(AB->ABC)      |
   |              |              |              | Commit(Add)       |
   |<---------------------------------------------------------------|
   |state.add(C)  |<------------------------------------------------|
   |              |state.add(C)  |              |                   |
   |              |              |              |                   |

   Subsequent additions of group members proceed in the same way.  Any
   member of the group can download a KeyPackage for a new client and
   broadcast an Add message that the current group can use to update
   their state, and 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 their leaf secret.  Any
   member can update this information at any time by generating a fresh
   KeyPackage and sending an Update message followed by a Commit
   message.  Once all members have processed both, the group's secrets
   will be unknown to an attacker that had compromised the sender's
   prior leaf secret.




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   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.

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

   Members are removed from the group in a similar way.  Any member of
   the group can send a Remove proposal followed by a Commit message,
   which adds new entropy to the group state that's known to all except
   the removed member.  Note that this does not necessarily imply that
   any member is actually allowed to evict other members; groups can
   enforce access control policies on top of these basic mechanism.

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

5.  Ratchet Trees

   The protocol uses "ratchet trees" for deriving shared secrets among a
   group of clients.




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5.1.  Tree Computation Terminology

   Trees consist of _nodes_. A node is a _leaf_ if it has no children,
   and a _parent_ otherwise; note that 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 parents, and _intermediate_ if
   it has both children and parents.  The _descendants_ of a node are
   that node, its children, and the descendants of its children, and we
   say a tree _contains_ a node if that node is a descendant of the root
   of the tree.  Nodes are _siblings_ if they share the same parent.

   A _subtree_ of a tree is the tree given by the descendants of any
   node, the _head_ of the subtree.  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
   (respectively _right subtree_).

   All trees used in this protocol are left-balanced binary trees.  A
   binary tree is _full_ (and _balanced_) if its size is a power of two
   and for any parent node in the tree, its left and right subtrees have
   the same size.

   A binary tree is _left-balanced_ if for every parent, either the
   parent is balanced, or the left subtree of that parent is the largest
   full subtree that could be constructed from the leaves present in the
   parent's own subtree.  Given a list of n items, there is a unique
   left-balanced binary tree structure with these elements as leaves.

   (Note that left-balanced binary trees are the same structure that is
   used for the Merkle trees in the Certificate Transparency protocol
   [I-D.ietf-trans-rfc6962-bis].)

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

   For example, in the below tree:

   *  The direct path of C is (CD, ABCD, ABCDEFG)

   *  The copath of C is (D, AB, EFG)








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                 7 = root
           ______|______
          /             \
         3              11
       __|__           __|
      /     \         /   \
     1       5       9     |
    / \     / \     / \    |
   A   B   C   D   E   F   G

                       1 1 1
   0 1 2 3 4 5 6 7 8 9 0 1 2

   Each node in the tree is assigned an _index_, starting at zero and
   running from left to right.  A node is a leaf node if and only if it
   has an even index.  The node indices for the nodes in the above tree
   are as follows:

   *  0 = A

   *  1 = AB

   *  2 = B

   *  3 = ABCD

   *  4 = C

   *  5 = CD

   *  6 = D

   *  7 = ABCDEFG

   *  8 = E

   *  9 = EF

   *  10 = F

   *  11 = EFG

   *  12 = G

   A tree with n leaves has 2*n - 1 nodes.  For example, the above tree
   has 7 leaves (A, B, C, D, E, F, G) and 13 nodes.  The root of a tree
   with n leaves is always the node with index 2^k - 1, where k is the
   largest number such that 2^k < n.



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5.2.  Ratchet Tree Nodes

   A particular instance of a ratchet tree is defined by the same
   parameters that define an instance of HPKE, namely:

   *  A Key Encapsulation Mechanism (KEM), including a DeriveKeyPair
      function that creates a key pair for the KEM from a symmetric
      secret

   *  A Key Derivation Function (KDF), including Extract and Expand
      functions

   *  An AEAD encryption scheme

   Each node in a ratchet tree contains up to five values:

   *  A private key (only within the member's direct path, see below)

   *  A public key

   *  An ordered list of node indices for "unmerged" leaves (see
      Section 5.3)

   *  A credential (only for leaf nodes)

   *  A hash of certain information about the node's parent, as of the
      last time the node was changed (see Section 7.5).

   The conditions under which each of these values must or must not be
   present are laid out in Section 5.3.

   A node in the tree may also be _blank_, indicating that no value is
   present at that node.  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 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 tree, where the "_" character
   represents a blank node and unmerged leaves are indicated in square
   brackets:



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         _
       __|__
      /     \
     _       5[C]
    / \     / \
   A   _   C   D

   0 1 2 3 4 5 6

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

   *  The resolution of node 5 is the list [CD, C]

   *  The resolution of node 2 is the empty list []

   *  The resolution of node 3 is the list [A, CD, C]

   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 7.6.

5.3.  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 that member's leaf is a descendant of
   the node.

   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 keys of all the intermediate nodes they're below.  Such a
   member has an _unmerged_ leaf.  Encrypting to an intermediate node



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   requires encrypting to the node's public key, as well as the public
   keys of all the unmerged leaves below it.  A leaf is unmerged when it
   is first added, because the process of adding the leaf does not give
   it access to all of the nodes above it in the tree.  Leaves are
   "merged" as they receive the private keys for nodes, as described in
   Section 5.4.

5.4.  Ratchet Tree Evolution

   A member of an MLS group advances the key schedule to provide forward
   secrecy and post-compromise security by providing the group with
   fresh key material to be added into the group's shared secret.  To do
   so, one member of the group generates fresh key material, applies it
   to their local tree state, and then sends this key material to other
   members in the group via an UpdatePath message (see Section 7.8) .
   All other group members then apply the key material in the UpdatePath
   to their own local tree state to derive the group's now-updated
   shared secret.

   To begin, the generator of the UpdatePath updates its leaf KeyPackage
   and its direct path to the root with new secret values.  The HPKE
   leaf public key within the KeyPackage MUST be derived from a freshly
   generated HPKE secret key to provide post-compromise security.

   The generator of the UpdatePath starts by sampling a fresh random
   value called "leaf_secret", and uses the leaf_secret to generate
   their leaf HPKE key pair (see Section 7) and to seed a sequence of
   "path secrets", one for each ancestor of its leaf.  In this setting,
   path_secret[0] refers to the node directly above the leaf,
   path_secret[1] for its parent, and so on.  At each step, the path
   secret is used to derive a new secret value for the corresponding
   node, from which the node's key pair is derived.

   leaf_node_secret = DeriveSecret(leaf_secret, "node")
   path_secret[0] = DeriveSecret(leaf_secret, "path")

   path_secret[n] = DeriveSecret(path_secret[n-1], "path")
   node_secret[n] = DeriveSecret(path_secret[n], "node")

   leaf_priv, leaf_pub = KEM.DeriveKeyPair(leaf_node_secret)
   node_priv[n], node_pub[n] = KEM.DeriveKeyPair(node_secret[n])

   For example, suppose there is a group with four members, with C an
   unmerged leaf at node 5:







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         3
       __|__
      /     \
     1       5[C]
    / \     / \
   A   B   C   D

   0 1 2 3 4 5 6

   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_key_package

   After applying the UpdatePath, the tree will have the following
   structure, where lp and np[i] represent the leaf_priv and node_priv
   values generated as described above:

       np[1] -> 3
              __|__
             /     \
   np[0] -> 1       5[C]
           / \     / \
          A   B   C   D
              ^
              |
              lp

          0 1 2 3 4 5 6

   After performing these operations, the generator of the UpdatePath
   MUST delete the leaf_secret.











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5.5.  Synchronizing Views of the Tree

   After generating fresh key material and applying it to ratchet
   forward their local tree state as described in the prior section, the
   generator must broadcast 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 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
   direct path of the sender's leaf, including the root:

   *  The public key for the node

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

   The path secret value for a given node is encrypted for the subtree
   corresponding to the parent's non-updated child, that is, 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.

   The recipient of an UpdatePath processes it with the following steps:

   1.  Compute the updated path secrets.

       *  Identify a node in the direct path for which the local member
          is in the subtree of the non-updated child.

       *  Identify a node in the resolution of the copath node for which
          this node has a private key.

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

       *  Derive path secrets for ancestors of that node using the
          algorithm described above.

       *  The recipient SHOULD verify that the received public keys
          agree with the public keys derived from the new path_secret
          values.

   2.  Merge the updated path secrets into the tree.



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       *  For all updated nodes,

          -  Replace the public key for each node with the received
             public key.

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

          -  Store the updated hash of the node's parent (represented as
             a ParentNode struct), going from root to leaf, so that each
             hash incorporates all the nodes above it.  The root node
             always has a zero-length hash for this value.

       *  For nodes where an updated path secret was computed in step 1,
          compute the corresponding node key pair and replace the values
          stored at the node with the computed values.

   For example, in order to communicate the example update described in
   the previous section, the sender would transmit the following values:

   +=============+====================================================+
   | Public Key  | Ciphertext(s)                                      |
   +=============+====================================================+
   | node_pub[1] | E(pk(5), path_secret[1]), E(pk(C), path_secret[1]) |
   +-------------+----------------------------------------------------+
   | node_pub[0] | E(pk(A), path_secret[0])                           |
   +-------------+----------------------------------------------------+

                                 Table 1

   In this table, the value pk(ns[X]) represents the public key derived
   from the node secret X, whereas pk(X) represents the public leaf key
   for user X.  The value E(K, S) represents the public-key encryption
   of the path secret S to the public key K (using HPKE).

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

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

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

6.  Cryptographic Objects

6.1.  Ciphersuites

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




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   *  HPKE parameters:

      -  A Key Encapsulation Mechanism (KEM)

      -  A Key Derivation Function (KDF)

      -  An AEAD encryption algorithm

   *  A hash algorithm

   *  A signature algorithm

   MLS uses draft-08 of HPKE [I-D.irtf-cfrg-hpke] for public-key
   encryption.  The DeriveKeyPair function associated to the KEM for the
   ciphersuite maps octet strings to HPKE key pairs.

   Ciphersuites are represented with the CipherSuite type.  HPKE public
   keys are opaque values in a format defined by the underlying protocol
   (see the Cryptographic Dependencies section of the HPKE specification
   for more information).

   opaque HPKEPublicKey<1..2^16-1>;

   The signature algorithm specified in the ciphersuite is the mandatory
   algorithm to be used for signatures in MLSPlaintext and the tree
   signatures.  It MUST be the same as the signature algorithm specified
   in the credential field of the KeyPackage objects in the leaves of
   the tree (including the InitKeys used to add new members).

   The ciphersuites are defined in section Section 16.1.

6.2.  Credentials

   A member of a group authenticates the identities of other
   participants by means of credentials issued by some authentication
   system, like a PKI.  Each type of credential MUST express the
   following data in the context of the group it is used with:

   *  The public key of a signature key pair matching the
      SignatureScheme specified by the CipherSuite of the group

   *  The identity of the holder of the private key

   Credentials MAY also include information that allows a relying party
   to verify the identity / signing key binding.

   Additionally, Credentials SHOULD specify the signature scheme
   corresponding to each contained public key.



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   // See RFC 8446 and the IANA TLS SignatureScheme registry
   uint16 SignatureScheme;

   // See IANA registry for registered values
   uint16 CredentialType;

   struct {
       opaque identity<0..2^16-1>;
       SignatureScheme signature_scheme;
       opaque signature_key<0..2^16-1>;
   } BasicCredential;

   struct {
       opaque cert_data<0..2^16-1>;
   } Certificate;

   struct {
       CredentialType credential_type;
       select (Credential.credential_type) {
           case basic:
               BasicCredential;

           case x509:
               Certificate chain<1..2^32-1>;
       };
   } Credential;

   A BasicCredential is a raw, unauthenticated assertion of an identity/
   key binding.  The format of the key in the public_key field is
   defined by the relevant ciphersuite: the group ciphersuite for a
   credential in a ratchet tree, the KeyPackage ciphersuite for a
   credential in a KeyPackage object.

