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Versions: (draft-barnes-mls-protocol) 00 01 02

Network Working Group                                          R. Barnes
Internet-Draft                                                     Cisco
Intended status: Informational                               J. Millican
Expires: April 25, 2019                                         Facebook
                                                                E. Omara
                                                                  Google
                                                          K. Cohn-Gordon
                                                    University of Oxford
                                                               R. Robert
                                                                    Wire
                                                        October 22, 2018


              The Messaging Layer Security (MLS) Protocol
                       draft-ietf-mls-protocol-02

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
   participants 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 April 25, 2019.






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Copyright Notice

   Copyright (c) 2018 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 . . . . . . . . . . . . . . . . . . . . . . . . .   5
   3.  Basic Assumptions . . . . . . . . . . . . . . . . . . . . . .   6
   4.  Protocol Overview . . . . . . . . . . . . . . . . . . . . . .   6
   5.  Ratchet Trees . . . . . . . . . . . . . . . . . . . . . . . .   9
     5.1.  Tree Computation Terminology  . . . . . . . . . . . . . .   9
     5.2.  Ratchet Tree Nodes  . . . . . . . . . . . . . . . . . . .  12
     5.3.  Blank Nodes and Resolution  . . . . . . . . . . . . . . .  13
     5.4.  Ratchet Tree Updates  . . . . . . . . . . . . . . . . . .  13
     5.5.  Cryptographic Objects . . . . . . . . . . . . . . . . . .  15
       5.5.1.  Curve25519, SHA-256, and AES-128-GCM  . . . . . . . .  15
       5.5.2.  P-256, SHA-256, and AES-128-GCM . . . . . . . . . . .  16
     5.6.  Credentials . . . . . . . . . . . . . . . . . . . . . . .  17
     5.7.  Group State . . . . . . . . . . . . . . . . . . . . . . .  17
     5.8.  Direct Paths  . . . . . . . . . . . . . . . . . . . . . .  19
     5.9.  Key Schedule  . . . . . . . . . . . . . . . . . . . . . .  20
   6.  Initialization Keys . . . . . . . . . . . . . . . . . . . . .  22
   7.  Handshake Messages  . . . . . . . . . . . . . . . . . . . . .  22
     7.1.  Init  . . . . . . . . . . . . . . . . . . . . . . . . . .  24
     7.2.  Add . . . . . . . . . . . . . . . . . . . . . . . . . . .  25
     7.3.  Update  . . . . . . . . . . . . . . . . . . . . . . . . .  27
     7.4.  Remove  . . . . . . . . . . . . . . . . . . . . . . . . .  27
   8.  Sequencing of State Changes . . . . . . . . . . . . . . . . .  28
     8.1.  Server-Enforced Ordering  . . . . . . . . . . . . . . . .  29
     8.2.  Client-Enforced Ordering  . . . . . . . . . . . . . . . .  29
     8.3.  Merging Updates . . . . . . . . . . . . . . . . . . . . .  30
   9.  Message Protection  . . . . . . . . . . . . . . . . . . . . .  31
     9.1.  Application Key Schedule  . . . . . . . . . . . . . . . .  31
       9.1.1.  Updating the Application Secret . . . . . . . . . . .  32
       9.1.2.  Application AEAD Key Calculation  . . . . . . . . . .  33



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     9.2.  Message Encryption and Decryption . . . . . . . . . . . .  33
       9.2.1.  Delayed and Reordered Application messages  . . . . .  35
   10. Security Considerations . . . . . . . . . . . . . . . . . . .  36
     10.1.  Confidentiality of the Group Secrets . . . . . . . . . .  36
     10.2.  Authentication . . . . . . . . . . . . . . . . . . . . .  36
     10.3.  Forward and post-compromise security . . . . . . . . . .  37
     10.4.  Init Key Reuse . . . . . . . . . . . . . . . . . . . . .  37
   11. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  37
   12. Contributors  . . . . . . . . . . . . . . . . . . . . . . . .  37
   13. References  . . . . . . . . . . . . . . . . . . . . . . . . .  38
     13.1.  Normative References . . . . . . . . . . . . . . . . . .  38
     13.2.  Informative References . . . . . . . . . . . . . . . . .  39
   Appendix A.  Tree Math  . . . . . . . . . . . . . . . . . . . . .  40
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  43

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 agents who want to send each other encrypted messages
   needs a way to derive shared symmetric encryption keys.  For two
   parties, this problem has been studied thoroughly, with the Double
   Ratchet emerging as a common solution [doubleratchet] [signal].
   Channels implementing the Double Ratchet enjoy fine-grained forward
   secrecy as well as post-compromise security, but are nonetheless
   efficient enough for heavy use over low-bandwidth networks.

