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Versions: (draft-barnes-mls-protocol) 00 01 02 03 04 05 06 07 08

Network Working Group                                          R. Barnes
Internet-Draft                                                     Cisco
Intended status: Informational                             B. Beurdouche
Expires: May 18, 2020                                              Inria
                                                             J. Millican
                                                                Facebook
                                                                E. Omara
                                                                  Google
                                                          K. Cohn-Gordon
                                                    University of Oxford
                                                               R. Robert
                                                                    Wire
                                                       November 15, 2019


              The Messaging Layer Security (MLS) Protocol
                       draft-ietf-mls-protocol-08

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.

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/.

   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 May 18, 2020.




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Copyright Notice

   Copyright (c) 2019 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  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Change Log  . . . . . . . . . . . . . . . . . . . . . . .   4
   2.  Terminology . . . . . . . . . . . . . . . . . . . . . . . . .   7
   3.  Basic Assumptions . . . . . . . . . . . . . . . . . . . . . .   7
   4.  Protocol Overview . . . . . . . . . . . . . . . . . . . . . .   8
   5.  Ratchet Trees . . . . . . . . . . . . . . . . . . . . . . . .  12
     5.1.  Tree Computation Terminology  . . . . . . . . . . . . . .  12
     5.2.  Ratchet Tree Nodes  . . . . . . . . . . . . . . . . . . .  14
     5.3.  Views of a Ratchet Tree . . . . . . . . . . . . . . . . .  15
     5.4.  Ratchet Tree Updates  . . . . . . . . . . . . . . . . . .  16
     5.5.  Synchronizing Views of the Tree . . . . . . . . . . . . .  17
   6.  Cryptographic Objects . . . . . . . . . . . . . . . . . . . .  19
     6.1.  Ciphersuites  . . . . . . . . . . . . . . . . . . . . . .  19
       6.1.1.  Curve25519, SHA-256, and AES-128-GCM  . . . . . . . .  20
       6.1.2.  P-256, SHA-256, and AES-128-GCM . . . . . . . . . . .  20
     6.2.  Credentials . . . . . . . . . . . . . . . . . . . . . . .  21
     6.3.  Tree Hashes . . . . . . . . . . . . . . . . . . . . . . .  23
     6.4.  Group State . . . . . . . . . . . . . . . . . . . . . . .  24
     6.5.  Direct Paths  . . . . . . . . . . . . . . . . . . . . . .  25
     6.6.  Key Schedule  . . . . . . . . . . . . . . . . . . . . . .  26
     6.7.  Encryption Keys . . . . . . . . . . . . . . . . . . . . .  28
   7.  Initialization Keys . . . . . . . . . . . . . . . . . . . . .  29
     7.1.  Supported Versions and Supported Ciphersuites . . . . . .  30
     7.2.  Expiration  . . . . . . . . . . . . . . . . . . . . . . .  31
   8.  Message Framing . . . . . . . . . . . . . . . . . . . . . . .  31
     8.1.  Metadata Encryption . . . . . . . . . . . . . . . . . . .  33
     8.2.  Content Signing and Encryption  . . . . . . . . . . . . .  34
   9.  Group Creation  . . . . . . . . . . . . . . . . . . . . . . .  35
   10. Group Evolution . . . . . . . . . . . . . . . . . . . . . . .  37
     10.1.  Proposals  . . . . . . . . . . . . . . . . . . . . . . .  37
       10.1.1.  Add  . . . . . . . . . . . . . . . . . . . . . . . .  38



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       10.1.2.  Update . . . . . . . . . . . . . . . . . . . . . . .  39
       10.1.3.  Remove . . . . . . . . . . . . . . . . . . . . . . .  39
       10.1.4.  External Proposals . . . . . . . . . . . . . . . . .  40
     10.2.  Commit . . . . . . . . . . . . . . . . . . . . . . . . .  40
       10.2.1.  Welcoming New Members  . . . . . . . . . . . . . . .  43
   11. Sequencing of State Changes . . . . . . . . . . . . . . . . .  45
     11.1.  Server-Enforced Ordering . . . . . . . . . . . . . . . .  46
     11.2.  Client-Enforced Ordering . . . . . . . . . . . . . . . .  47
   12. Application Messages  . . . . . . . . . . . . . . . . . . . .  47
     12.1.  Tree of Application Secrets  . . . . . . . . . . . . . .  48
     12.2.  Sender Ratchets  . . . . . . . . . . . . . . . . . . . .  49
     12.3.  Deletion Schedule  . . . . . . . . . . . . . . . . . . .  49
     12.4.  Further Restrictions . . . . . . . . . . . . . . . . . .  51
     12.5.  Message Encryption and Decryption  . . . . . . . . . . .  51
     12.6.  Delayed and Reordered Application messages . . . . . . .  52
   13. Security Considerations . . . . . . . . . . . . . . . . . . .  53
     13.1.  Confidentiality of the Group Secrets . . . . . . . . . .  53
     13.2.  Authentication . . . . . . . . . . . . . . . . . . . . .  53
     13.3.  Forward and post-compromise security . . . . . . . . . .  54
     13.4.  Init Key Reuse . . . . . . . . . . . . . . . . . . . . .  54
   14. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  54
     14.1.  MLS Ciphersuites . . . . . . . . . . . . . . . . . . . .  54
   15. Contributors  . . . . . . . . . . . . . . . . . . . . . . . .  55
   16. References  . . . . . . . . . . . . . . . . . . . . . . . . .  56
     16.1.  Normative References . . . . . . . . . . . . . . . . . .  56
     16.2.  Informative References . . . . . . . . . . . . . . . . .  57
   Appendix A.  Tree Math  . . . . . . . . . . . . . . . . . . . . .  58
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  61

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




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   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.

   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-08

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

   o  Decompose group operations into Proposals and Commits (*)

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

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

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

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

   draft-07




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

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

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

   o  Clarifications on message framing and HPKE contexts (*)

   draft-06

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

   o  Rename the GroupState structure to GroupContext (*)

   o  Rename UserInitKey to ClientInitKey

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

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

   draft-05

   o  Common framing for handshake and application messages (*)

   o  Handshake message encryption (*)

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

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

   o  Remove the secret field from tree node values

   draft-04

   o  Updating the language to be similar to the Architecture document

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

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

   draft-03

   o  Added ciphersuites and signature schemes (*)

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

   o  Fixed inconsistencies between Welcome and GroupState (*)



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   o  Added encryption of the Welcome message (*)

   draft-02

   o  Removed ART (*)

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

   o  Added explicit key confirmation (*)

   draft-01

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

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

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

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

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

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

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

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

   o  Added an appendix with example code for tree math

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

   draft-00

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





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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.  An application or user may use
      one client per device (keeping keys local to each device) or sync
      keys among a user's devices so that each user appears as a single
      client.  In the scenario where multiple devices share the
      cryptographic material the client is referred to as a "virtual"
      client.

   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.

   Initialization Key:  A short-lived HPKE key pair used to introduce a
      new client to a group.  Initialization keys are published for each
      client (ClientInitKey).

   Leaf Key:  A secret that represents a member's contribution to the
      group secret (so called because the members' leaf keys are the
      leaves in the group's ratchet tree).

   Identity Key:  A long-lived signing key pair used to authenticate the
      sender of a message.

   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 Messaging
   Service (MS) as described in [I-D.ietf-mls-architecture].  In
   particular, we assume the MS provides the following services:

   o  A long-term identity key provider which allows clients to
      authenticate protocol messages in a group.  These keys MUST be
      kept for the lifetime of the group as there is no mechanism in the
      protocol for changing a client's identity key.



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   o  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 11 for further considerations.)

   o  A directory to which clients can publish initialization keys and
      download initialization keys 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 and post-compromise secrecy with respect to compromise of a
   participant.