   For X509Credential, each entry in the chain represents a single DER-
   encoded X509 certificate.  The chain is ordered such that the first
   entry (chain[0]) is the end-entity certificate and each subsequent
   certificate in the chain MUST be the issuer of the previous
   certificate.  The algorithm for the public_key in the end-entity
   certificate MUST match the relevant ciphersuite.

   For ciphersuites using Ed25519 or Ed448 signature schemes, the public
   key is in the format specified [RFC8032].  For ciphersuites using
   ECDSA with the NIST curves P-256 or P-521, the public key is the
   output of the uncompressed Elliptic-Curve-Point-to-Octet-String
   conversion according to [SECG].






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   The signatures used throughout 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].

   Note that each new credential that has not already been validated by
   the application MUST be validated against the Authentication Service.

7.  Key Packages

   In order to facilitate asynchronous addition of clients to a group,
   it is possible to pre-publish key packages that provide some public
   information about a user.  KeyPackage structures provide information
   about a client that any existing member can use to add this client to
   the group asynchronously.

   A KeyPackage object specifies a ciphersuite that the client supports,
   as well as providing a public key that others can use for key
   agreement.

   The identity arising from the credential, together with the
   endpoint_id in the KeyPackage serve to uniquely identify a client in
   a group.

   When used as InitKeys, KeyPackages are intended to be used only once
   and SHOULD NOT be reused except in case of last resort.  (See
   Section 15.4).  Clients MAY generate and publish multiple InitKeys to
   support multiple ciphersuites.

   KeyPackages contain a public key chosen by the client, which the
   client MUST ensure uniquely identifies a given KeyPackage object
   among the set of KeyPackages created by this client.

   The value for hpke_init_key MUST be a public key for the asymmetric
   encryption scheme defined by cipher_suite.  The whole structure is
   signed using the client's signature key.  A KeyPackage object with an
   invalid signature field MUST be considered malformed.  The input to
   the signature computation comprises all of the fields except for the
   signature field.












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   enum {
       reserved(0),
       mls10(1),
       (255)
   } ProtocolVersion;

   // See IANA registry for registered values
   uint16 ExtensionType;

   struct {
       ExtensionType extension_type;
       opaque extension_data<0..2^32-1>;
   } Extension;

   struct {
       ProtocolVersion version;
       CipherSuite cipher_suite;
       HPKEPublicKey hpke_init_key;
       opaque endpoint_id<0..255>;
       Credential credential;
       Extension extensions<8..2^32-1>;
       opaque signature<0..2^16-1>;
   } KeyPackage;

   KeyPackage objects MUST contain at least two extensions, one of type
   capabilities, and one of type lifetime.  The capabilities extension
   allow MLS session establishment to be safe from downgrade attacks on
   the parameters described (as discussed in Section 10), while still
   only advertising one version / ciphersuite per KeyPackage.

   As the KeyPackage is a structure which is stored in the Ratchet Tree
   and updated depending on the evolution of this tree, each
   modification of its content MUST be reflected by a change of its
   signature.  This allow other members to control the validity of the
   KeyPackage at any time and in particular in the case of a newcomer
   joining the group.

7.1.  Key Package IDs

   When it is necessary to refer to a specific KeyPackage, protocol
   messages incorporate a KeyPackageID:

   struct { opaque key_package_hash<0..255>; } KeyPackageID

   This value is the hash of the KeyPackage, using the hash indicated by
   the cipher_suite field.  KeyPackage hashes are used in a Welcome
   message to indicate which KeyPackage is being used to include the new
   member.  Since members of a group are uniquely identified by their



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   leaf KeyPackages, messages within a group use the hash of this key
   package to refer to group members, e.g., to specify the target of a
   Remove proposal or the signer of an MLSPlaintext.

7.2.  Client Capabilities

   The capabilities extension indicates what protocol versions,
   ciphersuites, protocol extensions, and non-default proposal types are
   supported by a client.  Proposal types defined in this document are
   considered "default" and thus need not be listed.

   struct {
       ProtocolVersion versions<0..255>;
       CipherSuite ciphersuites<0..255>;
       ExtensionType extensions<0..255>;
       ProposalType proposals<0..255>;
   } Capabilities;

   This extension MUST be always present in a KeyPackage.  Extensions
   that appear in the extensions field of a KeyPackage MUST be included
   in the extensions field of the capabilities extension.

7.3.  Lifetime

   The lifetime extension represents the times between which clients
   will consider a KeyPackage valid.  This time is represented as an
   absolute time, measured in seconds since the Unix epoch
   (1970-01-01T00:00:00Z).  A client MUST NOT use the data in a
   KeyPackage for any processing before the not_before date, or after
   the not_after date.

   uint64 not_before;
   uint64 not_after;

   Applications MUST define a maximum total lifetime that is acceptable
   for a KeyPackage, and reject any KeyPackage where the total lifetime
   is longer than this duration.

   This extension MUST always be present in a KeyPackage.

7.4.  KeyPackage Identifiers

   Within MLS, a KeyPackage is identified by its hash (see, e.g.,
   Section 11.2.2).  The external_key_id extension allows applications
   to add an explicit, application-defined identifier to a KeyPackage.

   opaque external_key_id<0..2^16-1>;




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7.5.  Parent Hash

   The parent_hash extension carries information to authenticate the
   structure of the tree, as described below.

   opaque parent_hash<0..255>;

   Consider a ratchet tree with a parent node P and children V and S.
   The parent hash of P changes whenever an UpdatePath object is applied
   to the ratchet tree along a path traversing node V (and hence also
   P).  The new "Parent Hash of P (with Co-Path Child S)" is obtained by
   hashing P's ParentHashInput struct using the resolution of S to
   populate the original_child_resolution field.  This way, P's Parent
   Hash fixes the new HPKE public keys of all nodes on the path from P
   to the root.  Furthermore, for each such key PK the hash also binds
   the set of HPKE public keys to which PK's secret key was encrypted in
   the commit packet that anounced the UpdatePath object.

   struct {
       HPKEPublicKey public_key;
       opaque parent_hash<0..255>;
       HPKEPublicKey original_child_resolution<0..2^32-1>;
   } ParentHashInput;

   The Parent Hash of P with Co-Path Child S is the hash of a
   ParentHashInput object populated as follows.  The field public_key
   contains the HPKE public key of P.  If P is the root, then
   parent_hash is set to a zero-length octet string.  Otherwise
   parent_hash is the Parent Hash of P's parent with P's sibling as the
   co-path child.

   Finally, original_child_resolution is the array of HPKEPublicKey
   values of the nodes in the resolution of S but with the
   unmerged_leaves of P omitted.  For example, in the ratchet tree
   depicted in Section 5.2 the ParentHashInput of node 5 with co-path
   child 4 would contain an empty original_child_resolution since 4's
   resolution includes only itself but 4 is also an unmerged leaf of 5.
   Meanwhile, the ParentHashInput of node 5 with co-path child 6 has an
   array with one element in it: the HPKE public key of 6.

7.5.1.  Using Parent Hashes

   The Parent Hash of P appears in three types of structs.  If V is
   itself a parent node then P's Parent Hash is stored in the
   parent_hash fields of both V's ParentHashInput struct and V's
   ParentNode struct.  (The ParentNode struct is used to encapsulate all
   public information about V that must be conveyed to a new member
   joining the group as well as to define the Tree Hash of node V.)



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   If, on the other hand, V is a leaf and its KeyPackage contains the
   parent_hash extension then the Parent Hash of P (with V's sibling as
   co-path child) is stored in that field.  In particular, the extension
   MUST be present in the leaf_key_package field of an UpdatePath
   object.  (This way, the signature of such a KeyPackage also serves to
   attest to which keys the group member introduced into the ratchet
   tree and to whom the corresponding secret keys were sent.  This helps
   prevent malicious insiders from constructing artificial ratchet trees
   with a node V whose HPKE secret key is known to the insider yet where
   the insider isn't assigned a leaf in the subtree rooted at V.
   Indeed, such a ratchet tree would violate the tree invariant.)

7.5.2.  Verifying Parent Hashes

   To this end, when processing a Commit message 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_key_package.  Moreover, when joining a group, new members MUST
   authenticate each non-blank parent node P.  A parent node P is
   authenticated by performing the following check:

   *  Let L and R be the left and right children of P, respectively

   *  If L.parent_hash is equal to the Parent Hash of P with Co-Path
      Child R, the check passes

   *  If R is blank, replace R with its left child until R is either
      non-blank or a leaf node

   *  If R is a blank leaf node, the check fails

   *  If R.parent_hash is equal to the Parent Hash of P with Co-Path
      Child L, the check passes

   *  Otherwise, the check fails

   The left-child recursion under the right child of P is necessary
   because the expansion of the tree to the right due to Add proposals
   can cause blank nodes to be interposed between a parent node and its
   right child.











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7.6.  Tree Hashes

   To allow group members to verify that they agree on the public
   cryptographic state of the group, this section defines a scheme for
   generating a hash value (called the "tree hash") that represents the
   contents of the group's ratchet tree and the members' KeyPackages.
   The tree hash of a tree is the tree hash of its root node, which we
   define recursively, starting with the leaves.

   As some nodes may be blank while others contain data we use the
   following struct to include data if present.

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

   The tree hash of a leaf node is the hash of leaf's LeafNodeHashInput
   object which might include a Key Package depending on whether or not
   it is blank.

   struct {
       uint32 node_index;
       optional<KeyPackage> key_package;
   } LeafNodeHashInput;

   Now the tree hash of any non-leaf node is recursively defined to be
   the hash of its ParentNodeTreeHashInput.  This includes an optional
   ParentNode object depending on whether the node is blank or not.

   struct {
       HPKEPublicKey public_key;
       opaque parent_hash<0..255>;
       uint32 unmerged_leaves<0..2^32-1>;
   } ParentNode;

   struct {
       uint32 node_index;
       optional<ParentNode> parent_node;
       opaque left_hash<0..255>;
       opaque right_hash<0..255>;
   } ParentNodeTreeHashInput;

   The left_hash and right_hash fields hold the tree hashes of the
   node's left and right children, respectively.



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7.7.  Group State

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

   struct {
       opaque group_id<0..255>;
       uint64 epoch;
       opaque tree_hash<0..255>;
       opaque confirmed_transcript_hash<0..255>;
       Extension extensions<0..2^32-1>;
   } GroupContext;

   The fields in this state have the following semantics:

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

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

   *  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 7.6.

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

   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 11.1.  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 is updated with the data for an
      MLSPlaintext message encoding a Commit message in two parts:





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   struct {
       WireFormat wire_format;
       opaque group_id<0..255>;
       uint64 epoch;
       Sender sender;
       opaque authenticated_data<0..2^32-1>;
       ContentType content_type = commit;
       Commit commit;
       opaque signature<0..2^16-1>;
   } MLSPlaintextCommitContent;

   struct {
       optional<MAC> confirmation_tag;
   } MLSPlaintextCommitAuthData;

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

   confirmed_transcript_hash_[n] =
       Hash(interim_transcript_hash_[n] ||
           MLSPlaintextCommitContent_[n]);

   interim_transcript_hash_[n+1] =
       Hash(confirmed_transcript_hash_[n] ||
           MLSPlaintextCommitAuthData_[n]);

   Thus the confirmed_transcript_hash field in a GroupContext object
   represents a transcript over the whole history of MLSPlaintext Commit
   messages, up to the confirmation tag field in the current
   MLSPlaintext message.  The confirmation tag is then included in the
   transcript for the next epoch.  The interim transcript hash is
   computed by new members using the confirmation tag in the GroupInfo
   struct, and enables existing members to incorporate a Commit message
   into the transcript without having to store the whole
   MLSPlaintextCommitAuthData structure.