   For a group of size greater than two, a common strategy is to
   unilaterally broadcast symmetric "sender" keys over existing shared
   symmetric channels, and then for each agent to send messages to the
   group encrypted with their own sender key.  Unfortunately, while this
   improves efficiency over pairwise broadcast of individual messages
   and (with the addition of a hash ratchet) provides forward secrecy,
   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 sender's messages.  Generating and
   distributing a new sender key provides a form of post-compromise
   security with regard to that sender.  However, it requires




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   computation and communications resources that scale linearly as 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 mechanism presented here use a
   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-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 (*)




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   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.

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.

   Participant:  An agent that uses this protocol to establish shared
      cryptographic state with other participants.  A participant is
      defined by the cryptographic keys it holds.  An application may
      use one participant per device (keeping keys local to each device)
      or sync keys among a user's devices so that each user appears as a
      single participant.

   Group:  A collection of participants with shared cryptographic state.

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

   Initialization Key:  A short-lived Diffie-Hellman key pair used to
      introduce a new member to a group.  Initialization keys are
      published for individual participants (UserInitKey).

   Leaf Key:  A short-lived Diffie-Hellman key pair that represents a
      group member's contribution to the group secret, so called because
      the participants 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.



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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 participants 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 participant's identity key.

   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 8 for further considerations.)

   o  A directory to which participants can publish initialization keys,
      and from which participant can download initialization keys for
      other participants.

4.  Protocol Overview

   The goal of this protocol is to allow a group of participants to
   exchange confidential and authenticated messages.  It does so by
   deriving a sequence of secrets and keys known only to group 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 participant as a _state_,
   which includes both public and private data.  An initial state,
   including an initial set of participants, is set up by a group
   creator using the _Init_ algorithm and based on information pre-
   published by the initial members.  The creator sends the _GroupInit_
   message to the participants, who can then set up their own group
   state and derive the same shared secret.  Participants then exchange
   messages to produce new shared states which are causally linked to
   their predecessors, forming a logical Directed Acyclic Graph (DAG) of
   states.  Participants can send _Update_ messages for post-compromise
   secrecy and new participants can be added or existing participants
   removed from the group.

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

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




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   o  Adding a member, initiated by a current member;

   o  Adding a member, initiated by the new member;

   o  Updating the leaf secret of a member;

   o  Removing a member.

   Before the initialization of a group, participants publish
   UserInitKey objects to a directory provided to the Messaging Service.

                                                             Group
   A              B              C          Directory       Channel
   |              |              |              |              |
   | UserInitKeyA |              |              |              |
   |------------------------------------------->|              |
   |              |              |              |              |
   |              | UserInitKeyB |              |              |
   |              |---------------------------->|              |
   |              |              |              |              |
   |              |              | UserInitKeyC |              |
   |              |              |------------->|              |
   |              |              |              |              |

   When a participant A wants to establish a group with B and C, it
   first downloads InitKeys for B and C.  It then initializes a group
   state containing only itself and uses the InitKeys to compute Add
   messages to add B and C, in a sequence chosen by A.  These messages
   are broadcasted to the Group, and processed in sequence by B and C.
   Messages received before a participant 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
   |              |              |              |                   |
   |         UserInitKeyB, UserInitKeyC         |                   |
   |<-------------------------------------------|                   |
   |              |              |              |                   |
   |              |              |              | Add(A->AB)        |
   |--------------------------------------------------------------->|
   |              |              |              |                   |
   |              |              |              | Add(AB->ABC)      |
   |--------------------------------------------------------------->|
   |              |              |              |                   |
   |              |              |              | Add(A->AB)        |
   |<---------------------------------------------------------------|
   |state.add(B)  |<------------------------------------------------|
   |              |state.init()  |x---------------------------------|
   |              |              |              |                   |
   |              |              |              | Add(AB->ABC)      |
   |<---------------------------------------------------------------|
   |state.add(C)  |<------------------------------------------------|
   |              |state.add(C)  |<---------------------------------|
   |              |              |state.init()  |                   |
   |              |              |              |                   |

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

   To enforce forward secrecy and post-compromise security of messages,
   each participant 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 participants have
   processed this message, the group's secrets will be unknown to an
   attacker that had compromised the sender's prior leaf secret.