   We describe the information stored by each client as a _state_, which
   includes both public and private data.  An initial state, including
   an initial set of clients, is set up by a group creator using the
   _Init_ algorithm and based on information pre-published by clients.
   The creator sends the _Init_ message to the clients, who can then set
   up their own group state and derive the same shared secret.  Clients
   then exchange messages to produce new shared states which are
   causally linked to their predecessors, forming a logical Directed
   Acyclic Graph (DAG) of states.  Members can send _Update_ messages
   for post-compromise secrecy and new clients can be added or existing
   members removed from the group.

   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.

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

   o  Adding a member, initiated by a current member;

   o  Updating the leaf secret of a member;

   o  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.



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   Before the initialization of a group, clients publish ClientInitKey
   objects to a directory provided to the Messaging Service.

                                                                 Group
  A                B                C            Directory       Channel
  |                |                |                |              |
  | ClientInitKeyA |                |                |              |
  |------------------------------------------------->|              |
  |                |                |                |              |
  |                | ClientInitKeyB |                |              |
  |                |-------------------------------->|              |
  |                |                |                |              |
  |                |                | ClientInitKeyC |              |
  |                |                |--------------->|              |
  |                |                |                |              |

   When a client A wants to establish a group with B and C, it first
   downloads ClientInitKeys for B and C.  It then initializes a group
   state containing only itself and uses the ClientInitKeys to compute
   Welcome and Add messages to add B and C, in a sequence chosen by A.
   The Welcome messages are sent directly to the new members (there is
   no need to send them to the group).  The Add messages are broadcasted
   to the group, and processed in sequence by B and C.  Messages
   received before a client has joined the group are ignored.  Only
   after A has received its Add messages back from the server does it
   update its state to reflect their addition.

























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

   Subsequent additions of group members proceed in the same way.  Any
   member of the group can download an ClientInitKey for a new client
   and broadcast an Add message that the current group can use to update
   their state and the new client can use to initialize its state.

   To enforce forward secrecy and post-compromise security of messages,
   each member periodically updates its leaf secret which represents its
   contribution to the group secret.  Any member of the group can send
   an Update at any time by generating a fresh leaf secret and sending
   an Update message that describes how to update the group secret with
   that new information.  Once all members have processed this message,
   the group's secrets will be unknown to an attacker that had
   compromised the sender's prior leaf secret.




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   It is left to the application to determine the interval of time
   between Update messages.  This policy could require a change for each
   message, or it could require sending an update every week or more.

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

   Members are removed from the group in a similar way, as an update is
   effectively removing the old leaf from the group.  Any member of the
   group can generate a Remove message that adds new entropy to the
   group state that is known to all members except the removed member.
   After other participants have processed this message, the group's
   secrets will be unknown to the removed participant.  Note that this
   does not necessarily imply that any member is actually allowed to
   evict other members; groups can layer authentication-based access
   control policies on top of these basic mechanism.

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








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5.  Ratchet Trees

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

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.  If a subtree is full and it is not a subset of any
   other full subtree, then it is _maximal_.

   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.  Note that given a list of "n" items, there is
   a unique left-balanced binary tree structure with these elements as
   leaves.  In such a left-balanced tree, the "k-th" leaf node refers to
   the "k-th" leaf node in the tree when counting from the left,
   starting from 0.

   The _direct path_ of a root is the empty list, and of any other node
   is the concatenation of that node with the direct path of its parent.
   The _copath_ of a node is the list of siblings of nodes in its direct
   path.  The _frontier_ of a tree is the list of heads of the maximal
   full subtrees of the tree, ordered from left to right.

   For example, in the below tree:

   o  The direct path of C is (C, CD, ABCD)

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



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   o  The frontier of the tree is (ABCD, EF, G)

               ABCDEFG
              /      \
             /        \
            /          \
        ABCD            EFG
       /    \          /  \
      /      \        /    \
     AB      CD      EF    |
    / \     / \     / \    |
   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 _node 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:

   o  0 = A

   o  1 = AB

   o  2 = B

   o  3 = ABCD

   o  4 = C

   o  5 = CD

   o  6 = D

   o  7 = ABCDEFG

   o  8 = E

   o  9 = EF

   o  10 = F

   o  11 = EFG

   o  12 = G





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   (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 leaves of the tree are indexed separately, using a _leaf index_,
   since the protocol messages only need to refer to leaves in the tree.
   Like nodes, leaves are numbered left to right.  Note that given the
   above numbering, a node is a leaf node if and only if it has an even
   node index, and a leaf node's leaf index is half its node index.  The
   leaf indices in the above tree are as follows:

   o  0 = A

   o  1 = B

   o  2 = C

   o  3 = D

   o  4 = E

   o  5 = F

   o  6 = G

5.2.  Ratchet Tree Nodes

   A particular instance of a ratchet tree is based on the following
   cryptographic primitives, defined by the ciphersuite in use:

   o  An HPKE ciphersuite, which specifies a Key Encapsulation Method
      (KEM), an AEAD encryption scheme, and a hash function

   o  A Derive-Key-Pair function that produces an asymmetric key pair
      for the specified KEM from a symmetric secret, using the specified
      hash function.

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

   o  A private key (only within direct path, see below)

   o  A public key

   o  An ordered list of leaf indices for "unmerged" leaves (see
      Section 5.3)

   o  A credential (only for leaf nodes)




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   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.

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

   o  The resolution of a blank leaf node is the empty list

   o  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:

         _
       /   \
      /     \
     _       CD[C]
    / \     / \
   A   _   C   D

   0 1 2 3 4 5 6

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

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

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

   o  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 6.3.

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.



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   No participant in an MLS group has full knowledge of the secret state
   of the tree, i.e., private keys associated to the nodes.  Instead,
   each member is assigned to a leaf of the tree, which determines the
   set of secret state known to the member.  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 or equal to it.

   In other words, if a node is not blank, then it holds a key pair, and
   the private key of that key pair is known only to members holding
   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
   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 Updates

   Nodes in a tree are always updated along the direct path from a leaf
   to the root.  The generator of the update chooses a random secret
   value "path_secret[0]", and generates a sequence of "path secrets",
   one for each node from the leaf to the root.  That is, path_secret[0]
   is used for 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.

   path_secret[n] = HKDF-Expand-Label(path_secret[n-1],
                                      "path", "", Hash.Length)
   node_secret[n] = HKDF-Expand-Label(path_secret[n],
                                      "node", "", Hash.Length)
   node_priv[n], node_pub[n] = Derive-Key-Pair(node_secret[n])

   For example, suppose there is a group with four members:







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         G
        / \
       /   \
      /     \
     E       _
    / \     / \
   A   B   C   D

   If the second participant (B) subsequently generates an update based
   on a secret X, then the sender would generate the following sequence
   of path secrets and node secrets:

       path_secret[2] ---> node_secret[2]
            ^
            |
       path_secret[1] ---> node_secret[1]
            ^
            |
   X = path_secret[0] ---> node_secret[0]

   After the update, the tree will have the following structure, where
   "ns[i]" represents the node_secret values generated as described
   above:

             ns[2]
            /     \
        ns[1]      _
        /  \      / \
       A   ns[0] C   D

5.5.  Synchronizing Views of the Tree

   The members of the group need to keep their views of the tree in sync
   and up to date.  When a client proposes a change to the tree (e.g.,
   to add or remove a member), it transmits a handshake message
   containing a set of public values for intermediate nodes in the
   direct path of a leaf.  The other members of the group can use these
   public values to update their view of the tree, aligning their copy
   of the tree to the sender's.