   As shown above, when a new group is created, the
   interim_transcript_hash field is set to the zero-length octet string.

7.8.  Update Paths

   As described in Section 11.2, each MLS Commit message may optionally
   transmit a KeyPackage leaf and node values along its direct path.
   The path contains a public key and encrypted secret value for all
   intermediate nodes in the path above the leaf.  The path is ordered
   from the closest node to the leaf to the root; each node MUST be the
   parent of its predecessor.





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   struct {
       opaque kem_output<0..2^16-1>;
       opaque ciphertext<0..2^16-1>;
   } HPKECiphertext;

   struct {
       HPKEPublicKey public_key;
       HPKECiphertext encrypted_path_secret<0..2^32-1>;
   } UpdatePathNode;

   struct {
       KeyPackage leaf_key_package;
       UpdatePathNode nodes<0..2^32-1>;
   } UpdatePath;

   For each UpdatePathNode, the resolution of the corresponding copath
   node MUST be filtered by removing all new leaf nodes added as part of
   this MLS Commit message.  The number of ciphertexts in the
   encrypted_path_secret vector MUST be equal to the length of the
   filtered resolution, with each ciphertext being the encryption to the
   respective resolution node.

   The HPKECiphertext values are computed as

   kem_output, context = SetupBaseS(node_public_key, group_context)
   ciphertext = context.Seal("", path_secret)

   where node_public_key is the public key of the node that the path
   secret is being encrypted for, group_context is the current
   GroupContext object for the group, and the functions SetupBaseS and
   Seal are defined according to [I-D.irtf-cfrg-hpke].

   Decryption is performed in the corresponding way, using the private
   key of the resolution node and the ephemeral public key transmitted
   in the message.

8.  Key Schedule

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










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

   Where KDFLabel is specified as:

   struct {
       uint16 length = Length;
       opaque label<7..255> = "mls10 " + Label;
       opaque context<0..2^32-1> = Context;
   } KDFLabel;

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

   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 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:
















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                   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]

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

















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               +=======================+==================+
               | Secret                | Label            |
               +=======================+==================+
               | sender_data_secret    | "sender data"    |
               +-----------------------+------------------+
               | encryption_secret     | "encryption"     |
               +-----------------------+------------------+
               | exporter_secret       | "exporter"       |
               +-----------------------+------------------+
               | authentication_secret | "authentication" |
               +-----------------------+------------------+
               | external_secret       | "external"       |
               +-----------------------+------------------+
               | confirmation_key      | "confirm"        |
               +-----------------------+------------------+
               | membership_key        | "membership"     |
               +-----------------------+------------------+
               | resumption_secret     | "resumption"     |
               +-----------------------+------------------+

                                 Table 2

   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
   PublicGroupState struct in order to allow non-members to join the
   group using an external commit.

8.1.  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 an 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 PublicGroupState 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)




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   Members of the group receive the kem_output in an ExternalInit
   proposal and preform 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)

   In both cases, the info input to HPKE is set to the PublicGroupState
   for the previous epoch, encoded using the TLS serialization.

8.2.  Pre-Shared Keys

   Groups which already have an out-of-band mechanism to generate shared
   group secrets can inject those into the MLS key schedule to seed the
   MLS group secrets computations by this external entropy.

   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 (FS) or Post-
   Compromise Security (PCS) guarantees as a Commit message.  Unlike the
   key pairs populated in the tree by an Update or Commit, which always
   freshly generated, PSKs may be pre-distributed and stored.  This
   creates the risk that a PSK may be compromised in the process of
   distribution and storage.  The security that the group gets from
   injecting a PSK thus depends on both the entropy of the PSK and the
   risk of compromise.  These factors are outside of the scope of this
   document, but should be considered by application designers relying
   on PSKs.

   Each PSK in MLS has a type that designates how it was provisioned.
   External PSKs are provided by the application, while recovery and re-
   init 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 group state.  In particular, in addition to external PSK types,
   a PSK derived from within MLS may be used in the following cases:

   *  Re-Initialization: If during the lifetime of a group, the group
      members decide to switch to a more secure ciphersuite or newer
      protocol version, a PSK can be used to carry entropy from the old
      group forward into a new group with the desired parameters.







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   *  Branching: A PSK may be used to bootstrap a subset of current
      group members into a new group.  This applies if a subset of
      current group members wish to branch based on the current group
      state.

   The injection of one or more PSKs into the key schedule is signaled
   in two ways: 1) as a PreSharedKey proposal, and 2) in the
   GroupSecrets object of a Welcome message sent to new members added in
   that epoch.

   enum {
     reserved(0),
     external(1),
     reinit(2),
     branch(3)
     (255)
   } PSKType;

   struct {
     PSKType psktype;
     select (PreSharedKeyID.psktype) {
       case external:
         opaque psk_id<0..255>;

       case reinit:
         opaque psk_group_id<0..255>;
         uint64 psk_epoch;

       case branch:
         opaque psk_group_id<0..255>;
         uint64 psk_epoch;
     }
     opaque psk_nonce<0..255>;
   } PreSharedKeyID;

   struct {
       PreSharedKeyID psks<0..2^16-1>;
   } PreSharedKeys;

   On 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_secret of the group and epoch specified in the
   PreSharedKeyID object.  Specifically, psk_secret is computed as
   follows:





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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, as follows:

                0                                   0       = psk_secret_[0]
                |                                   |
                V                                   V
psk_[0] --> KDF.Extract --> ExpandWithLabel --> KDF.Extract = psk_secret_[1]
                                                    |
                0                                   |
                |                                   |
                V                                   V
psk_[1] --> KDF.Extract --> ExpandWithLabel --> KDF.Extract = psk_secret_[1]
                                                    |
                0                                  ...
                |                                   |
                V                                   V
psk_[n] --> KDF.Extract --> ExpandWithLabel --> KDF.Extract = psk_secret_[n]

   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.














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8.3.  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.  Nodes are also assigned
   an index according to their position in the array representation of
   the tree (described in Appendix A).  If N is a node index in the
   Secret Tree then left(N) and right(N) denote the children of N (if
   they exist).

   The secret of any other node in the tree is derived from its parent's
   secret using a call to DeriveTreeSecret:

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

   Where TreeContext is specified as:

   struct {
       uint32 node = Node;
       uint32 generation = Generation;
   } TreeContext;

   If N is a node index in the Secret Tree then the secrets of the
   children of N are defined to be:

   tree_node_[N]_secret
           |
           |
           +--> DeriveTreeSecret(., "tree", left(N), 0, KDF.Nh)
           |    = tree_node_[left(N)]_secret
           |
           +--> DeriveTreeSecret(., "tree", right(N), 0, KDF.Nh)
                = tree_node_[right(N)]_secret

   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 8.4.  The root of each
   ratchet is computed as:










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

8.4.  Encryption Keys

   As described in Section 9, 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".

   A sender ratchet starts from a per-sender base secret derived from a
   Secret Tree, as described in Section 8.3.  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 index
   of the sender's leaf in the ratchet tree and the current position in
   the ratchet.  In particular, the node index of the sender's leaf in
   the ratchet tree is the same as the node index of the leaf in the
   Secret Tree used to initialize the sender's ratchet.








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   ratchet_secret_[N]_[j]
         |
         +--> DeriveTreeSecret(., "nonce", N, j, AEAD.Nn)
         |    = ratchet_nonce_[N]_[j]
         |
         +--> DeriveTreeSecret(., "key", N, j, AEAD.Nk)
         |    = ratchet_key_[N]_[j]
         |
         V
   DeriveTreeSecret(., "secret", N, 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 ciphersuite.

8.5.  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 if

   *  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,
   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 node index N 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, 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 index N,




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   *  the first j secrets in the application data ratchet of node index
      N and

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

   Concretely, suppose we have the following Secret Tree and ratchet for
   participant D:

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

   Then if a client uses key K1 and nonce N1 during epoch n then it must
   consume (at least) values G, F, D, AR0, AR1, K1, N1 as well as the
   key schedule secrets used to derive G (the encryption_secret), namely
   init_secret of epoch n-1 and commit_secret, joiner_secret,
   epoch_secret of epoch n.  The client MAY retain (not consume) the
   values K0 and N0 to allow for out-of-order delivery, and SHOULD
   retain AR2 for processing future messages.

8.6.  Exporters

   The main MLS key schedule provides an exporter_secret which can be
   used by an application as the basis to derive new secrets called
   exported_value outside the MLS layer.

   MLS-Exporter(Label, Context, key_length) =
          ExpandWithLabel(DeriveSecret(exporter_secret, Label),
                            "exporter", Hash(Context), key_length)

   Each application SHOULD provide a unique label to MLS-Exporter that
   identifies its use case.  This is to prevent two exported outputs
   from being generated with the same values and used for different
   functionalities.



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

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

8.7.  Resumption Secret

   The main MLS key schedule provides a resumption_secret which can
   provide extra security in some cross-group operations.

   The application SHOULD specify an upper limit on the number of past
   epochs for which the resumption_secret may be stored.

   There are two ways in which a resumption_secret can be used: to re-
   initialize the group with different parameters, or to create a sub-
   group of an existing group as detailed in Section 8.2.

   Resumption keys are distinguished from exporter keys in that they
   have specific use inside the MLS protocol, whereas the use of
   exporter secrets may be decided by an external application.  They are
   thus derived separately to avoid key material reuse.

8.8.  State Authentication Keys

   The main MLS key schedule provides a per-epoch authentication_secret.
   If one of the parties is being actively impersonated by an attacker,
   their authentication_secret will differ from that of the other group
   members.  Thus, members of a group MAY use their
   authentication_secrets within an out-of-band authentication protocol
   to ensure that they share the same view of the group.

9.  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 within the
   group.












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   The two main structures involved are MLSPlaintext and MLSCiphertext.
   MLSCiphertext represents a signed and encrypted message, with
   protections for both the content of the message and related metadata.
   MLSPlaintext represents a message that is only signed, and not
   encrypted.  Applications MUST use MLSCiphertext to encrypt
   application messages and SHOULD use MLSCiphertext to encode handshake
   messages, but MAY transmit handshake messages encoded as MLSPlaintext
   objects in cases where it is necessary for the Delivery Service to
   examine such messages.

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

   enum {
       reserved(0),
       member(1),
       preconfigured(2),
       new_member(3),
       (255)
   } SenderType;

   struct {
       SenderType sender_type;
       switch (sender_type) {
           case member:        KeyPackageID member;
           case preconfigured: opaque external_key_id<0..255>;
           case new_member:    struct{};
       }
   } Sender;

   struct {
       opaque mac_value<0..255>;
   } MAC;

   enum {
     reserved(0),
     mls_plaintext(1),
     mls_ciphertext(2),
     (255)
   } WireFormat;

   struct {
       WireFormat wire_format;



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       opaque group_id<0..255>;
       uint64 epoch;
       Sender sender;
       opaque authenticated_data<0..2^32-1>;

       ContentType content_type;
       select (MLSPlaintext.content_type) {
           case application:
             opaque application_data<0..2^32-1>;

           case proposal:
             Proposal proposal;

           case commit:
             Commit commit;
       }

       opaque signature<0..2^16-1>;
       optional<MAC> confirmation_tag;
       optional<MAC> membership_tag;
   } MLSPlaintext;

   struct {
       WireFormat wire_format = mls_ciphertext;
       opaque group_id<0..255>;
       uint64 epoch;
       ContentType content_type;
       opaque authenticated_data<0..2^32-1>;
       opaque encrypted_sender_data<0..255>;
       opaque ciphertext<0..2^32-1>;
   } MLSCiphertext;

   The field confirmation_tag MUST be present if content_type equals
   commit.  Otherwise, it MUST NOT be present.