   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.










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

   Users 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)    |              |
   |              |              |---------------------------->|
   |              |              |              |              |
   |              |              |              | Remove(B)    |
   |<----------------------------------------------------------|
   |state.del(B)  |              |<----------------------------|
   |              |              |state.del(B)  |              |
   |              |              |              |              |
   |              |              |              |              |

5.  Ratchet Trees

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

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 ratchet 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



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   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 it 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, excluding the root.  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)

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












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               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 _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 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

   (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].)



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5.2.  Ratchet Tree Nodes

   Ratchet trees are used for generating shared group secrets.  In this
   section, we describe the structure of a ratchet tree.  A particular
   instance of a ratchet tree is based on the following cryptographic
   primitives, defined by the ciphersuite in use:

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

   o  A Derive-Key-Pair function that produces a key pair from an octet
      string

   o  A hash function

   A ratchet tree is a left-balanced binary tree, in which each node
   contains up to three values:

   o  A secret octet string (optional)

   o  An asymmetric private key (optional)

   o  An asymmetric public key

   The private key and public key for a node are derived from its secret
   value using the Derive-Key-Pair operation.

   The contents of a parent node are computed from one of its children
   as follows:

   parent_secret = Hash(child_secret)
   parent_private, parent_public = Derive-Key-Pair(parent_secret)

   The contents of the parent are based on the latest-updated child.
   For example, if participants with leaf secrets A, B, C, and D join a
   group in that order, then the resulting tree will have the following
   structure:

        H(H(D))
       /       \
    H(B)       H(D)
    /  \       /  \
   A    B     C    D

   If the first participant subsequently changes its leaf secret to be
   X, then the tree will have the following structure.






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        H(H(X))
       /       \
    H(X)       H(D)
    /  \       /  \
   X    B     C    D

5.3.  Blank Nodes and Resolution

   A node in the tree may be _blank_, indicating that no value is
   present at that node.  The _resolution_ of a node is an ordered list
   of non-blank nodes that collectively cover all non-blank descendants
   of the node.  The nodes in a resolution are ordered according to
   their indices.

   o  The resolution of a non-blank node is a one element list
      containing the node itself

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

   o  The resolution of a blank intermediate node is the result of
      concatinating 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
    / \     / \
   A   _   C   D

   0 1 2 3 4 5 6

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

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

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

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

5.4.  Ratchet Tree Updates

   In order to update the state of the group such as adding and removing
   participants, MLS messages are used to make changes to the group's
   ratchet tree.  The participant proposing an update to the tree



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   transmits a representation of a set of tree nodes along the direct
   path from a leaf to the root.  Other participants in the group can
   use these nodes 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 transmits the following
   information for each node in the direct path from leaf leaf to the
   root:

   o  The public key for the node

   o  Zero or more encrypted copies of the node's secret value

   The secret value is encrypted for the subtree corresponding to the
   node's non-updated child, i.e., the child not on the direct path.
   There is one encrypted 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 secret values * Identify a node in the direct
       path for which the local participant is in the subtree of the
       non-updated child * Identify a node in the resolution of the non-
       updated child for which this node has a private key * Decrypt the
       secret value for the direct path node using the private key from
       the resolution node * Compute secret values for ancestors of that
       node by hashing the decrypted secret

   2.  Merge the updated secrets into the tree * Replace the public keys
       for nodes on the direct path with the received public keys * For
       nodes where an updated secret was computed in step 1, replace the
       secret value for the node with the updated value

   For example, suppose we had the following tree:

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

   If an update is made along the direct path B-E-G, then the following
   values will be transmitted (using pk(X) to represent the public key
   corresponding to the secret value X and E(K, S) to represent public-
   key encryption to the public key K of the secret value S):