   To perform an update for a leaf, the sender broadcasts to the group
   the following information for each node in the direct path of the
   leaf, as well as the root:

   o  The public key for the node

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



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   The path secret value for a given node is encrypted for the subtree
   corresponding to the parent's non-updated child, i.e., the child on
   the copath of the leaf node.  There is one encrypted path secret for
   each public key in the resolution of the non-updated child.  In
   particular, for the leaf node, there are no encrypted secrets, since
   a leaf node has no children.

   The recipient of an update 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 node_secret
          values.

   2.  Merge the updated path secrets into the tree.

       *  Replace the public keys for nodes on the direct path with the
          received public keys.

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

       *  For all updated nodes, set the list of unmerged leaves to the
          empty list.

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









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             +------------+----------------------------------+
             | Public Key | Ciphertext(s)                    |
             +------------+----------------------------------+
             | pk(ns[2])  | E(pk(C), ps[2]), E(pk(D), ps[2]) |
             |            |                                  |
             | pk(ns[1])  | E(pk(A), ps[1])                  |
             |            |                                  |
             | pk(ns[0])  |                                  |
             +------------+----------------------------------+

   In this table, the value pk(X) represents the public key derived from
   the node secret X.  The value E(K, S) represents the public-key
   encryption of the path secret S to the public key K.

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:

   o  A hash function

   o  A Diffie-Hellman finite-field group or elliptic curve group

   o  An AEAD encryption algorithm [RFC5116]

   The ciphersuite's Diffie-Hellman group is used to instantiate an HPKE
   [I-D.irtf-cfrg-hpke] instance for the purpose of public-key
   encryption.  The ciphersuite must specify an algorithm "Derive-Key-
   Pair" that maps octet strings with length Hash.length to HPKE key
   pairs.

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

   enum {
       P256_SHA256_AES128GCM(0x0000),
       X25519_SHA256_AES128GCM(0x0001),
       (0xFFFF)
   } CipherSuite;

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






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6.1.1.  Curve25519, SHA-256, and AES-128-GCM

   This ciphersuite uses the following primitives:

   o  Hash function: SHA-256

   o  AEAD: AES-128-GCM

   When HPKE is used with this ciphersuite, it uses the following
   algorithms:

   o  KEM: 0x0002 = DHKEM(Curve25519)

   o  KDF: 0x0001 = HKDF-SHA256

   o  AEAD: 0x0001 = AES-GCM-128

   Given an octet string X, the private key produced by the Derive-Key-
   Pair operation is SHA-256(X).  (Recall that any 32-octet string is a
   valid Curve25519 private key.)  The corresponding public key is
   X25519(SHA-256(X), 9).

   Implementations SHOULD use the approach specified in [RFC7748] to
   calculate the Diffie-Hellman shared secret.  Implementations MUST
   check whether the computed Diffie-Hellman shared secret is the all-
   zero value and abort if so, as described in Section 6 of [RFC7748].
   If implementers use an alternative implementation of these elliptic
   curves, they SHOULD perform the additional checks specified in
   Section 7 of [RFC7748]

6.1.2.  P-256, SHA-256, and AES-128-GCM

   This ciphersuite uses the following primitives:

   o  Hash function: SHA-256

   o  AEAD: AES-128-GCM

   When HPKE is used with this ciphersuite, it uses the following
   algorithms:

   o  KEM: 0x0001 = DHKEM(P-256)

   o  KDF: 0x0001 = HKDF-SHA256

   o  AEAD: 0x0001 = AES-GCM-128





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   Given an octet string X, the private key produced by the Derive-Key-
   Pair operation is SHA-256(X), interpreted as a big-endian integer.
   The corresponding public key is the result of multiplying the
   standard P-256 base point by this integer.

   P-256 ECDH calculations (including parameter and key generation as
   well as the shared secret calculation) are performed according to
   [IEEE1363] using the ECKAS-DH1 scheme with the identity map as key
   derivation function (KDF), so that the shared secret is the
   x-coordinate of the ECDH shared secret elliptic curve point
   represented as an octet string.  Note that this octet string (Z in
   IEEE 1363 terminology) as output by FE2OSP, the Field Element to
   Octet String Conversion Primitive, has constant length for any given
   field; leading zeros found in this octet string MUST NOT be
   truncated.

   (Note that this use of the identity KDF is a technicality.  The
   complete picture is that ECDH is employed with a non-trivial KDF
   because MLS does not directly use this secret for anything other than
   for computing other secrets.)

   Clients MUST validate remote public values by ensuring that the point
   is a valid point on the elliptic curve.  The appropriate validation
   procedures are defined in Section 4.3.7 of [X962] and alternatively
   in Section 5.6.2.3 of [keyagreement].  This process consists of three
   steps: (1) verify that the value is not the point at infinity (O),
   (2) verify that for Y = (x, y) both integers are in the correct
   interval, (3) ensure that (x, y) is a correct solution to the
   elliptic curve equation.  For these curves, implementers do not need
   to verify membership in the correct subgroup.

6.2.  Credentials

   A member of a group authenticates the identities of other
   participants by means of credentials issued by some authentication
   system, e.g., a PKI.  Each type of credential MUST express the
   following data:

   o  The public key of a signature key pair

   o  The identity of the holder of the private key

   o  The signature scheme that the holder will use to sign MLS messages

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





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   enum {
       basic(0),
       x509(1),
       (255)
   } CredentialType;

   struct {
       opaque identity<0..2^16-1>;
       SignatureScheme algorithm;
       SignaturePublicKey public_key;
   } BasicCredential;

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

           case x509:
               opaque cert_data<1..2^24-1>;
       };
   } Credential;

   The SignatureScheme type represents a signature algorithm.  Signature
   public keys are opaque values in a format defined by the signature
   scheme.

   enum {
       ecdsa_secp256r1_sha256(0x0403),
       ed25519(0x0807),
       (0xFFFF)
   } SignatureScheme;

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

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

   [[OPEN ISSUE: 1.  SHOULD vs MUST.  2.  A client that wants to update
   its identity key can perform the operation UNDER THIS CONDITION by
   adding a new version of herself using a new credential signed under a
   new IdentityKey, then performing a remove of the old leaf.  This is
   fine as long as the credential binds to the same identity for the
   application.  If this verfication is not met, there is no
   authentication guarantee at the application layer anyway.]]





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6.3.  Tree Hashes

   To allow group members to verify that they agree on the cryptographic
   state of the group, this section defines a scheme for generating a
   hash value that represents the contents of the group's ratchet tree
   and the members' credentials.

   The hash of a tree is the hash of its root node, which we define
   recursively, starting with the leaves.  The hash of a leaf node is
   the hash of a "LeafNodeHashInput" object:

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

   struct {
       HPKEPublicKey public_key;
       Credential credential;
   } LeafNodeInfo;

   struct {
       uint8 hash_type = 0;
       optional<LeafNodeInfo> info;
   } LeafNodeHashInput;

   The "public_key" and "credential" fields represent the leaf public
   key and the credential for the member holding that leaf,
   respectively.  The "info" field is equal to the null optional value
   when the leaf is blank (i.e., no member occupies that leaf).

   Likewise, the hash of a parent node (including the root) is the hash
   of a "ParentNodeHashInput" struct:

   struct {
       HPKEPublicKey public_key;
       uint32_t unmerged_leaves<0..2^32-1>;
   } ParentNodeInfo;

   struct {
       uint8 hash_type = 1;
       optional<ParentNodeInfo> info;
       opaque left_hash<0..255>;
       opaque right_hash<0..255>;
   } ParentNodeHashInput;



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   The "left_hash" and "right_hash" fields hold the hashes of the node's
   left and right children, respectively.  The "public_key" field holds
   the hash of the public key stored at this node, represented as an
   "optional<HPKEPublicKey>" object, which is null if and only if the
   node is blank.