   External sender types are sent as MLSPlaintext, see Section 11.1.9
   for their use.

   The remainder of this section describes how to compute the signature
   of an MLSPlaintext object and how to convert it to an MLSCiphertext
   object for member sender types.  The steps are:

   *  Set group_id, epoch, content_type and authenticated_data fields
      from the MLSPlaintext object directly

   *  Identify the key and key generation depending on the content type





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   *  Encrypt an MLSCiphertextContent for the ciphertext field using the
      key identified and MLSPlaintext object

   *  Encrypt the sender data using a key and nonce derived from the
      sender_data_secret for the epoch and a sample of the encrypted
      MLSCiphertextContent.

   Decryption is done by decrypting the sender data, then the message,
   and then verifying the content signature.

   The following sections describe the encryption and signing processes
   in detail.

9.1.  Content Authentication

   The signature field in an MLSPlaintext object is computed using the
   signing private key corresponding to the public key, which was
   authenticated by the credential at the leaf of the tree indicated by
   the sender field.  The signature covers the plaintext metadata and
   message content, which is all of MLSPlaintext except for the
   signature, the confirmation_tag and membership_tag fields.  If the
   sender is a member of the group, the signature also covers the
   GroupContext for the current epoch, so that signatures are specific
   to a given group and epoch.



























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   struct {
       select (MLSPlaintextTBS.sender.sender_type) {
           case member:
               GroupContext context;

           case preconfigured:
           case new_member:
               struct{};
       }

       WireFormat wire_format;
       opaque group_id<0..255>;
       uint64 epoch;
       Sender sender;
       opaque authenticated_data<0..2^32-1>;

       ContentType content_type;
       select (MLSPlaintextTBS.content_type) {
           case application:
             opaque application_data<0..2^32-1>;

           case proposal:
             Proposal proposal;

           case commit:
             Commit commit;
       }
   } MLSPlaintextTBS;

   The membership_tag field in the MLSPlaintext object authenticates the
   sender's membership in the group.  For an MLSPlaintext with a sender
   type other than member, this field MUST be omitted.  For messages
   sent by members, it MUST be present and set to the following value:

   struct {
     MLSPlaintextTBS tbs;
     opaque signature<0..2^16-1>;
     optional<MAC> confirmation_tag;
   } MLSPlaintextTBM;

   membership_tag = MAC(membership_key, MLSPlaintextTBM);

   Note that the membership_tag only needs to be computed for
   MLSPlaintext messages that will be sent over the wire (wire_format ==
   mls_plaintext).  It isn't needed for messages that will be encrypted
   and transmitted as MLSCiphertext messages (wire_format ==
   mls_ciphertext).




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9.2.  Content Encryption

   The ciphertext field of the MLSCiphertext object is produced by
   supplying the inputs described below to the AEAD function specified
   by the ciphersuite in use.  The plaintext input contains the content
   and signature of the MLSPlaintext, plus optional padding.  These
   values are encoded in the following form:

   struct {
       select (MLSCiphertext.content_type) {
           case application:
             opaque application_data<0..2^32-1>;

           case proposal:
             Proposal proposal;

           case commit:
             Commit commit;
       }

       opaque signature<0..2^16-1>;
       optional<MAC> confirmation_tag;
       opaque padding<0..2^16-1>;
   } MLSCiphertextContent;

   In the MLS key schedule, the sender creates two distinct key ratchets
   for handshake and application messages for each member of the group.
   When encrypting a message, the sender looks at the ratchets it
   derived for its own member and chooses an unused generation from
   either the handshake or application ratchet depending on the content
   type of the message.  This generation of the ratchet is used to
   derive a provisional nonce and key.

   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 4-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.




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   +-+-+-+-+---------...---+
   |   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<0..255>;
       uint64 epoch;
       ContentType content_type;
       opaque authenticated_data<0..2^32-1>;
   } MLSCiphertextContentAAD;

9.3.  Sender Data Encryption

   The "sender data" used to look up the key for the content encryption
   is encrypted with the ciphersuite'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 {
       KeyPackageID sender;
       uint32 generation;
       opaque reuse_guard[4];
   } MLSSenderData;

   MLSSenderData.sender is assumed to be a member sender type.  When
   constructing an MLSSenderData from a Sender object, the sender MUST
   verify Sender.sender_type is member and use Sender.sender for
   MLSSenderData.sender.

   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 9.2.






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   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 without padding.  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 Additional Authenticated Data (AAD) for the SenderData ciphertext
   is all the fields of MLSCiphertext excluding encrypted_sender_data:

   struct {
       opaque group_id<0..255>;
       uint64 epoch;
       ContentType content_type;
   } MLSSenderDataAAD;

   When parsing a SenderData struct as part of message decryption, the
   recipient MUST verify that the KeyPackageID indicated in the sender
   field identifies a member of the group.

10.  Group Creation

   A group is always created with a single member, the "creator".  The
   other members are added when the creator effectively sends itself an
   Add proposal and commits it, then sends the corresponding Welcome
   message to the new participants.  These processes are described in
   detail in Section 11.1.1, Section 11.2, and Section 11.2.2.

   The creator of a group MUST take the following steps to initialize
   the group:

   *  Fetch KeyPackages for the members to be added, and select a
      version and ciphersuite according to the capabilities of the
      members.  To protect against downgrade attacks, the creator MUST
      use the capabilities extensions in these KeyPackages to verify
      that the chosen version and ciphersuite is the best option
      supported by all members.

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

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

      -  Group ID: A value set by the creator



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      -  Epoch: 0

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

      -  Confirmed transcript hash: The zero-length octet string

      -  Interim transcript hash: The zero-length octet string

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

      -  Extensions: Any values of the creator's choosing

   *  For each member, construct an Add proposal from the KeyPackage for
      that member (see Section 11.1.1)

   *  Construct a Commit message that commits all of the Add proposals,
      in any order chosen by the creator (see Section 11.2)

   *  Process the Commit message to obtain a new group state (for the
      epoch in which the new members are added) and a Welcome message

   *  Transmit the Welcome message to the other new members

   The recipient of a Welcome message processes it as described in
   Section 11.2.2.

   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, the leaf secret from which the Commit is built, and the
   intermediate key pairs along the direct path to the root.

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

   struct {
       ExtensionType extensions<0..255>;
       ProposalType proposals<0..255>;
   } RequiredCapabilities;





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   This extension lists the extensions and proposal types that must be
   supported by all members of the group.  For new members, it 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 can be updated, a GroupContextExtensions proposal is
   invalid if it contains a required_capabilities extension that
   requires capabililities not supported by all current members.

10.2.  Linking a New Group to an Existing Group

   A new group may be tied to an already existing group for the purpose
   of re-initializing the existing group, or to branch into a sub-group.
   Re-initializing an existing group may be used, for example, to
   restart the group with a different ciphersuite or protocol version.
   Branching may be used to bootstrap a new group consisting of a subset
   of current group members, based on the current group state.

   In both cases, the psk_nonce included in the PreSharedKeyID object
   must be a randomly sampled nonce of length KDF.Nh to avoid key re-
   use.

10.2.1.  Sub-group Branching

   If a client wants to create a subgroup of an existing group, they MAY
   choose to include a PreSharedKeyID in the GroupSecrets object of the
   Welcome message choosing the psktype branch, the group_id of the
   group from which a subgroup is to be branched, as well as an epoch
   within the number of epochs for which a resumption_secret is kept.

11.  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









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   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.

11.1.  Proposals

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

   // See IANA registry for registered values
   uint16 ProposalType;

   struct {
       ProposalType msg_type;
       select (Proposal.msg_type) {
           case add:                      Add;
           case update:                   Update;
           case remove:                   Remove;
           case psk:                      PreSharedKey;
           case reinit:                   ReInit;
           case external_init:            ExternalInit;
           case app_ack:                  AppAck;
           case group_context_extensions: GroupContextExtensions;
       };
   } Proposal;

   On receiving an MLSPlaintext containing a Proposal, a client MUST
   verify the signature on the enclosing MLSPlaintext.  If the signature
   verifies successfully, 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.

11.1.1.  Add

   An Add proposal requests that a client with a specified KeyPackage be
   added to the group.  The proposer of the Add MUST validate the
   KeyPackage in the same way as receipients are required to do below.

   struct {
       KeyPackage key_package;
   } Add;






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   The proposer of the Add does not control where in the group's ratchet
   tree the new member is added.  Instead, the sender of the Commit
   message chooses a location for each added member and states it in the
   Commit message.

   An Add is applied after being included in a Commit message.  The
   position of the Add in the list of proposals determines the node
   index index of the leaf node where the new member will be added.  For
   the first Add in the Commit, index is the leftmost empty leaf in the
   tree, for the second Add, the next empty leaf to the right, etc.

   *  Validate the KeyPackage:

      -  Verify that the signature on the KeyPackage is valid using the
         public key in the KeyPackage's credential

      -  Verify that the following fields in the KeyPackage are unique
         among the members of the group (including any other members
         added in the same Commit):

         o  (credential.identity, endpoint_id) tuple

         o  credential.signature_key

         o  hpke_init_key

      -  Verify that the KeyPackage is compatible with the group's
         parameters.  The ciphersuite and protocol version of the
         KeyPackage must match those in use in the group.  If the
         GroupContext has a required_capabilities extension, then the
         required extensions and proposals MUST be listed in the
         KeyPackage's capabilities extension.

   *  If necessary, extend the tree to the right until it has at least
      index + 1 leaves

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

   *  Set the leaf node in the tree at position index to a new node
      containing the public key from the KeyPackage in the Add, as well
      as the credential under which the KeyPackage was signed








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11.1.2.  Update

   An Update proposal is a similar mechanism to Add with the distinction
   that it is the sender's leaf KeyPackage in the tree which would be
   updated with a new KeyPackage.

   struct {
       KeyPackage key_package;
   } Update;

   The values in the following fields of the KeyPackage contained in an
   Update proposal MUST be the same as those of the KeyPackage it
   replaces in the tree. version, cipher_suite, credential.identity,
   endpoint_id.  However, the value of the credential.signature_key
   field of the new KeyPackage MUST be different from that of all other
   KeyPackages in the tree.  Furthermore, the value of the hpke_init_key
   field of the new KeyPackage MUST be different from that of the
   KeyPackage it replaces.

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

   *  Replace the sender's leaf KeyPackage with the one contained in the
      Update proposal

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

11.1.3.  Remove

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

   struct {
       KeyPackageID removed;
   } Remove;

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

   *  Identify a leaf node containing a key package matching removed.
      This lookup MUST be done on the tree before any non-Remove
      proposals have been applied (the "old" tree in the terminology of
      Section 11.2), since proposals such as Update can change the
      KeyPackage stored at a leaf.  Let removed_index be the node index
      of this leaf node.

   *  Replace the leaf node at removed_index with a blank node



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   *  Blank the intermediate nodes along the path from removed_index to
      the root

   *  Truncate the tree by reducing the size of tree until the rightmost
      non-blank leaf node

11.1.4.  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;

   The psktype of the pre-shared key MUST be external and the psk_nonce
   MUST be a randomly sampled nonce of length KDF.Nh.  When processing a
   Commit message that includes one or more PreSharedKey proposals,
   group members derive psk_secret as described in Section 8.2, where
   the order of the PSKs corresponds to the order of the PreSharedKey
   proposals in the Commit.