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                 +------------+--------------------------+
                 | Public Key | Ciphertext(s)            |
                 +------------+--------------------------+
                 | pk(G)      | E(pk(C), G), E(pk(D), G) |
                 |            |                          |
                 | pk(E)      | E(pk(A), E)              |
                 |            |                          |
                 | pk(B)      |                          |
                 +------------+--------------------------+

5.5.  Cryptographic Objects

   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

   o  An AEAD encryption algorithm [RFC5116]

   The ciphersuite must also specify an algorithm "Derive-Key-Pair" that
   maps octet strings with the same length as the output of the hash
   function to key pairs for the asymmetric encryption scheme.

   Public keys used in the protocol are opaque values in a format
   defined by the ciphersuite, using the following types:

   uint16 CipherSuite;
   opaque DHPublicKey<1..2^16-1>;
   opaque SignaturePublicKey<1..2^16-1>;

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

   This ciphersuite uses the following primitives:

   o  Hash function: SHA-256

   o  Diffie-Hellman group: Curve25519 [RFC7748]

   o  AEAD: AES-128-GCM

   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).





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   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]

   Encryption keys are derived from shared secrets by taking the first
   16 bytes of H(Z), where Z is the shared secret and H is SHA-256.

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

   This ciphersuite uses the following primitives:

   o  Hash function: P-256

   o  Diffie-Hellman group: secp256r1 (NIST P-256)

   o  AEAD: AES-128-GCM

   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



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   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.

   Encryption keys are derived from shared secrets by taking the first
   16 bytes of H(Z), where Z is the shared secret and H is SHA-256.

5.6.  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
   holder's identity as well as the public key of a signature key pair
   that the holder of the credential will use to sign MLS messages.
   Credentials MAY also include information that allows a relying party
   to verify the identity / signing key binding.

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

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

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

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

5.7.  Group State

   Each participant in the group maintains a representation of the state
   of the group:








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

   struct {
     opaque group_id<0..255>;
     uint32 epoch;
     optional<Credential> roster<1..2^32-1>;
     optional<PublicKey> tree<1..2^32-1>;
     opaque transcript_hash<0..255>;
   } GroupState;

   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 "roster" field contains credentials for the occupied slots in
      the tree, including the identity and signature public key for the
      holder of the slot.

   o  The "tree" field contains the public keys corresponding to the
      nodes of the ratchet tree for this group.  The length of this
      vector MUST be "2*size + 1", where "size" is the length of the
      roster, since this is the number of nodes in a tree with "size"
      leaves, according to the structure described in Section 5.

   o  The "transcript" field contains the list of "GroupOperation"
      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 GroupState.

   Different group operations will have different effects on the group
   state.  These effects are described in their respective subsections
   of Section 7.  The following rules apply to all operations:

   o  The "group_id" field is constant





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

   o  The "transcript_hash" is updated by a GroupOperation message
      "operation" in the following way:

   transcript\_hash\_[n] = Hash(transcript\_hash\_[n-1] || operation)

   When a new one-member group is created (which requires no
   GroupOperation), the "transcript_hash" field is set to an all-zero
   vector of length Hash.length.

5.8.  Direct Paths

   As described in Section 5.4, each MLS message needs to transmit node
   values along the direct path from a leaf to the root.  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.

   struct {
       DHPublicKey ephemeral_key;
       opaque ciphertext<0..255>;
   } ECIESCiphertext;

   struct {
       DHPublicKey public_key;
       ECIESCiphertext node_secrets<0..2^16-1>;
   } RatchetNode

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

   The length of the "node\_secrets" vector MUST be zero for the first
   node in the path.  For the remaining elements in the vector, the
   number of ciphertexts in the "node\_secrets" 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 ECIESCiphertext values encoding the encrypted secret values are
   computed as follows:

   o  Generate an ephemeral DH key pair (x, x*G) in the DH group
      specified by the ciphersuite in use




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   o  Compute the shared secret Z with the node's other child

   o  Derive a key and nonce as described below

   o  Encrypt the node's secret value using the AEAD algorithm specified
      by the ciphersuite in use, with the following inputs:

      *  Key: The key derived from Z

      *  Nonce: The nonce derived from Z

      *  Additional Authenticated Data: The empty octet string

      *  Plaintext: The secret value, without any further formatting

   o  Encode the ECIESCiphertext with the following values:

      *  ephemeral_key: The ephemeral public key x*G

      *  ciphertext: The AEAD output

   key = HKDF-Expand(Secret, ECIESLabel("key"), Length)
   nonce = HKDF-Expand(Secret, ECIESLabel("nonce"), Length)

   Where ECIESLabel is specified as:

   struct {
     uint16 length = Length;
     opaque label<12..255> = "mls10 ecies " + Label;
   } ECIESLabel;

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

5.9.  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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   Derive-Secret(Secret, Label, State) =
        HKDF-Expand(Secret, HkdfLabel, Hash.length)

   Where HkdfLabel is specified as:

   struct {
       uint16 length = Length;
       opaque label<6..255> = "mls10 " + Label;
       GroupState state = State;
   } HkdfLabel;

   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 participant 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 GroupState object for current epoch

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

                  init_secret_[n-1] (or 0)
                        |
                        V
   update_secret -> HKDF-Extract = epoch_secret
                        |
                        +--> Derive-Secret(., "app", GroupState_[n])
                        |    = application_secret
                        |
                        +--> Derive-Secret(., "confirm", GroupState_[n])
                        |    = confirmation_key
                        |
                        V
                  Derive-Secret(., "init", GroupState_[n])
                        |
                        V
                  init_secret_[n]




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6.  Initialization Keys

   In order to facilitate asynchronous addition of participants to a
   group, it is possible to pre-publish initialization keys that provide
   some public information about a user.  UserInitKey messages provide
   information about a potential group member, that a group member can
   use to add this user to a group asynchronously.

   A UserInitKey object specifies what ciphersuites a client supports,
   as well as providing public keys that the client can use for key
   derivation and signing.  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 a very limited number
   of times, potentially once. (see Section 10.4).

   The init_keys array MUST have the same length as the cipher_suites
   array, and each entry in the init_keys array MUST be a public key for
   the DH group defined by the corresponding entry in the cipher_suites
   array.

   The whole structure is signed using the client's identity key.  A
   UserInitKey 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.

   struct {
       CipherSuite cipher_suites<0..255>;
       DHPublicKey init_keys<1..2^16-1>;
       SignaturePublicKey identity_key;
       SignatureScheme algorithm;
       opaque signature<0..2^16-1>;
   } UserInitKey;

7.  Handshake Messages

   Over the lifetime of a group, its state will change for:

   o  Group initialization

   o  A current member adding a new participant

   o  A current participant updating its leaf key

   o  A current member deleting another current member

   In MLS, these changes are accomplished by broadcasting "handshake"
   messages to the group.  Note that unlike TLS and DTLS, there is not a
   consolidated handshake phase to the protocol.  Rather, handshake



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   messages are exchanged throughout the lifetime of a group, whenever a
   change is made to the group state.  This means an unbounded number of
   interleaved application and handshake messages.

   An MLS handshake message encapsulates a specific "key exchange"
   message that accomplishes a change to the group state.  It also
   includes a signature by the sender of the message over the GroupState
   object representing the state of the group after the change has been
   made.

   enum {
       init(0),
       add(1),
       update(2),
       remove(3),
       (255)
   } GroupOperationType;

   struct {
       GroupOperationType msg_type;
       select (GroupOperation.msg_type) {
           case init:      Init;
           case add:       Add;
           case update:    Update;
           case remove:    Remove;
       };
   } GroupOperation;

   struct {
       uint32 prior_epoch;
       GroupOperation operation;

       uint32 signer_index;
       SignatureScheme algorithm;
       opaque signature<1..2^16-1>;
       opaque confirmation[Hash.length];
   } Handshake;

   The high-level flow for processing a Handshake message is as follows:

   1.  Verify that the "prior_epoch" field of the Handshake message is
       equal the "epoch" field of the current GroupState object.

   2.  Use the "operation" message to produce an updated, provisional
       GroupState object incorporating the proposed changes.

   3.  Look up the public key for slot index "signer_index" from the
       roster in the current GroupState object (before the update).



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   4.  Use that public key to verify the "signature" field in the
       Handshake message, with the updated GroupState object as input.