6.4.  Group State

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

   struct {
       opaque group_id<0..255>;
       uint32 epoch;
       opaque tree_hash<0..255>;
       opaque confirmed_transcript_hash<0..255>;
   } GroupContext;

   The fields in this state have the following semantics:

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

   o  The "epoch" field represents the current version of the group key.

   o  The "tree_hash" field contains a commitment to the contents of the
      group's rachet tree and the credentials for the members of the
      group, as described in Section 6.3.

   o  The "confirmed_transcript_hash" field contains a running hash over
      the handshake 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 10.1.  The following general rules apply:

   o  The "group_id" field is constant

   o  The "epoch" field increments by one for each Commit message that
      is processed

   o  The "tree_hash" is updated to represent the current tree and
      credentials



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   o  The "confirmed_transcript_hash" is updated with the data for an
      MLSPlaintext message encoding a Commit message in two parts:

   struct {
     opaque group_id<0..255>;
     uint32 epoch;
     uint32 sender;
     ContentType content_type = commit;
     Proposal proposals<0..2^32-1>;
     Commit commit;
   } MLSPlaintextCommitContent;

   struct {
     opaque confirmation<0..255>;
     opaque signature<0..2^16-1>;
   } MLSPlaintextCommitAuthData;

   confirmed_transcript_hash_[n] =
       Hash(interim_transcript_hash_[n-1] ||
            MLSPlaintextCommitContent_[n]);

   interim_transcript_hash_[n] =
       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 field in the current MLSPlaintext
   message.  The confirmation and signature fields are then included in
   the transcript for the next epoch.  The interim transcript hash is
   passed to new members in the WelcomeInfo struct, and enables existing
   members to incorporate a handshake message into the transcript
   without having to store the whole MLSPlaintextCommitAuthData
   structure.

   When a new group is created, the "interim_transcript_hash" field is
   set to the zero-length octet string.

6.5.  Direct Paths

   As described in Section 5.4, each MLS message needs to transmit node
   values along the direct path of a leaf.  The path contains a public
   key for the leaf node, and a public key and encrypted secret value
   for intermediate nodes in the path.  In both cases, the path is
   ordered from 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..2^16-1>;
   } DirectPathNode;

   struct {
       DirectPathNode nodes<0..2^16-1>;
   } DirectPath;

   The length of the "encrypted_path_secret" vector MUST be zero for the
   first node in the path.  For the remaining elements in the vector,
   the number of ciphertexts in the "encrypted_path_secret" vector MUST
   be equal to the length of the resolution of the corresponding copath
   node.  Each ciphertext in the list is the encryption to the
   corresponding node in the resolution.

   The HPKECiphertext values are computed as

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

6.6.  Key Schedule

   Group keys are derived using the HKDF-Extract and HKDF-Expand
   functions as defined in [RFC5869], as well as the functions defined
   below:











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   HKDF-Expand-Label(Secret, Label, Context, Length) =
       HKDF-Expand(Secret, HkdfLabel, Length)

   Where HkdfLabel is specified as:

   struct {
     opaque group_context<0..255> = Hash(GroupContext_[n]);
     uint16 length = Length;
     opaque label<7..255> = "mls10 " + Label;
     opaque context<0..2^32-1> = Context;
   } HkdfLabel;

   Derive-Secret(Secret, Label) =
       HKDF-Expand-Label(Secret, Label, "", Hash.length)

   The Hash function used by HKDF is the ciphersuite hash algorithm.
   Hash.length is its output length in bytes.  In the below diagram:

   o  HKDF-Extract takes its salt argument from the top and its IKM
      argument from the left

   o  Derive-Secret takes its Secret argument from the incoming arrow

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

   o  The init secret from the previous epoch

   o  The update secret for the current epoch

   o  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] (or 0)
                     |
                     V
update_secret -> HKDF-Extract = epoch_secret
                     |
                     +--> Derive-Secret(., "sender data", GroupContext_[n])
                     |    = sender_data_secret
                     |
                     +--> Derive-Secret(., "handshake", GroupContext_[n])
                     |    = handshake_secret
                     |
                     +--> Derive-Secret(., "app", GroupContext_[n])
                     |    = application_secret
                     |
                     +--> Derive-Secret(., "confirm", GroupContext_[n])
                     |    = confirmation_key
                     |
                     V
               Derive-Secret(., "init", GroupContext_[n])
                     |
                     V
               init_secret_[n]

6.7.  Encryption Keys

   As described in Section 8, MLS encrypts three different types of
   information:

   o  Metadata (sender information)

   o  Proposal and Commit messages

   o  Application messages

   The sender information used to look up the key for the content
   encryption is encrypted under AEAD using a random nonce and the
   sender_data_key which is derived from the sender_data_secret as
   follows:

   sender_data_key =
       HKDF-Expand-Label(sender_data_secret, "sd key", "", key_length)

   Each handshake message is encrypted using a key and a nonce derived
   from the handshake_secret for a specific sender to prevent two
   senders to perform in the following way:






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handshake_nonce_[sender] =
    HKDF-Expand-Label(handshake_secret, "hs nonce", [sender], nonce_length)

handshake_key_[sender] =
    HKDF-Expand-Label(handshake_secret, "hs key", [sender], key_length)

   Here the value [sender] represents the index of the member that will
   use this key to send, encoded as a uint32.  Each sender maintains two
   "generation" counters, one for application messages and one for
   handshake messages.  These counters are incremented by one each time
   the sender sends a message.

   For application messages, a chain of keys is derived for each sender
   in a similar fashion.  This allows forward secrecy at the level of
   application messages within and out of an epoch.  A step in this
   chain (the second subscript) is called a "generation".  The details
   of application key derivation are described in the Section 12.1
   section below.

   For handshake messages (Proposals and Commits), the same key is used
   for all messages, but the nonce is updated according to the
   generation of the message:

handshake_nonce_[sender]_[generation] = handshake_nonce_[sender]
                                        XOR encode_big_endian(generation)

   where "encode_big_endian()" encodes the generation in a big-endian
   integer of the same size as the base handshake nonce.

7.  Initialization Keys

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

   A ClientInitKey object specifies a ciphersuite that the client
   supports, as well as providing a public key that others can use for
   key agreement.  The client's identity key is intended to be stable
   throughout the lifetime of the group; there is no mechanism to change
   it.  Init keys are intended to be used only once and SHOULD NOT be
   reused except in case of last resort.  (See Section 13.4).  Clients
   MAY generate and publish multiple ClientInitKey objects to support
   multiple ciphersuites.  ClientInitKeys contain an identifier chosen
   by the client, which the client MUST ensure uniquely identifies a
   given ClientInitKey object among the set of ClientInitKeys created by
   this client.



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   The value for 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 identity key.  A ClientInitKey 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.

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

   enum {
       invalid(0),
       supported_versions(1),
       supported_ciphersuites(2),
       expiration(3),
       (65535)
   } ExtensionType;

   struct {
       ExtensionType extension_type;
       opaque extension_data<0..2^16-1>;
   } Extension;

   struct {
       ProtocolVersion supported_version;
       opaque client_init_key_id<0..255>;
       CipherSuite cipher_suite;
       HPKEPublicKey init_key;
       Credential credential;
       Extension extensions<0..2^16-1>;
       opaque signature<0..2^16-1>;
   } ClientInitKey;

   ClientInitKey objects MUST contain at least two extensions, one of
   type "supported_versions" and one of type "supported_ciphersuites".
   These extensions allow MLS session establishment to be safe from
   downgrade attacks on these two parameters (as discussed in
   Section 9), while still only advertising one version / ciphersuite
   per ClientInitKey.

7.1.  Supported Versions and Supported Ciphersuites

   The "supported_versions" extension contains a list of MLS versions
   that are supported by the client.  The "supported_ciphersuites"
   extension contains a list of MLS ciphersuites that are supported by
   the client.