11.1.5.  ReInit

   A ReInit proposal represents a request to re-initialize the group
   with different parameters, for example, to increase the version
   number or to change the ciphersuite.  The re-initialization is done
   by creating a completely new group and shutting down the old one.

   struct {
       opaque group_id<0..255>;
       ProtocolVersion version;
       CipherSuite cipher_suite;
       Extension extensions<0..2^32-1>;
   } ReInit;

   A member of the group applies a ReInit proposal by waiting for the
   committer to send the Welcome message and by checking that the
   group_id and the parameters of the new group corresponds to the ones
   specified in the proposal.  The Welcome message MUST specify exactly
   one pre-shared key with psktype = reinit, and with psk_group_id and
   psk_epoch equal to the group_id and epoch of the existing group after
   the Commit containing the reinit Proposal was processed.  The Welcome
   message may specify the inclusion of other pre-shared keys with a
   psktype different from reinit.





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   If a ReInit proposal is included in a Commit, it MUST be the only
   proposal referenced by the Commit.  If other non-ReInit proposals
   have been sent during the epoch, the committer SHOULD prefer them
   over the ReInit proposal, allowing the ReInit to be resent and
   applied in a subsequent epoch.  The version field in the ReInit
   proposal MUST be no less than the version for the current group.

11.1.6.  ExternalInit

   An ExternalInit proposal is used by new members that want to join a
   group by using an external commit.  This propsal can only be used in
   that context.

   struct {
     opaque kem_output<0..2^16-1>;
   } ExternalInit;

   A member of the group applies an ExternalInit message by initializing
   the next epoch using an init secret computed as described in
   Section 8.1.  The kem_output field contains the required KEM output.

11.1.7.  AppAck

   An AppAck proposal is used to acknowledge receipt of application
   messages.  Though this information implies no change to the group, it
   is structured as a Proposal message so that it is included in the
   group's transcript by being included in Commit messages.

   struct {
       KeyPackageID sender;
       uint32 first_generation;
       uint32 last_generation;
   } MessageRange;

   struct {
       MessageRange received_ranges<0..2^32-1>;
   } AppAck;

   An AppAck proposal represents a set of messages received by the
   sender in the current epoch.  Messages are represented by the sender
   and generation values in the MLSCiphertext for the message.  Each
   MessageRange represents receipt of a span of messages whose
   generation values form a continuous range from first_generation to
   last_generation, inclusive.

   AppAck proposals are sent as a guard against the Delivery Service
   dropping application messages.  The sequential nature of the
   generation field provides a degree of loss detection, since gaps in



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   the generation sequence indicate dropped messages.  AppAck completes
   this story by addressing the scenario where the Delivery Service
   drops all messages after a certain point, so that a later generation
   is never observed.  Obviously, there is a risk that AppAck messages
   could be suppressed as well, but their inclusion in the transcript
   means that if they are suppressed then the group cannot advance at
   all.

   The schedule on which sending AppAck proposals are sent is up to the
   application, and determines which cases of loss/suppression are
   detected.  For example:

   *  The application might have the committer include an AppAck
      proposal whenever a Commit is sent, so that other members could
      know when one of their messages did not reach the committer.

   *  The application could have a client send an AppAck whenever an
      application message is sent, covering all messages received since
      its last AppAck.  This would provide a complete view of any losses
      experienced by active members.

   *  The application could simply have clients send AppAck proposals on
      a timer, so that all participants' state would be known.

   An application using AppAck proposals to guard against loss/
   suppression of application messages also needs to ensure that AppAck
   messages and the Commits that reference them are not dropped.  One
   way to do this is to always encrypt Proposal and Commit messages, to
   make it more difficult for the Delivery Service to recognize which
   messages conatain AppAcks.  The application can also have clients
   enforce an AppAck schedule, reporting loss if an AppAck is not
   received at the expected time.

11.1.8.  GroupContextExtensions

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

   struct { Extension extensions<0..2^32-1>; } GroupContextExtensions;

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

   *  If the new extensions include a required_capabilities extension,
      verify that all members of the group support the required
      capabilities (including those added in the same commit, and
      excluding those removed).




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   *  Remove all of the existing extensions from the GroupContext object
      for the group and replacing them with the list of extensions in
      the proposal.  (This is a wholesale replacement, not a merge.  An
      extension is only carried over if the sender of the proposal
      includes it in the new list.)

   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.

11.1.9.  External Proposals

   Add and Remove proposals can be constructed and sent to the group by
   a party that is outside the group.  For example, a Delivery Service
   might propose to remove a member of a group who has been inactive for
   a long time, or propose adding a newly-hired staff member to a group
   representing a real-world team.  Proposals originating outside the
   group are identified by a preconfigured or new_member SenderType in
   MLSPlaintext.

   ReInit proposals can also be sent to the group by a preconfigured
   sender, for example to enforce a changed policy regarding MLS version
   or ciphersuite.

   The new_member SenderType is used for clients proposing that they
   themselves be added.  For this ID type the sender value MUST be zero
   and the Proposal type MUST be Add. The MLSPlaintext MUST be signed
   with the private key corresponding to the KeyPackage in the Add
   message.  Recipients MUST verify that the MLSPlaintext carrying the
   Proposal message is validly signed with this key.

   The preconfigured SenderType is reserved for signers that are pre-
   provisioned to the clients within a group.  If proposals with these
   sender IDs are to be accepted within a group, the members of the
   group MUST be provisioned by the application with a mapping between
   these IDs and authorized signing keys.  Recipients MUST verify that
   the MLSPlaintext carrying the Proposal message is validly signed with
   the corresponding key.  To ensure consistent handling of external
   proposals, the application MUST ensure that the members of a group
   have the same mapping and apply the same policies to external
   proposals.

   An external proposal MUST be sent as an MLSPlaintext object, since
   the sender will not have the keys necessary to construct an
   MLSCiphertext object.






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11.2.  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.  Proposals supplied by value are included directly in the
   Commit object.  Proposals supplied by reference are specified by
   including the hash of the MLSPlaintext in which the Proposal was
   sent, using the hash function from the group's ciphersuite.  For
   proposals supplied by value, the sender of the proposal is the same
   as the sender of the Commit.  Conversely, proposals sent by people
   other than the committer MUST be included by reference.

   enum {
     reserved(0),
     proposal(1)
     reference(2),
     (255)
   } ProposalOrRefType;

   struct {
     ProposalOrRefType type;
     select (ProposalOrRef.type) {
       case proposal:  Proposal proposal;
       case reference: opaque hash<0..255>;
     }
   } ProposalOrRef;

   struct {
       ProposalOrRef proposals<0..2^32-1>;
       optional<UpdatePath> path;
   } Commit;

   A group member that has observed one or more 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.

   The sender of a Commit MUST include all valid proposals that it has
   received during the current epoch.  Invalid proposals include, for
   example, proposals with an invalid signature or proposals that are
   semantically invalid, such as an Add when the sender does not have
   the application-level permission to add new users.  Proposals with a



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   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 (i.e., not including any members being added or
   removed by the Commit).

   If there are multiple proposals that apply to the same leaf, the
   committer chooses one and includes only that one in the Commit,
   considering the rest invalid.  The committer MUST prefer any Remove
   received, or the most recent Update for the leaf if there are no
   Removes.  If there are multiple Add proposals containing KeyPackages
   with the same tuple (credential.identity, endpoint_id) the committer
   again chooses one to include and considers the rest invalid.  Add
   proposals that contain KeyPackages with an (credential.identity,
   endpoint_id) tuple that matches that of an existing KeyPackage in the
   group MUST be considered invalid.  The comitter MUST consider invalid
   any Add or Update proposal if the Credential in the contained
   KeyPackage shares the same signature key with a Credential in any
   leaf of the group, or indeed if the KeyPackage shares the same
   hpke_init_key with another KeyPackage in the group.

   The Commit MUST NOT combine proposals sent within different epochs.
   In the event that a valid proposal is omitted from the next Commit,
   the sender of the proposal SHOULD retransmit it in the new 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.

   The path field of a Commit message MUST be populated if the Commit
   covers at least one Update or Remove proposal.  The path field MUST
   also be populated if the Commit covers no proposals at all (i.e., if
   the proposals vector is empty).  The path field MAY be omitted if the
   Commit covers only Add proposals.  In pseudocode, the logic for
   validating a Commit is as follows:













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   hasUpdates = false
   hasRemoves = false

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

       hasUpdates = hasUpdates || proposal.msg_type == update
       hasRemoves = hasRemoves || proposal.msg_type == remove

   if len(commit.proposals) == 0 || hasUpdates || hasRemoves:
     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 Add, PreSharedKey, or ReInit
       proposals but 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.

   When creating or processing a Commit, three different ratchet trees
   and their associated GroupContexts are used:

   1.  "Old" refers to the ratchet tree and GroupContext for the epoch
       before the commit.  The old GroupContext is used when signing the
       MLSPlainText so that existing group members can verify the
       signature before processing the commit.

   2.  "Provisional" refers to the ratchet tree and GroupContext
       constructed after applying the proposals that are referenced by
       the Commit.  The provisional GroupContext uses the epoch number
       for the new epoch, and the old confirmed transcript hash.  This
       is used when creating the UpdatePath, if the UpdatePath is
       needed.









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   3.  "New" refers to the ratchet tree and GroupContext constructed
       after applying the proposals and the UpdatePath (if any).  The
       new GroupContext uses the epoch number for the new epoch, and the
       new confirmed transcript hash.  This is used when deriving the
       new epoch secrets, and is the only GroupContext that newly-added
       members will have.

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

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

   *  Generate the provisional ratchet tree and GroupContext by applying
      the proposals referenced in the initial Commit object, as
      described in Section 11.1.  Update proposals are applied first,
      followed by Remove proposals, and then finally Add proposals.  Add
      proposals are applied in the order listed in the proposals vector,
      and always to the leftmost unoccupied leaf in the tree, or the
      right edge of the tree if all leaves are occupied.

      -  Note that the order in which different types of proposals are
         applied should be updated by the implementation to include any
         new proposals added by negotiated group extensions.

      -  PreSharedKey proposals are processed later when deriving the
         psk_secret for the Key Schedule.

   *  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: Create an UpdatePath using the
      provisional ratchet tree and GroupContext.  Any new member (from
      an add proposal) MUST be exluded from the resolution during the
      computation of the UpdatePath.  The leaf_key_package for this
      UpdatePath must have a parent_hash extension.  Note that the
      KeyPackage in the UpdatePath effectively updates an existing
      KeyPackage in the group and thus MUST adhere to the same
      restrictions as KeyPackages used in Update proposals.

      -  Assign this UpdatePath to the path field in the Commit.







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      -  Apply the UpdatePath to the tree, as described in Section 5.5,
         creating the new ratchet tree.  Define commit_secret as the
         value path_secret[n+1] derived from the path_secret[n] value
         assigned to the root node.

   *  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).  In this case, the new ratchet tree is the same as the
      provisional ratchet tree.

   *  Derive the psk_secret as specified in Section 8.2, where the order
      of PSKs in the derivation corresponds to the order of PreSharedKey
      proposals in the proposals vector.

   *  Construct an MLSPlaintext object containing the Commit object.
      Sign the MLSPlaintext using the old GroupContext as context.

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

      -  Use the init_secret from the previous epoch, the commit_secret
         and the psk_secret as 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, and the membership_key for the old
         epoch to compute the membership_tag value in the MLSPlaintext.