   5.  If the signature fails to verify, discard the updated GroupState
       object and consider the Handshake message invalid.

   6.  Use the "confirmation_key" for the new group state to compute the
       finished MAC for this message, as described below, and verify
       that it is the same as the "finished_mac" field.

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

   The "finished_mac" value is computed over the provisional group state
   and the current handshake message (with the confirmation value set to
   zero):

   struct {
     GroupState state;     // Provisional group state
     Handshake handshake;  // Handshake message, confirmation = 0
   } ConfirmationData;

   confirmation = HMAC(confirmation_key, ConfirmationData)

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

   [[ OPEN ISSUE: The Add and Remove operations create a "double-join"
   situation, where a participants leaf key is also known to another
   participant.  When a participant A is double-joined to another B,
   deleting A will not remove them from the conversation, since they
   will still hold the leaf key for B.  These situations are resolved by
   updates, but since operations are asynchronous and participants may
   be offline for a long time, the group will need to be able to
   maintain security in the presence of double-joins. ]]

   [[ 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. ]]

7.1.  Init

   [[ OPEN ISSUE: Direct initialization is currently undefined.  A
   participant can create a group by initializing its own state to
   reflect a group including only itself, then adding the initial



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   participants.  This has computation and communication complexity O(N
   log N) instead of the O(N) complexity of direct initialization. ]]

7.2.  Add

   In order to add a new member to the group, an existing member of the
   group must take two actions:

   1.  Send a Welcome message to the new member

   2.  Send an Add message to the group (including the new member)

   The Welcome message contains the information that the new member
   needs to initialize a GroupState object that can be updated to the
   current state using the Add message:

   struct {
     opaque group_id<0..255>;
     uint32 epoch;
     Credential roster<1..2^32-1>;
     PublicKey tree<1..2^32-1>;
     GroupOperation transcript<0..2^32-1>;
     opaque init_secret<0..255>;
   } Welcome;

   Note that the "init_secret" in the Welcome message is the
   "init_secret" at the output of the key schedule diagram in
   Section 5.9.  That is, if the "epoch" value in the Welcome message is
   "n", then the "init_secret" value is "init_secret_[n]".  The new
   member can combine this init secret with the update secret
   transmitted in the corresponding Add message to get the epoch secret
   for the epoch in which it is added.  No secrets from prior epochs are
   revealed to the new member.

   Since the new member is expected to process the Add message for
   itself, the Welcome message should reflect the state of the group
   before the new user is added.  The sender of the Welcome message can
   simply copy all fields except the "leaf_secret" from its GroupState
   object.

   [[ OPEN ISSUE: The Welcome message needs to be sent encrypted for the
   new member.  This should be done using the public key in the
   UserInitKey, either with ECIES or X3DH. ]]

   [[ OPEN ISSUE: The Welcome message needs to be synchronized in the
   same way as the Add.  That is, the Welcome should be sent only if the
   Add succeeds, and is not in conflict with another, simultaneous Add.
   ]]



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   An Add message provides existing group members with the information
   they need to update their GroupState with information about the new
   member:

   struct {
       UserInitKey init_key;
   } Add;

   A group member generates this message by requesting a UserInitKey
   from the directory for the user to be added, and encoding it into an
   Add message.

   The new participant processes Welcome and Add messages together as
   follows:

   o  Prepare a new GroupState object based on the Welcome message

   o  Process the Add message as an existing participant would

   An existing participant receiving a Add message first verifies the
   signature on the message, then updates its state as follows:

   o  Increment the size of the group

   o  Verify the signature on the included UserInitKey; if the signature
      verification fails, abort

   o  Append an entry to the roster containing the credential in the
      included UserInitKey

   o  Update the ratchet tree by adding a new leaf node for the new
      member, containing the public key from the UserInitKey in the Add
      corresponding to the ciphersuite in use

   o  Update the ratchet tree by setting to blank all nodes in the
      direct path of the new node, except for the leaf (which remains
      set to the new member's public key)

   The update secret resulting from this change is an all-zero octet
   string of length Hash.length.

   On receipt of an Add message, new participants SHOULD send an update
   immediately to their key.  This will help to limit the tree structure
   degrading into subtrees, and thus maintain the protocol's efficiency.