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   ProtocolVersion supported_versions<0..255>;
   CipherSuite supported_ciphersuites<0..255>;

7.2.  Expiration

   The "expiration" extension represents the time at which clients MUST
   consider this ClientInitKey invalid.  This time is represented as an
   absolute time, measured in seconds since the Unix epoch
   (1970-01-01T00:00:00Z).  If a client receives a ClientInitKey that
   contains an expiration extension at a time after its expiration time,
   then it MUST consider the ClientInitKey invalid and not use it for
   any further processing.

   uint64 expiration;

   Note that as an extension, it is not required that any given
   ClientInitKey have an expiration time.  In particular, applications
   that rely on "last resort" ClientInitKeys to ensure continued
   reachability may choose to omit the expiration extension from these
   keys, or give them much longer lifetimes than other ClientInitKeys.

8.  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.

   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 SHOULD use MLSCiphertext to encode both
   application and 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.















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

   struct {
       opaque group_id<0..255>;
       uint32 epoch;
       uint32 sender;
       ContentType content_type;
       opaque authenticated_data<0..2^32-1>;

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

           case proposal:
             Proposal proposals<1..2^32-1>;

           case commit:
             Proposal proposals<1..2^32-1>;
             Commit commit;
             opaque confirmation<0..255>;
       }

       opaque signature<0..2^16-1>;
   } MLSPlaintext;

   struct {
       opaque group_id<0..255>;
       uint32 epoch;
       ContentType content_type;
       opaque authenticated_data<0..2^32-1>;
       opaque sender_data_nonce<0..255>;
       opaque encrypted_sender_data<0..255>;
       opaque ciphertext<0..2^32-1>;
   } MLSCiphertext;

   The remainder of this section describes how to compute the signature
   of an MLSPlaintext object and how to convert it to an MLSCiphertext
   object.  The overall process is as follows:

   o  Gather the required metadata:

      *  Group ID



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      *  Epoch

      *  Content Type

      *  Nonce

      *  Sender index

      *  Key generation

   o  Sign the plaintext metadata - the group ID, epoch, sender index,
      and content type - as well as the authenticated data and message
      content

   o  Randomly generate sender_data_nonce and encrypt the sender
      information using it and the key derived from the
      sender_data_secret

   o  Encrypt the content using a content encryption key identified by
      the metadata

   The group identifier, epoch, content_type and authenticated data
   fields are copied from the MLSPlaintext object directly.  The content
   encryption process populates the ciphertext field of the
   MLSCiphertext object.  The metadata encryption step populates the
   encrypted_sender_data field.

   Decryption follows the same step in reverse: Decrypt the metadata,
   then the message and verify the content signature.

8.1.  Metadata Encryption

   The "sender data" used to look up the key for the content encryption
   is encrypted under AEAD using the MLSCiphertext sender_data_nonce and
   the sender_data_key from the keyschedule.  It is encoded as an object
   of the following form:

   struct {
       uint32 sender;
       uint32 generation;
   } MLSSenderData;

   The Additional Authenticated Data (AAD) for the SenderData ciphertext
   computation is its prefix in the MLSCiphertext, namely:







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   struct {
       opaque group_id<0..255>;
       uint32 epoch;
       ContentType content_type;
       opaque authenticated_data<0..2^32-1>;
       opaque sender_data_nonce<0..255>;
   } MLSCiphertextSenderDataAAD;

   When parsing a SenderData struct as part of message decryption, the
   recipient MUST verify that the sender field represents an occupied
   leaf in the ratchet tree.  In particular, the sender index value MUST
   be less than the number of leaves in the tree.

8.2.  Content Signing and Encryption

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

   struct {
       GroupContext context;

       opaque group_id<0..255>;
       uint32 epoch;
       uint32 sender;
       ContentType content_type;
       opaque authenticated_data<0..2^32-1>;

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

           case proposal:
             Proposal proposals<1..2^32-1>;

           case commit:
             Proposal proposals<1..2^32-1>;
             Commit commit;
             opaque confirmation<0..255>;
       }
   } MLSPlaintextSignatureInput;

   The ciphertext field of the MLSCiphertext object is produced by
   supplying the inputs described below to the AEAD function specified



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   by the ciphersuite in use.  The plaintext input contains content and
   signature of the MLSPlaintext, plus optional padding.  These values
   are encoded in the following form:

   struct {
       select (MLSCiphertext.content_type) {
           case handshake:
               GroupOperation operation;
               opaque confirmation<0..255>;

           case application:
               opaque application_data<0..2^32-1>;
       }

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

   The key and nonce used for the encryption of the message depend on
   the content type of the message.  The sender chooses the handshake
   key for a handshake message or an ununsed generation from its (per-
   sender) application key chain for the current epoch, according to the
   type of message being encrypted.

   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>;
       uint32 epoch;
       ContentType content_type;
       opaque authenticated_data<0..2^32-1>;
       opaque sender_data_nonce<0..255>;
       opaque encrypted_sender_data<0..255>;
   } MLSCiphertextContentAAD;

   The ciphertext field of the MLSCiphertext object is produced by
   supplying these inputs to the AEAD function specified by the
   ciphersuite in use.

9.  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 10.1.1, Section 10.2, and Section 10.2.1.



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

   o  Fetch ClientInitKeys for the members to be added, and selects a
      version and ciphersuite according to the capabilities of the
      members.  To protect against downgrade attacks, the creator MUST
      use the "supported_versions" and "supported_ciphersuites" fields
      in these ClientInitKeys to verify that the chosen version and
      ciphersuite is the best option supported by all members.

   o  Initialize a one-member group with the following initial values
      (where "0" represents an all-zero vector of size Hash.length):

      *  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

      *  Epoch: 0x00000000

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

      *  Confirmed transcript hash: 0

      *  Interim transcript hash: 0

      *  Init secret: 0

   o  For each member, construct an Add proposal from the ClientInitKey
      for that member (see Section 10.1.1)

   o  Construct a Commit message that commits all of the Add proposals,
      in any order chosen by the creator (see Section 10.2)

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

   o  Transmit the Welcome message to the other new members

   The recipient of a Welcome message processes it as described in
   Section 10.2.1.

   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 HPKE




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

   A new member receiving a Welcome message can recognize group creation
   if the number of entries in the "members" array is equal to the
   number of leaves in the tree minus one.  A client receiving a Welcome
   message SHOULD verify whether it is a newly created group, and if so,
   SHOULD verify that the above process was followed by reconstructing
   the Add and Commit messages and verifying that the resulting
   transcript hashes and epoch secret match those found in the Welcome
   message.

10.  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 broadcasts a Commit message that causes one
       or more proposed changes to enter into effect

   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 four-octet epoch values.  When a new group is
   initialized, its initial state epoch 0x00000000.  Each time a state
   transition occurs, the epoch number is incremented by one.

   [[ OPEN ISSUE: It would be better to have non-linear epochs, in order
   to tolerate forks in the history. ]]

10.1.  Proposals

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












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   enum {
       invalid(0),
       add(1),
       update(2),
       remove(3),
       (255)
   } ProposalType;

   struct {
       ProposalType msg_type;
       select (Proposal.msg_type) {
           case add:    Add;
           case update: Update;
           case remove: Remove;
       };
   } 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 using a ProposalID in a later Commit
   message.

10.1.1.  Add

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

   struct {
       ClientInitKey init_key;
   } Add;

   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 adds determines the leaf index
   "index" 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.