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

   *  Construct a GroupInfo reflecting the new state:

      -  Group ID, epoch, tree, confirmed transcript hash, interim
         transcript hash, and group context extensions from the new
         state

      -  The confirmation_tag from the MLSPlaintext object

      -  Other extensions as defined by the application

      -  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 11.2.2)



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   *  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 a Welcome message 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.

   *  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 psktype reinit
      and with psk_group_id and psk_epoch corresponding to the current
      group and the epoch after the commit was processed.

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

   *  Verify that the epoch field of the enclosing MLSPlaintext message
      is equal to the epoch field of the current GroupContext object

   *  Verify that the signature on the MLSPlaintext message verifies
      using the public key from the credential stored at the leaf in the
      tree indicated by the sender field.

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

   *  Generate the provisional ratchet tree and GroupContext by applying
      the proposals referenced in the initial Commit object, as
      described in Section 11.1.  Update proposals are applied first,
      followed by Remove proposals, and then finally Add proposals.  Add
      proposals are applied in the order listed in the proposals vector,
      and always to the leftmost unoccupied leaf in the tree, or the
      right edge of the tree if all leaves are occupied.

      -  Note that the order in which different types of proposals are
         applied should be updated by the implementation to include any
         new proposals added by negotiated group extensions.



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   *  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: Process the path value using the
      provisional ratchet tree and GroupContext, to generate the new
      ratchet tree and the commit_secret:

      -  Apply the UpdatePath to the tree, as described in Section 5.5,
         and store leaf_key_package at the Committer's leaf.

      -  Verify that the KeyPackage has a parent_hash extension and that
         its value matches the new parent of the sender's leaf node.

      -  Define commit_secret as the value path_secret[n+1] derived from
         the path_secret[n] value assigned to the root node.

   *  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 8.2, 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
      the psk_secret as 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
      MLSPlaintext 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 and check that







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      -  The version, cipher_suite and extensions fields of the new
         group corresponds to the ones in the ReInit proposal, and that
         the version is greater than or equal to that of the original
         group.

      -  The psks field in the Welcome message includes a PreSharedKeyID
         with psktype = reinit, and psk_epoch and psk_group_id equal to
         the epoch and group ID of the original group after processing
         the Commit.

   The confirmation tag value confirms that the members of the group
   have arrived at the same state of the group:

   MLSPlaintext.confirmation_tag =
       MAC(confirmation_key, GroupContext.confirmed_transcript_hash)

11.2.1.  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

   *  ciphersuite

   *  public tree hash

   *  interim transcript hash

   *  group extensions

   *  external public key

   This information is aggregated in a PublicGroupState object as
   follows:





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   struct {
       CipherSuite cipher_suite;
       opaque group_id<0..255>;
       uint64 epoch;
       opaque tree_hash<0..255>;
       opaque interim_transcript_hash<0..255>;
       Extension group_context_extensions<0..2^32-1>;
       Extension other_extensions<0..2^32-1>;
       HPKEPublicKey external_pub;
       KeyPackageID signer;
       opaque signature<0..2^16-1>;
   } PublicGroupState;

   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 Section 11.3.

   The signature MUST verify using the public key taken from the
   credential in the leaf node of the member with KeyPackageID signer.
   The signature covers the following structure, comprising all the
   fields in the PublicGroupState above signature:

   struct {
       opaque group_id<0..255>;
       uint64 epoch;
       opaque tree_hash<0..255>;
       opaque interim_transcript_hash<0..255>;
       Extension group_context_extensions<0..2^32-1>;
       Extension other_extensions<0..2^32-1>;
       HPKEPublicKey external_pub;
       KeyPackageID signer;
   } PublicGroupStateTBS;

   This signature authenticates the HPKE public key, so that the joiner
   knows that the public key was provided by a member of the group.  The
   fields that are not signed are included in the key schedule via the
   GroupContext object.  If the joiner is provided an inaccurate data
   for these fields, then its external Commit will have an incorrect
   confirmation_tag and thus be rejected.

   The information in a PublicGroupState is not deemed public in
   general, but applications can choose to make it available to new
   members in order to allow External Commits.

   External Commits work like regular Commits, with a few differences:

   *  The proposals included by value in an External Commit MUST meet
      the following conditions:



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      -  There MUST be a single Add proposal that adds the new issuing
         new member to the group

      -  There MUST be a single ExternalInit proposal

      -  There MUST NOT be any Update proposals

      -  If a Remove proposal is present, then the credential and
         endpoint_id of the removed leaf MUST be the same as the
         corresponding values in the Add KeyPackage.

   *  The proposals included by reference in an External Commit MUST
      meet the following conditions:

      -  There MUST NOT be any ExternalInit proposals

   *  External Commits MUST contain a path field (and is therefore a
      "full" Commit)

   *  External Commits MUST be signed by the new member.  In particular,
      the signature on the enclosing MLSPlaintext MUST verify using the
      public key for the credential in the leaf_key_package of the path
      field.

   *  When processing a Commit, both existing and new members MUST use
      the external init secret as described in Section 8.1.

   *  The sender type for the MLSPlaintext encapsulating the External
      Commit MUST be new_member

   In other words, 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 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 attacke
   would need to compromise the PSK as well as the signing key, but the
   application will need to ensure that continuing, non-resync'ing
   members have the required PSK.




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11.2.2.  Welcoming New Members

   The sender of a Commit message is responsible for sending a Welcome
   message to any new members added via Add proposals.  The Welcome
   message provides the new members with the current state of the group,
   after the application of the Commit message.  The new members will
   not be able to decrypt or verify the Commit message, but will have
   the secrets they need to participate in the epoch initiated by the
   Commit message.

   In order to allow the same Welcome message to be sent to all 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 node 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.




























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   struct {
     opaque group_id<0..255>;
     uint64 epoch;
     opaque tree_hash<0..255>;
     opaque confirmed_transcript_hash<0..255>;
     Extension group_context_extensions<0..2^32-1>;
     Extension other_extensions<0..2^32-1>;
     MAC confirmation_tag;
     KeyPackageID signer;
     opaque signature<0..2^16-1>;
   } GroupInfo;

   struct {
     opaque path_secret<1..255>;
   } PathSecret;

   struct {
     opaque joiner_secret<1..255>;
     optional<PathSecret> path_secret;
     PreSharedKeys psks;
   } GroupSecrets;

   struct {
     KeyPackageID new_member<1..255>;
     HPKECiphertext encrypted_group_secrets;
   } EncryptedGroupSecrets;

   struct {
     ProtocolVersion version = mls10;
     CipherSuite cipher_suite;
     EncryptedGroupSecrets secrets<0..2^32-1>;
     opaque encrypted_group_info<1..2^32-1>;
   } 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:








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   *  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 ciphersuite indicated in the KeyPackage does not match the
      one in the Welcome message, return an error.

   *  Decrypt the encrypted_group_secrets using HPKE with the algorithms
      indicated by the ciphersuite and the HPKE private key
      corresponding to the GroupSecrets.  If a PreSharedKeyID is part of
      the GroupSecrets and the client is not in possession of the
      corresponding PSK, return an error.

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

   welcome_nonce = KDF.Expand(welcome_secret, "nonce", AEAD.Nn)
   welcome_key = KDF.Expand(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 and algorithm are taken from the
      credential in the leaf node of the member with KeyPackageID
      signer.  If there is no matching leaf node, or if signature
      verification fails, return an error.

   *  Verify the integrity of the ratchet tree.

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

      -  For each non-empty parent node, verify that exactly one of the
         node's children are non-empty and have the hash of this node
         set as their parent_hash value (if the child is another parent)
         or has a parent_hash extension in the KeyPackage containing the
         same value (if the child is a leaf).  If either of the node's
         children is empty, and in particular does not have a parent
         hash, then its respective children's parent_hash values have to
         be considered instead.

      -  For each non-empty leaf node, verify the signature on the
         KeyPackage.

   *  Identify a leaf in the tree array (any even-numbered node) whose
      key_package field is identical to the KeyPackage.  If no such
      field exists, return an error.  Let index represent the index of
      this node in the tree.



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

      -  The GroupContext contains the group_id, epoch, tree_hash,
         confirmed_transcript_hash, and group_context_extensions fields
         from the GroupInfo object.

      -  The new member's position in the tree is index, as defined
         above.

      -  Update the leaf at index index with the private key
         corresponding to the public key in the node.

      -  If the path_secret value is set in the GroupSecrets object:
         Identify the lowest common ancestor of the node index index and
         of the node index of the member with KeyPackageID
         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.

11.3.  Ratchet Tree Extension

   By default, a GroupInfo message only provides the joiner with a
   commitment to the group's ratchet tree.  In order to process or
   generate handshake messages, the joiner will need to get a copy of
   the ratchet tree from some other source.  (For example, the DS might
   provide a cached copy.)  The inclusion of the tree hash in the
   GroupInfo message means that the source of the ratchet tree need not
   be trusted to maintain the integrity of tree.




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   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:

   enum {
       reserved(0),
       leaf(1),
       parent(2),
       (255)
   } NodeType;

   struct {
       NodeType node_type;
       select (Node.node_type) {
           case leaf:   KeyPackage key_package;
           case parent: ParentNode node;
       };
   } Node;

   optional<Node> ratchet_tree<1..2^32-1>;

   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.

12.  Extensibility

   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 client capabilities and aspects of
      their participation in the group (once in the ratchet tree)




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   *  In the Welcome message, 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 KeyPackage
   extensions.  New members of a group are informed of the group's
   GroupContext extensions via the group_context_extensions field in the
   GroupInfo or PublicGroupState object.  The other_extensions field in
   a GroupInfo object 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 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 initiating a group MUST ignore all unrecognized
      ciphersuites, extensions, and other parameters.  Otherwise, it may
      fail to interoperate with newer clients.

   *  A client adding a new member to a group MUST verify that the
      KeyPackage for the new member contains extensions that are
      consistent with the group's extensions.  For each extension in the
      GroupContext, the KeyPackage MUST have an extension of the same
      type, and the contents of the extension MUST be consistent with
      the value of the extension in the GroupContext, according to the
      semantics of the specific extension.

   *  If any extension in a GroupInfo message is unrecognized (i.e., not
      contained in the corresponding KeyPackage), then the client MUST
      reject the Welcome message and not join the group.

   *  The extensions populated into a GroupContext object are drawn from
      those in the GroupInfo object, according to the definitions of
      those extensions.

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




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   This document does not define any way for the parameters of the group
   to change once it has been created; such a behavior could be
   implemented as an extension.

13.  Sequencing of State Changes

   Each Commit message is premised on a given starting state, indicated
   by the epoch field of the enclosing MLSPlaintext message.  If the
   changes implied by a Commit messages 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.

   When this happens, there is a need for the members of the group to
   deconflict the simultaneous Commit messages.  There are two general
   approaches:

   *  Have the Delivery Service enforce a total order

   *  Have a signal in the message that clients can use to break ties

   As long as Commit messages cannot be merged, there is a risk of
   starvation.  In a sufficiently busy group, a given member may never
   be able to send a Commit message, because he always loses to other
   members.  The degree to which this is a practical problem will depend
   on the dynamics of the application.

   It might be possible, because of the non-contributivity of
   intermediate nodes, that Commit messages could be applied one after
   the other without the Delivery Service having to reject any Commit
   message, which would make MLS more resilient regarding the
   concurrency of Commit messages.  The Messaging system can decide to
   choose the order for applying the state changes.  Note that there are
   certain cases (if no total ordering is applied by the Delivery
   Service) where the ordering is important for security, ie. all
   updates must be executed before removes.

   Regardless of how messages are kept in sequence, implementations MUST
   only update their cryptographic state when valid Commit messages are
   received.  Generation of Commit messages MUST NOT modify a client's
   state, since the endpoint doesn't know at that time whether the
   changes implied by the Commit message will succeed or not.





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13.1.  Server-Enforced Ordering

   With this approach, the Delivery Service ensures that incoming
   messages are added to an ordered queue and outgoing messages are
   dispatched in the same order.  The server is trusted to break ties
   when two members send a Commit message at the same time.

   Messages should have a counter field sent in clear-text that can be
   checked by the server and used for tie-breaking.  The counter starts
   at 0 and is incremented for every new incoming message.  If two group
   members send a message with the same counter, the first message to
   arrive will be accepted by the server and the second one will be
   rejected.  The rejected message needs to be sent again with the
   correct counter number.

   To prevent counter manipulation by the server, the counter's
   integrity can be ensured by including the counter in a signed message
   envelope.

   This applies to all messages, not only state changing messages.

13.2.  Client-Enforced Ordering

   Order enforcement can be implemented on the client as well, one way
   to achieve it is to use a two step update protocol: the first client
   sends a proposal to update and the proposal is accepted when it gets
   50%+ approval from the rest of the group, then it sends the approved
   update.  Clients which didn't get their proposal accepted, will wait
   for the winner to send their update before retrying new proposals.

   While this seems safer as it doesn't rely on the server, it is more
   complex and harder to implement.  It also could cause starvation for
   some clients if they keep failing to get their proposal accepted.

14.  Application Messages

   The primary purpose of the Handshake protocol is to provide an
   authenticated group key exchange to clients.  In order to protect
   Application messages sent among the members of a group, the
   Application secret provided by the Handshake key schedule is used to
   derive nonces and encryption keys for the Message Protection Layer
   according to the Application Key Schedule.  That is, each epoch is
   equipped with a fresh Application Key Schedule which consist of a
   tree of Application Secrets as well as one symmetric ratchet per
   group member.






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   Each client maintains their own local copy of the Application 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.

   Application messages MUST be protected with the Authenticated-
   Encryption with Associated-Data (AEAD) encryption scheme associated
   with the MLS ciphersuite using the common framing mechanism.  Note
   that "Authenticated" in this context does not mean messages are known
   to be sent by a specific client but only from a legitimate member of
   the group.  To authenticate a message from a particular member,
   signatures are required.  Handshake messages MUST use asymmetric
   signatures to strongly authenticate the sender of a message.

14.1.  Message Encryption and Decryption

   The group members MUST use the AEAD algorithm associated with the
   negotiated MLS ciphersuite to AEAD encrypt and decrypt their
   Application messages according to the Message Framing section.

   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 and keys.  The sender identifier is used to identify
   the member's symmetric ratchet from the initial group Application
   secret.  The application generation field is used to determine how
   far into the ratchet to iterate in order to reproduce the required
   AEAD keys and nonce for performing decryption.

   Application messages SHOULD 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 ?" the answer
   "Wednesday" might be leaked to an adversary by the ciphertext length.
   An attacker expecting Alice to answer Bob with a day of the week
   might find out the plaintext by correlation between the question and
   the length.

   Similarly to TLS 1.3, if padding is used, the MLS messages MUST be
   padded with zero-valued bytes before AEAD encryption.  Upon AEAD
   decryption, the length field of the plaintext is used to compute the
   number of bytes to be removed from the plaintext to get the correct
   data.  As the padding mechanism is used to improve protection against
   traffic analysis, removal of the padding SHOULD be implemented in a
   "constant-time" manner at the MLS layer and above layers to prevent
   timing side-channels that would provide attackers with information on
   the size of the plaintext.  The padding length length_of_padding can



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   be chosen at the time of the message encryption by the sender.
   Recipients can calculate the padding size from knowing the total size
   of the ApplicationPlaintext and the length of the content.

14.2.  Restrictions

   During each epoch senders MUST NOT encrypt more data than permitted
   by the security bounds of the AEAD scheme used.

   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.

14.3.  Delayed and Reordered Application messages

   Since each Application message contains the group identifier, the
   epoch and a message counter, a client can receive messages out of
   order.  If they are able to retrieve or recompute the correct AEAD
   decryption key from currently stored cryptographic material clients
   can decrypt these messages.

   For usability, MLS clients might be required to keep the AEAD key and
   nonce for a certain amount of time to retain the ability to decrypt
   delayed or out of order messages, possibly still in transit while a
   decryption is being done.

15.  Security Considerations

   The security goals of MLS are described in
   [I-D.ietf-mls-architecture].  We describe here how the protocol
   achieves its goals at a high level, though a complete security
   analysis is outside of the scope of this document.

15.1.  Confidentiality of the 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 _ratchet
   tree invariant_ and it makes it possible to encrypt to all group
   members except one, with a number of ciphertexts that's logarithmic
   in the number of group members.





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   The ability to efficiently encrypt to all members except one allows
   members to be securely removed from a group.  It also allows a member
   to rotate their keypair such that the old private key can no longer
   be used to decrypt new messages.

15.2.  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 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 to have the
   required PSKs.

15.3.  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 previously compromised public keys.





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   Forward-secrecy between epochs is provided by deleting private keys
   from past version 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.

   Post-compromise security is also provided for new groups by members
   regularly generating new InitKeys and uploading them to the Delivery
   Service, such that compromised key material won't be used when the
   member is added to a new group.

15.4.  InitKey Reuse

   InitKeys are intended to be used only once.  That is, once an InitKey
   has been used to introduce the corresponding client to a group, it
   SHOULD be deleted from the InitKey publication system.  Reuse of
   InitKeys can lead to replay attacks.

   An application MAY allow for reuse of a "last resort" InitKey in
   order to prevent denial of service attacks.  Since an InitKey is
   needed to add a client to a new group, an attacker could prevent a
   client being added to new groups by exhausting all available
   InitKeys.

15.5.  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 5.4, but the UpdatePath syntax
   allows the sender to encrypt arbitrary, unrelated secrets.  The
   syntax also does not guarantee that the encrypted path secret
   encrypted 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 reject the
   commit and roll back to a previous state if necessary.




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   Even with such an error reporting mechanism in place, however, it is
   still possible for members to get locked out of the group by a
   malformed commit.  Since malformed Commits can only be recognized by
   certain members of the group, in an asynchronous application, it may
   be the case that all members that could detect a fault in a Commit
   are offline.  In such a case, the Commit will be accepted by the
   group, and the resulting state possibly used as the basis for further
   Commits.  When the affected members come back online, they will
   reject the first commit, and thus be unable to catch up with the
   group.

   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.

16.  IANA Considerations

   This document requests the creation of the following new IANA
   registries:

   *  MLS Ciphersuites (Section 16.1)

   *  MLS Extension Types (Section 16.2)

   *  MLS Proposal Types (Section 16.3)

   *  MLS Credential Types (Section 16.4)

   All of these registries should be under a heading of "Messaging Layer
   Security", and assignments are made via the Specification Required
   policy [RFC8126].  See Section 16.5 for additional information about
   the MLS Designated Experts (DEs).

   RFC EDITOR: Please replace XXXX throughout with the RFC number
   assigned to this document

16.1.  MLS Ciphersuites

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

   Ciphersuite names follow the naming convention:

   CipherSuite MLS_LVL_KEM_AEAD_HASH_SIG = VALUE;



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   Where VALUE is represented as a sixteen-bit integer:

   uint16 CipherSuite;

          +===========+========================================+
          | Component | Contents                               |
          +===========+========================================+
          | MLS       | The string "MLS" followed by the major |
          |           | and minor version, e.g.  "MLS10"       |
          +-----------+----------------------------------------+
          | LVL       | The security level                     |
          +-----------+----------------------------------------+
          | KEM       | The KEM algorithm used for HPKE in     |
          |           | TreeKEM group 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 3

   The columns in the registry are as follows:

   *  Value: The numeric value of the ciphersuite

   *  Name: The name of the ciphersuite

   *  Recommended: Whether support for this ciphersuite is recommended
      by the IETF MLS WG.  Valid values are "Y" and "N".  The
      "Recommended" column is assigned a value of "N" unless explicitly
      requested, and adding a value with a "Recommended" value of "Y"
      requires Standards Action [RFC8126].  IESG Approval is REQUIRED
      for a Y->N transition.

   *  Reference: The document where this ciphersuite is defined

   Initial contents:








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   +======+=====================================================+===========+=========+
   |Value |Name                                                 |Recommended|Reference|
   +======+=====================================================+===========+=========+
   |0x0000|RESERVED                                             |N/A        |RFC XXXX |
   +------+-----------------------------------------------------+-----------+---------+
   |0x0001|MLS10_128_DHKEMX25519_AES128GCM_SHA256_Ed25519       |Y          |RFC XXXX |
   +------+-----------------------------------------------------+-----------+---------+
   |0x0002|MLS10_128_DHKEMP256_AES128GCM_SHA256_P256            |Y          |RFC XXXX |
   +------+-----------------------------------------------------+-----------+---------+
   |0x0003|MLS10_128_DHKEMX25519_CHACHA20POLY1305_SHA256_Ed25519|Y          |RFC XXXX |
   +------+-----------------------------------------------------+-----------+---------+
   |0x0004|MLS10_256_DHKEMX448_AES256GCM_SHA512_Ed448           |Y          |RFC XXXX |
   +------+-----------------------------------------------------+-----------+---------+
   |0x0005|MLS10_256_DHKEMP521_AES256GCM_SHA512_P521            |Y          |RFC XXXX |
   +------+-----------------------------------------------------+-----------+---------+
   |0x0006|MLS10_256_DHKEMX448_CHACHA20POLY1305_SHA512_Ed448    |Y          |RFC XXXX |
   +------+-----------------------------------------------------+-----------+---------+
   |0xff00|Reserved for Private Use                             |N/A        |RFC XXXX |
   |-     |                                                     |           |         |
   |0xffff|                                                     |           |         |
   +------+-----------------------------------------------------+-----------+---------+

                                  Table 4

   All of these ciphersuites use HMAC [RFC2104] as their MAC function,
   with different hashes per ciphersuite.  The mapping of ciphersuites
   to HPKE primitives, HMAC hash functions, and TLS signature schemes is
   as follows [I-D.irtf-cfrg-hpke] [RFC8446]:

   +======+========+========+========+========+========================+
   |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                  |
   +------+--------+--------+--------+--------+------------------------+

                                  Table 5





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   The hash used for the MLS transcript hash is the one referenced in
   the ciphersuite name.  In the ciphersuites defined above, "SHA256"
   and "SHA512" refer to the SHA-256 and SHA-512 functions defined in
   [SHS].

   It is advisable to keep the number of ciphersuites low to increase
   the chances clients can interoperate in a federated environment,
   therefore the ciphersuites only inlcude modern, yet well-established
   algorithms.  Depending on their requirements, clients can choose
   between two security levels (roughly 128-bit and 256-bit).  Within
   the security levels clients can choose between faster X25519/X448
   curves and FIPS 140-2 compliant curves for Diffie-Hellman key
   negotiations.  Additionally clients that run predominantly on mobile
   processors can choose ChaCha20Poly1305 over AES-GCM for performance
   reasons.  Since ChaCha20Poly1305 is not listed by FIPS 140-2 it is
   not paired with FIPS 140-2 compliant curves.  The security level of
   symmetric encryption algorithms and hash functions is paired with the
   security level of the curves.

   The mandatory-to-implement ciphersuite for MLS 1.0 is
   MLS10_128_DHKEMX25519_AES128GCM_SHA256_Ed25519 which uses Curve25519
   for key exchange, AES-128-GCM for HPKE, HKDF over SHA2-256, and
   Ed25519 for signatures.