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






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   o  For each intermediate node along the path from the leaf at
      position "index" to the root, add "index" to the "unmerged_leaves"
      list for the node.

   o  Blank the path from the leaf at position "index" to the root

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

10.1.2.  Update

   An Update proposal requests that the sender's leaf node in the tree
   be updated with a new HPKE public key.

   struct {
       HPKEPublicKey leaf_key;
   } Update;

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

   o  Update the sender's leaf node by replacing the HPKE public key
      with the public key in the Update proposal

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

10.1.3.  Remove

   A Remove proposal requests that the client at a specified index in
   the tree be removed from the group.

   struct {
       uint32 removed;
   } Remove;

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

   o  Replace the leaf node at position "removed" with a blank node

   o  Blank the intermediate nodes along the path from the removed leaf
      to the root







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10.1.4.  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 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 having a "sender" value in the range
   0xFFFFFF00 - 0xFFFFFFFF.

   The specific value 0xFFFFFFFF is reserved for clients proposing that
   they themselves be added.  Proposals with types other than Add MUST
   NOT be sent with this sender index.  In such cases, the MLSPlaintext
   MUST be signed with the private key corresponding to the
   ClientInitKey in the Add message.  Recipients MUST verify that the
   MLSPlaintext carrying the Proposal message is validly signed with
   this key.

   The remaining values 0xFFFFFF00 - 0xFFFFFFFE are reserved for signer
   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 sender indices in this range and authorized signing keys.  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.

   [[ TODO: Should recognized external signers be added to some object
   that the group explicitly agrees on, e.g., as an extension to the
   GroupContext? ]]

10.2.  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.

   A group member that has observed one or more Proposal messages 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
   information is transmitted.




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   The sender of a Commit message MUST include in it all valid Proposals
   that the sender has received during the current epoch.  Invalid
   Proposals include, for example, Proposals with an invalid signature
   or Proposals that are semantically inconsistent, such as a Remove
   proposal for an unoccupied leaf.  The Commit MUST NOT combine
   Proposals sent within different epochs.  Despite these requirements,
   it is still possible for a valid Proposal not to be covered by a
   Commit, e.g., because the sender of the Commit did not receive the
   Proposal.  In such cases, the sender of the proposal can retransmit
   the Proposal in the new epoch.

   Each proposal covered by the Commit is identified by a ProposalID
   structure.  The "sender" field in this structure indicates the member
   of the group that sent the proposal (according to their index in the
   ratchet tree).  The "hash" field contains the hash of the
   MLSPlaintext in which the Proposal was sent, using the hash function
   for the group's ciphersuite.

   struct {
       uint32 sender;
       opaque hash<0..255>;
   } ProposalID;

   struct {
       ProposalID updates<0..2^16-1>;
       ProposalID removes<0..2^16-1>;
       ProposalID adds<0..2^16-1>;
       ProposalID ignored<0..2^16-1>;
       DirectPath path;
   } Commit;

   The sender of a Commit message MUST include in it all proposals that
   it has received during the current epoch.  Proposals that recipients
   should implement are placed in the "updates", "removes", and "adds"
   vector, according to their type.  Proposals that should not be
   implemented are placed in the "ignored" vector.  For example, if two
   Update proposals are issued for the same leaf, then one of them
   (presumably the earlier one) should be ignored and the other
   (presumably the later) should be added to the "updates" vector.

   [[ OPEN ISSUE: This structure loses the welcome_info_hash, because
   new participants are no longer expected to have access to the Commit
   message adding them to the group.  It might be we need to re-
   introduce this assumption, though it seems like the information
   confirmed by the welcome_info_hash is confirmed at the next epoch
   change anyway. ]]





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

   1.  Verify that the "epoch" field of the enclosing MLSPlaintext
       message is equal to the "epoch" field of the current GroupContext
       object

   2.  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.

   3.  Generate a provisional GroupContext object by applying the
       proposals referenced in the commit object in the order provided,
       as described in Section 10.1.  Add proposals are applied left to
       right: Each Add proposal is applied at the leftmost unoccupied
       leaf, or appended to the right edge of the tree if all leaves are
       occupied.

   4.  Process the "path" value to update the ratchet tree referenced by
       the provisional GroupContext and generate the update secret:

       *  Update the ratchet tree by replacing nodes in the direct path
          of the sender with the corresponding nodes in the path (see
          Section 6.5).

       *  The update secret is the value "path_secret[n+1]" derived from
          the "path_secret[n]" value associated to the root node.

   5.  Use the update secret, the provisional GroupContext, and the init
       secret from the previous epoch to compute the epoch secret and
       derived secrets for the new epoch.

   6.  Use the "confirmation_key" for the new epoch to compute the
       confirmation MAC for this message, as described below, and verify
       that it is the same as the "confirmation" field in the
       MLSPlaintext object.

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

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

   MLSPlaintext.confirmation =
       HMAC(confirmation_key, GroupContext.confirmed_transcript_hash)

   HMAC [RFC2104] uses the Hash algorithm for the ciphersuite in use.




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   [[ OPEN ISSUE: It is not possible for the recipient of a handshake
   message to verify that ratchet tree information in the message is
   accurate, because each node can only compute the secret and private
   key for nodes in its direct path.  This creates the possibility that
   a malicious participant could cause a denial of service by sending a
   handshake message with invalid values for public keys in the ratchet
   tree. ]]

10.2.1.  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 randomly chosen by the sender.  This key and
   nonce are 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.
























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   struct {
       HPKEPublicKey public_key;
       uint32_t unmerged_leaves<0..2^32-1>;
       optional<Credential> credential;
   } RatchetNode;

   struct {
     // GroupContext inputs
     opaque group_id<0..255>;
     uint32 epoch;
     optional<RatchetNode> tree<1..2^32-1>;
     opaque confirmed_transcript_hash<0..255>;

     // Inputs to the next round of the key schedule
     opaque interim_transcript_hash<0..255>;
     opaque epoch_secret<0..255>;

     uint32 signer_index;
     opaque signature<0..255>;
   } GroupInfo;

   struct {
     opaque group_info_key<1..255>;
     opaque group_info_nonce<1..255>;
     opaque path_secret<1..255>;
   } KeyPackage;

   struct {
     opaque client_init_key_hash<1..255>;
     HPKECiphertext encrypted_key_package;
   } EncryptedKeyPackage;

   struct {
     ProtocolVersion version = mls10;
     CipherSuite cipher_suite;
     EncryptedKeyPackage key_packages<1..V>;
     opaque encrypted_group_info;
   } Welcome;

   In the description of the tree as a list of nodes, the "credential"
   field for a node MUST be populated if and only if that node is a leaf
   in the tree (i.e., a node with an even index).

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

   o  Identify an entry in the "key_packages" array where the
      "client_init_key_hash" value corresponds to one of this client's



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      ClientInitKeys, using the hash indicated by the "cipher_suite"
      field.  If no such field exists, or if the ciphersuite indicated
      in the ClientInitKey does not match the one in the Welcome
      message, return an error.

   o  Decrypt the "encrypted_key_package" using HPKE with the algorithms
      indicated by the ciphersuite and the HPKE public key in the
      ClientInitKey.

   o  Decrypt the "encrypted_group_info" field using the key and nonce
      in the decrypted KeyPackage object.

   o  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 at position "signer_index".  If this
      verification fails, return an error.

   o  Identify a leaf in the "tree" array (i.e., an even-numbered node)
      whose "public_key" and "credential" fields are identical to the
      corresponding fields in the ClientInitKey.  If no such field
      exists, return an error.  Let "index" represent the index of this
      node among the leaves in the tree, namely the index of the node in
      the "tree" array divided by two.

   o  Construct a new group state using the information in the GroupInfo
      object.  The new member's position in the tree is "index", as
      defined above.

   o  Identify the lowest node at which the direct paths from "index"
      and "signer_index" overlap.  Set private keys for that node and
      its parents up to the root of the tree, using the "path_secret"
      from the KeyPackage and following the algorithm in Section 5.4 to
      move up the tree.