   Values with the first byte 255 (decimal) are reserved for Private
   Use.

   New ciphersuite values are assigned by IANA as described in
   Section 16.

16.2.  MLS Extension Types

   This registry lists identifiers for extensions to the MLS protocol.
   The extension type field is two bytes wide, so valid extension type
   values are in the range 0x0000 to 0xffff.

   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 messages





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      -  GC: GroupContext objects (and the group_context_extensions
         field of GroupInfo objects)

      -  GI: The other_extensions field of GroupInfo objects

   *  Recommended: Whether support for this extension is recommended by
      the IETF MLS WG.  Valid values are "Y" and "N".  The "Recommended"
      column is assigned a value of "N" unless explicitly requested, and
      adding a value with a "Recommended" value of "Y" requires
      Standards Action [RFC8126].  IESG Approval is REQUIRED for a Y->N
      transition.

   *  Reference: The document where this extension is defined

   Initial contents:

   +==========+=================+============+=============+===========+
   | Value    | Name            | Message(s) | Recommended | Reference |
   +==========+=================+============+=============+===========+
   | 0x0000   | RESERVED        | N/A        | N/A         | RFC XXXX  |
   +----------+-----------------+------------+-------------+-----------+
   | 0x0001   | capabilities    | KP         | Y           | RFC XXXX  |
   +----------+-----------------+------------+-------------+-----------+
   | 0x0002   | lifetime        | KP         | Y           | RFC XXXX  |
   +----------+-----------------+------------+-------------+-----------+
   | 0x0003   | external_key_id | KP         | Y           | RFC XXXX  |
   +----------+-----------------+------------+-------------+-----------+
   | 0x0004   | parent_hash     | KP         | Y           | RFC XXXX  |
   +----------+-----------------+------------+-------------+-----------+
   | 0x0005   | ratchet_tree    | GI         | Y           | RFC XXXX  |
   +----------+-----------------+------------+-------------+-----------+
   | 0xff00   | Reserved for    | N/A        | N/A         | RFC XXXX  |
   | -        | Private Use     |            |             |           |
   | 0xffff   |                 |            |             |           |
   +----------+-----------------+------------+-------------+-----------+

                                  Table 6

16.3.  MLS Proposal Types

   This registry lists identifiers for types of proposals that can be
   made for changes to an MLS group.  The extension type field is two
   bytes wide, so valid extension type values are in the range 0x0000 to
   0xffff.

   Template:

   *  Value: The numeric value of the proposal type



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   *  Name: The name of the proposal type

   *  Recommended: Whether support for this extension is recommended by
      the IETF MLS WG.  Valid values are "Y" and "N".  The "Recommended"
      column is assigned a value of "N" unless explicitly requested, and
      adding a value with a "Recommended" value of "Y" requires
      Standards Action [RFC8126].  IESG Approval is REQUIRED for a Y->N
      transition.

   *  Reference: The document where this extension is defined

   Initial contents:

     +==========+==========================+=============+===========+
     | Value    | Name                     | Recommended | Reference |
     +==========+==========================+=============+===========+
     | 0x0000   | RESERVED                 | N/A         | RFC XXXX  |
     +----------+--------------------------+-------------+-----------+
     | 0x0001   | add                      | Y           | RFC XXXX  |
     +----------+--------------------------+-------------+-----------+
     | 0x0002   | update                   | Y           | RFC XXXX  |
     +----------+--------------------------+-------------+-----------+
     | 0x0003   | remove                   | Y           | RFC XXXX  |
     +----------+--------------------------+-------------+-----------+
     | 0x0004   | psk                      | Y           | RFC XXXX  |
     +----------+--------------------------+-------------+-----------+
     | 0x0005   | reinit                   | Y           | RFC XXXX  |
     +----------+--------------------------+-------------+-----------+
     | 0x0006   | external_init            | Y           | RFC XXXX  |
     +----------+--------------------------+-------------+-----------+
     | 0x0007   | app_ack                  | Y           | RFC XXXX  |
     +----------+--------------------------+-------------+-----------+
     | 0x0008   | group_context_extensions | Y           | RFC XXXX  |
     +----------+--------------------------+-------------+-----------+
     | 0xff00 - | Reserved for Private Use | N/A         | RFC XXXX  |
     | 0xffff   |                          |             |           |
     +----------+--------------------------+-------------+-----------+

                                  Table 7

16.4.  MLS Credential Types

   This registry lists identifiers for types of credentials that can be
   used for authentication in the MLS protocol.  The credential type
   field is two bytes wide, so valid credential type values are in the
   range 0x0000 to 0xffff.

   Template:



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   *  Value: The numeric value of the credential type

   *  Name: The name of the credential type

   *  Recommended: Whether support for this credential is recommended by
      the IETF MLS WG.  Valid values are "Y" and "N".  The "Recommended"
      column is assigned a value of "N" unless explicitly requested, and
      adding a value with a "Recommended" value of "Y" requires
      Standards Action [RFC8126].  IESG Approval is REQUIRED for a Y->N
      transition.

   *  Reference: The document where this credential is defined

   Initial contents:

       +=================+==============+=============+===========+
       | Value           | Name         | Recommended | Reference |
       +=================+==============+=============+===========+
       | 0x0000          | RESERVED     | N/A         | RFC XXXX  |
       +-----------------+--------------+-------------+-----------+
       | 0x0001          | basic        | Y           | RFC XXXX  |
       +-----------------+--------------+-------------+-----------+
       | 0x0002          | x509         | Y           | RFC XXXX  |
       +-----------------+--------------+-------------+-----------+
       | 0xff00 - 0xffff | Reserved for | N/A         | RFC XXXX  |
       |                 | Private Use  |             |           |
       +-----------------+--------------+-------------+-----------+

                                 Table 8

16.5.  MLS Designated Expert Pool

   Specification Required [RFC8126] registry requests are registered
   after a three-week review period on the MLS DEs' mailing list: mls-
   reg-review@ietf.org (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").









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   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 iesg@ietf.org (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, the MLS DEs will apply the ciphersuite-related
   advisory found in Section 6.1.

   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 be appointed who are able to
   represent the perspectives of different applications using this
   specification, in order to enable broadly informed review of
   registration decisions.  In cases where a registration decision could
   be perceived as creating a conflict of interest for a particular MLS
   DE, that MLS DE SHOULD defer to the judgment of the other MLS DEs.

17.  Contributors

   *  Joel Alwen
      Wickr
      joel.alwen@wickr.com

   *  Karthikeyan Bhargavan
      INRIA
      karthikeyan.bhargavan@inria.fr

   *  Cas Cremers
      University of Oxford
      cremers@cispa.de

   *  Alan Duric
      Wire
      alan@wire.com

   *  Britta Hale
      Naval Postgraduate School
      britta.hale@nps.edu





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   *  Srinivas Inguva
      Twitter
      singuva@twitter.com

   *  Konrad Kohbrok
      Aalto University
      konrad.kohbrok@datashrine.de

   *  Albert Kwon
      MIT
      kwonal@mit.edu

   *  Brendan McMillion
      Cloudflare
      brendan@cloudflare.com

   *  Eric Rescorla
      Mozilla
      ekr@rtfm.com

   *  Michael Rosenberg
      Trail of Bits
      michael.rosenberg@trailofbits.com

   *  Thyla van der Merwe
      Royal Holloway, University of London
      thyla.van.der@merwe.tech

18.  References

18.1.  Normative References

   [I-D.irtf-cfrg-hpke]
              Barnes, R. L., Bhargavan, K., Lipp, B., and C. A. Wood,
              "Hybrid Public Key Encryption", Work in Progress,
              Internet-Draft, draft-irtf-cfrg-hpke-12, 2 September 2021,
              <https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-
              hpke-12>.

   [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/rfc/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/rfc/rfc2119>.



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   [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/rfc/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/rfc/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/rfc/rfc8446>.

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", 18
              January 2018, <https://eprint.iacr.org/2017/666.pdf>.

   [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>.

   [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, DOI 10.1186/s13635-016-0030-7,
              February 2016,
              <https://doi.org/10.1186/s13635-016-0030-7>.

   [I-D.ietf-mls-architecture]
              Beurdouche, B., Rescorla, E., Omara, E., Inguva, S., Kwon,
              A., and A. Duric, "The Messaging Layer Security (MLS)
              Architecture", Work in Progress, Internet-Draft, draft-
              ietf-mls-architecture-07, 4 October 2021,
              <https://datatracker.ietf.org/doc/html/draft-ietf-mls-
              architecture-07>.



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   [I-D.ietf-trans-rfc6962-bis]
              Laurie, B., Langley, A., Kasper, E., Messeri, E., and R.
              Stradling, "Certificate Transparency Version 2.0", Work in
              Progress, Internet-Draft, draft-ietf-trans-rfc6962-bis-42,
              31 August 2021, <https://datatracker.ietf.org/doc/html/
              draft-ietf-trans-rfc6962-bis-42>.

   [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/rfc/rfc8032>.

   [SECG]     "Elliptic Curve Cryptography, Standards for Efficient
              Cryptography Group, ver. 2", 2009,
              <https://secg.org/sec1-v2.pdf>.

   [SHS]      Dang, Q., "Secure Hash Standard", National Institute of
              Standards and Technology report,
              DOI 10.6028/nist.fips.180-4, July 2015,
              <https://doi.org/10.6028/nist.fips.180-4>.

   [signal]   Perrin(ed), T. and M. Marlinspike, "The Double Ratchet
              Algorithm", 20 November 2016,
              <https://www.signal.org/docs/specifications/
              doubleratchet/>.

Appendix A.  Tree Math

   One benefit of using left-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, an 11-element tree has
   the following structure:

                                                X
                        X
            X                       X                       X
      X           X           X           X           X
   X     X     X     X     X     X     X     X     X     X     X
   0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20

   This allows us to compute relationships between tree nodes simply by
   manipulating indices, rather than having to maintain complicated
   structures in memory, even for partial trees.  The basic rule is that
   the high-order bits of parent and child nodes have the following
   relation (where x is an arbitrary bit string):

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



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   The following python code demonstrates the tree computations
   necessary for MLS.  Test vectors can be derived from the diagram
   above.

# 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. Note that because the tree is
# left-balanced, there is no dependency on the size of the tree.
def left(x):
    k = level(x)
    if k == 0:
        raise Exception('leaf node has no children')

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




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# The right child of an intermediate node. Depends on the number of
# leaves because the straightforward calculation can take you beyond the
# edge of the tree.
def right(x, n):
    k = level(x)
    if k == 0:
        raise Exception('leaf node has no children')

    r = x ^ (0x03 << (k - 1))
    while r >= node_width(n):
        r = left(r)
    return r

# The immediate parent of a node. May be beyond the right edge of the
# tree.
def parent_step(x):
    k = level(x)
    b = (x >> (k + 1)) & 0x01
    return (x | (1 << k)) ^ (b << (k + 1))

# The parent of a node. As with the right child calculation, we have to
# walk back until the parent is within the range of the tree.
def parent(x, n):
    if x == root(n):
        raise Exception('root node has no parent')

    p = parent_step(x)
    while p >= node_width(n):
        p = parent_step(p)
    return p

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



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        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

Authors' Addresses

   Richard Barnes
   Cisco

   Email: rlb@ipv.sx



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   Benjamin Beurdouche
   Inria & Mozilla

   Email: ietf@beurdouche.com


   Raphael Robert

   Email: ietf@raphaelrobert.com


   Jon Millican
   Facebook

   Email: jmillican@fb.com


   Emad Omara
   Google

   Email: emadomara@google.com


   Katriel Cohn-Gordon
   University of Oxford

   Email: me@katriel.co.uk
























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