11.  Sequencing of State Changes

   [[ OPEN ISSUE: This section has an initial set of considerations
   regarding sequencing.  It would be good to have some more detailed
   discussion, and hopefully have a mechanism to deal with this issue.
   ]]

   Each handshake message is premised on a given starting state,
   indicated in its "prior_epoch" field.  If the changes implied by a
   handshake messages are made starting from a different state, the
   results will be incorrect.





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   This need for sequencing is not a problem as long as each time a
   group member sends a handshake message, it is based on the most
   current state of the group.  In practice, however, there is a risk
   that two members will generate handshake messages simultaneously,
   based on the same state.

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

   o  Have the delivery service enforce a total order

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

   As long as handshake 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 handshake 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 update messages could be applied one after
   the other without the Delivery Service having to reject any handshake
   message, which would make MLS more resilient regarding the
   concurrency of handshake 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 handshake messages
   are received.  Generation of handshake messages MUST be stateless,
   since the endpoint cannot know at that time whether the change
   implied by the handshake message will succeed or not.

11.1.  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 resolve
   conflicts during race-conditions (when two members send a message at
   the same time), as the server doesn't have any additional knowledge
   thanks to the confidentiality of the messages.

   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



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   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.

11.2.  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.

12.  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.

   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,




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   signatures are required.  Handshake messages MUST use asymmetric
   signatures to strongly authenticate the sender of a message.

12.1.  Tree of Application Secrets

   The application key schedule begins with the application secrets
   which are arranged in an "Application Secret Tree" or AS Tree for
   short; a left balanced binary tree with the same set of nodes and
   edges as the epoch's ratchet tree.  Each leaf in the AS 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 AS Tree then left(N) and
   right(N) denote the children of N (if they exist).

   Each node in the tree is assigned a secret.  The root's secret is
   simply the application_secret of that epoch.  (See Section 6.6 for
   the definition of application_secret.)

   astree_node_[root]_secret = application_secret

   The secret of any other node in the tree is derived from its parent's
   secret using a call to Derive-App-Secret.

   Derive-App-Secret(Secret, Label, Node, Generation, Length) =
       HKDF-Expand-Label(Secret, Label, ApplicationContext, Length)

   Where ApplicationContext is specified as:

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

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

   astree_node_[N]_secret
           |
           |
           +--> Derive-App-Secret(., "tree", left(N), 0, Hash.length)
           |    = astree_node_[left(N)]_secret
           |
           +--> Derive-App-Secret(., "tree", right(N), 0, Hash.length)
                = astree_node_[right(N)]_secret

   Note that fixing concrete values for GroupContext_[n] and
   application_secret completely defines all secrets in the AS Tree.



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12.2.  Sender Ratchets

   The secret of a leaf in the AS Tree is used to initiate a symmetric
   hash ratchet which generates a sequence of keys and nonces.  The
   group member assigned to that leaf uses the j-th key/nonce pair in
   the sequence to encrypt (using the AEAD) the j-th message they send
   during that epoch.  In particular, each key/nonce pair MUST NOT be
   used to encrypt more than one message.

   More precisely, the initial secret of the ratchet for the group
   member assigned to the leaf with node index N is simply the secret of
   that leaf.

   application_[N]_[0]_secret = astree_node_[N]_secret

   Keys, nonces and secrets of ratchets are derived using Derive-App-
   Secret.  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 index of the sender's leaf in the
   ratchet tree is the same as the index of the leaf in the AS Tree used
   to initialize the sender's ratchet.

   application_[N]_[j]_secret
         |
         +--> Derive-App-Secret(., "app-nonce", N, j, AEAD.nonce_length)
         |    = application_[N]_[j]_nonce
         |
         +--> Derive-App-Secret(., "app-key", N, j, AEAD.key_length)
         |    = application_[N]_[j]_key
         |
         V
   Derive-App-Secret(., "app-secret", N, j, Hash.length)
   = application_[N]_[j+1]_secret

   Here, AEAD.nonce_length and AEAD.key_length denote the lengths in
   bytes of the nonce and key for the AEAD scheme defined by the
   ciphersuite.

12.3.  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

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

   o  a key, nonce, or secret derived from S has been consumed.  (This
      goes for values derived via Derive-Secret as well as HKDF-Expand-
      Label.)



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   Here, S may be the "init_secret", "update_secret", "epoch_secret",
   "application_secret" as well as any secret in the AS 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 even if
   their generating secret was already consumed (e.g. due to out of
   order message delivery).

   For example, suppose a group member encrypts or (successfully)
   decrypts a message using the j-th key and nonce in the i-th ratchet.
   Then, for that member, at least the following values have been
   consumed and MUST be deleted:

   o  the "init_secret", "update_secret", "epoch_secret",
      "application_secret" of that epoch,

   o  all node secrets in the AS Tree on the path from the root to the
      leaf with index i,

   o  the first j secrets in the i-th ratchet and

   o  "application_[i]_[j]_key" and "application_[i]_[j]_nonce".

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

          G
        /   \
       /     \
      E       F
     / \     / \
   A0  B0  C0  D0 -+- KD0
               |   |
               |   +- ND0
               |
               D1 -+- KD1
               |   |
               |   +- ND1
               |
               D2

   Then if a client uses key KD1 and nonce ND1 during epoch n then it
   must consume (at least) values G, F, D0, D1, KD1, ND1 as well as the
   update_secret and init_secret used to derive G (i.e. the
   application_secret).  The client MAY retain (i.e., not consume) the



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   values KD0 and ND0 to allow for out-of-order delivery, and SHOULD
   retain D2 to allow for processing future messages.

12.4.  Further 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 application_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.

   [[ OPEN ISSUE: At the moment there is no contributivity of
   Application secrets chained from the initial one to the next
   generation of Epoch secret.  While this seems safe because
   cryptographic operations using the application secrets can't affect
   the group init_secret, it remains to be proven correct. ]]

12.5.  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



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   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
   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.

   [[ TODO: A preliminary formal security analysis has yet to be
   performed on this authentication scheme.]]

   [[ OPEN ISSUE: Currently, the group identifier, epoch and generation
   are contained as meta-data of the Signature.  A different solution
   could be to include the GroupContext instead, if more information is
   required to achieve the security goals regarding cross-group attacks.
   ]]

   [[ OPEN ISSUE: Should the padding be required for handshake messages
   ? Can an adversary get more than the position of a participant in the
   tree without padding ? Should the base ciphertext block length be
   negotiated or is is reasonable to allow to leak a range for the
   length of the plaintext by allowing to send a variable number of
   ciphertext blocks ? ]]

12.6.  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.

   [[TODO: Describe here or in the Architecture spec the details.
   Depending on which Secret or key is kept alive, the security
   guarantees will vary.]]








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13.  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.

13.1.  Confidentiality of the Group Secrets

   Group secrets are derived from (i) previous group secrets, and (ii)
   the root key of a ratcheting tree.  Only group members know their
   leaf private key in the group, therefore, the root key of the group's
   ratcheting tree is secret and thus so are all values derived from it.

   Initial leaf keys are known only by their owner and the group
   creator, because they are derived from an authenticated key exchange
   protocol.  Subsequent leaf keys are known only by their owner.
   [[TODO: or by someone who replaced them.]]

   Note that the long-term identity keys used by the protocol MUST be
   distributed by an "honest" authentication service for clients to
   authenticate their legitimate peers.

13.2.  Authentication

   There are two forms of authentication we consider.  The first form
   considers authentication with respect to the group.  That is, the
   group members can verify that a message originated from one of the
   members of the group.  This is implicitly guaranteed by the secrecy
   of the shared key derived from the ratcheting trees: if all members
   of the group are honest, then the shared group key is only known to
   the group members.  By using AEAD or appropriate MAC with this shared
   key, we can guarantee that a member in the group (who knows the
   shared secret key) has sent a message.

   The second form considers authentication with respect to the sender,
   meaning the group members can verify that a message originated from a
   particular member of the group.  This property is provided by digital
   signatures on the messages under identity keys.

   [[ OPEN ISSUE: Signatures under the identity keys, while simple, have
   the side-effect of preclude deniability.  We may wish to allow other
   options, such as (ii) a key chained off of the identity key, or (iii)
   some other key obtained through a different manner, such as a
   pairwise channel that provides deniability for the message
   contents.]]





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13.3.  Forward and post-compromise security

   Message encryption keys are derived via a hash ratchet, which
   provides a form of forward secrecy: learning a message key does not
   reveal previous message or root keys.  Post-compromise security is
   provided by Update operations, in which a new root key is generated
   from the latest ratcheting tree.  If the adversary cannot derive the
   updated root key after an Update operation, it cannot compute any
   derived secrets.

   In the case where the client could have been compromised (device
   loss...), the client SHOULD signal the delivery service to expire all
   the previous ClientInitKeys and publish fresh ones for PCS.

13.4.  Init Key Reuse

   Initialization keys are intended to be used only once and then
   deleted.  Reuse of init keys can lead to replay attacks.

14.  IANA Considerations

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

   o  MLS Ciphersuites

   All of these registries should be under a heading of "Message Layer
   Security", and administered under a Specification Required policy
   [RFC8126].

14.1.  MLS Ciphersuites

   The "MLS Ciphersuites" registry lists identifiers for suites of
   cryptographic algorithms defined for use with MLS.  These are two-
   byte values, so the maximum possible value is 0xFFFF = 65535.  Values
   in the range 0xF000 - 0xFFFF are reserved for vendor-internal usage.

   Template:

   o  Value: The two-byte identifier for the ciphersuite

   o  Name: The name of the ciphersuite

   o  Reference: Where this algorithm is defined

   The initial contents for this registry are as follows:





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             +--------+-------------------------+-----------+
             | Value  | Name                    | Reference |
             +--------+-------------------------+-----------+
             | 0x0000 | P256_SHA256_AES128GCM   | RFC XXXX  |
             |        |                         |           |
             | 0x0001 | X25519_SHA256_AES128GCM | RFC XXXX  |
             +--------+-------------------------+-----------+

   [[ Note to RFC Editor: Please replace "XXXX" above with the number
   assigned to this RFC. ]]

15.  Contributors

   o  Joel Alwen
      Wickr
      joel.alwen@wickr.com

   o  Karthikeyan Bhargavan
      INRIA
      karthikeyan.bhargavan@inria.fr

   o  Cas Cremers
      University of Oxford
      cas.cremers@cs.ox.ac.uk

   o  Alan Duric
      Wire
      alan@wire.com

   o  Srinivas Inguva
      Twitter
      singuva@twitter.com

   o  Albert Kwon
      MIT
      kwonal@mit.edu

   o  Eric Rescorla
      Mozilla
      ekr@rtfm.com

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

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



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16.  References

16.1.  Normative References

   [I-D.irtf-cfrg-hpke]
              Barnes, R. and K. Bhargavan, "Hybrid Public Key
              Encryption", draft-irtf-cfrg-hpke-00 (work in progress),
              July 2019.

   [IEEE1363]
              "IEEE Standard Specifications for Password-Based Public-
              Key Cryptographic Techniques", IEEE standard,
              DOI 10.1109/ieeestd.2009.4773330, n.d..

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

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

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

   [RFC5869]  Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
              Key Derivation Function (HKDF)", RFC 5869,
              DOI 10.17487/RFC5869, May 2010,
              <https://www.rfc-editor.org/info/rfc5869>.

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

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

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






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   [X962]     ANSI, "Public Key Cryptography For The Financial Services
              Industry: The Elliptic Curve Digital Signature Algorithm
              (ECDSA)", ANSI X9.62, 1998.

16.2.  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", 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.

   [dhreuse]  Menezes, A. and B. Ustaoglu, "On reusing ephemeral keys in
              Diffie-Hellman key agreement protocols", International
              Journal of Applied Cryptography Vol. 2, pp. 154,
              DOI 10.1504/ijact.2010.038308, 2010.

   [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.

   [HCJ16]    Husak, M., &#268;ermak, M., Jirsik, T., and P.
              &#268;eleda, "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.

   [I-D.ietf-trans-rfc6962-bis]
              Laurie, B., Langley, A., Kasper, E., Messeri, E., and R.
              Stradling, "Certificate Transparency Version 2.0", draft-
              ietf-trans-rfc6962-bis-33 (work in progress), September
              2019.

   [keyagreement]
              Barker, E., Chen, L., Roginsky, A., and M. Smid,
              "Recommendation for Pair-Wise Key Establishment Schemes
              Using Discrete Logarithm Cryptography", National Institute
              of Standards and Technology report,
              DOI 10.6028/nist.sp.800-56ar2, May 2013.





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   [RFC7748]  Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
              for Security", RFC 7748, DOI 10.17487/RFC7748, January
              2016, <https://www.rfc-editor.org/info/rfc7748>.

   [signal]   Perrin(ed), T. and M. Marlinspike, "The Double Ratchet
              Algorithm", n.d.,
              <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, a 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

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

   # The largest power of 2 less than n.  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



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   # parents are level 1, etc.  If a node's children are at different
   # level, 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):
       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.  The child of a leaf node is itself.
   def left(x):
       k = level(x)
       if k == 0:
           return x

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

   # The right child of an intermediate node.  Depends on the size of
   # the tree because the straightforward calculation can take you
   # beyond the edge of the tree.  The child of a leaf node is itself.
   def right(x, n):
       k = level(x)
       if k == 0:
           return x

       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



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       return (x | (1 << k)) ^ (b << (k + 1))

   # The parent of a node.  As with the right child calculation, have
   # to walk back until the parent is within the range of the tree.
   def parent(x, n):
       if x == root(n):
           return x

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

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

       return p

   # The direct path of a node, ordered from the root
   # down, not including the root or the terminal node
   def direct_path(x, n):
       d = []
       p = parent(x, n)
       r = root(n)
       while p != r:
           d.append(p)
           p = parent(p, n)
       return d

   # The copath of the node is the siblings of the nodes on its direct
   # path (including the node itself)
   def copath(x, n):
       d = dirpath(x, n)
       if x != sibling(x, n):
           d.append(x)

       return [sibling(y, n) for y in d]

   # Frontier is the list of full subtrees, from left to right.  A
   # balanced binary tree with n leaves has a full subtree for every
   # power of two where n has a bit set, with the largest subtrees
   # furthest to the left.  For example, a tree with 11 leaves has full
   # subtrees of size 8, 2, and 1.



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   def frontier(n):
       st = [1 << k for k in range(log2(n) + 1) if n & (1 << k) != 0]
       st = reversed(st)

       base = 0
       f = []
       for size in st:
           f.append(root(size) + base)
           base += 2*size
       return f

   # Leaves are in even-numbered nodes
   def leaves(n):
       return [2*i for i in range(n)]

   # The resolution of a node is the collection of non-blank
   # descendants of this node.  Here the tree is represented by a list
   # of nodes, where blank nodes are represented by None
   def resolve(tree, x, n):
       if tree[x] != None:
           return [x]

       if level(x) == 0:
           return []

       L = resolve(tree, left(x), n)
       R = resolve(tree, right(x, n), n)
       return L + R

Authors' Addresses

   Richard Barnes
   Cisco

   Email: rlb@ipv.sx


   Benjamin Beurdouche
   Inria

   Email: benjamin.beurdouche@inria.fr


   Jon Millican
   Facebook

   Email: jmillican@fb.com




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   Emad Omara
   Google

   Email: emadomara@google.com


   Katriel Cohn-Gordon
   University of Oxford

   Email: me@katriel.co.uk


   Raphael Robert
   Wire

   Email: raphael@wire.com



































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