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7.3.  Update

   An Update message is sent by a group participant to update its leaf
   key pair.  This operation provides post-compromise security with
   regard to the participant's prior leaf private key.

   struct {
       DirectPath path;
   } Update;

   The sender of an Update message creates it in the following way:

   o  Generate a fresh leaf key pair

   o  Compute its direct path in the current ratchet tree

   An existing participant receiving a Update message first verifies the
   signature on the message, then updates its state as follows:

   o  Update the cached ratchet tree by replacing nodes in the direct
      path from the updated leaf using the information contained in the
      Update message

   The update secret resulting from this change is the secret for the
   root node of the ratchet tree.

7.4.  Remove

   A Remove message is sent by a group member to remove one or more
   participants from the group.

   struct {
       uint32 removed;
       DirectPath path;
   } Remove;

   The sender of a Remove message generates it as as follows:

   o  Generate a fresh leaf key pair

   o  Compute its direct path in the current ratchet tree, starting from
      the removed leaf

   An existing participant receiving a Remove message first verifies the
   signature on the message, then verifies its identity proof against
   the identity tree held by the participant.  The participant then
   updates its state as follows:




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   o  Update the roster by setting the credential in the removed slot to
      the null optional value

   o  Update the ratchet tree by replacing nodes in the direct path from
      the removed leaf using the information in the Remove message

   o  Update the ratchet tree by setting to blank all nodes in the
      direct path from the removed leaf to the root

   The update secret resulting from this change is the secret for the
   root node of the ratchet tree after the second step (after the third
   step, the root is blank).

8.  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.

   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



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   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.

8.1.  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
   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.

8.2.  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.



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8.3.  Merging Updates

   It is possible in principle to partly address the problem of
   concurrent changes by having the recipients of the changes merge
   them, rather than having the senders retry.  Because the value of
   intermediate node is determined by its last updated child, updates
   can be merged by recipients as long as the recipients agree on an
   order - the only question is which node was last updated.

   Recall that the processing of an update proceeds in two steps:

   1.  Compute updated secret values by hashing up the tree

   2.  Update the tree with the new secret and public values

   To merge an ordered list of updates, a recipient simply performs
   these updates in the specified order.

   For example, suppose we have a tree in the following configuration:

         H(H(D))
        /       \
     H(B)      H(D)
     /  \      /  \
    A    B    C    D

   Now suppose B and C simultaneously decide to update to X and Y,
   respectively.  They will send out updates of the following form:

     Update from B      Update from C
     =============      =============
         H(H(X))            H(H(Y))
        /                         \
     H(X)                         H(Y)
        \                         /
         X                       Y

   Assuming that the ordering agreed by the group says that B's update
   should be processed before C's, the other participants in the group
   will overwrite the root value for B with the root value from C, and
   all arrive at the following state:

         H(H(Y))
        /       \
     H(X)      H(Y)
     /  \      /  \
    A    X    Y    D




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9.  Message Protection

   The primary purpose of the handshake protocol is to provide an
   authenticated group key exchange to participants.  In order to
   protect Application messages sent among those participants, the
   Application secret provided by the Handshake key schedule is used to
   derive encryption keys for the Message Protection Layer.

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

   Each participant maintains their own chain of Application secrets,
   where the first one is derived based on a secret chained from the
   Epoch secret.  As shown in Section 5.9, the initial Application
   secret is bound to the identity of each participant to avoid
   collisions and allow support for decryption of reordered messages.

   Subsequent Application secrets MUST be rotated for each message sent
   in order to provide stronger cryptographic security guarantees.  The
   Application Key Schedule use this rotation to generate fresh AEAD
   encryption keys and nonces used to encrypt and decrypt future
   Application messages.  In all cases, a participant MUST NOT encrypt
   more than expected by the security bounds of the AEAD scheme used.

   Note that each change to the Group through a Handshake message will
   cause a change of the Group Secret.  Hence this change MUST be
   applied before encrypting any new Application message.  This is
   required for confidentiality reasons in order for Members to avoid
   receiving messages from the group after leaving, being added to, or
   excluded from the Group.

9.1.  Application Key Schedule

   After computing the initial Application Secret shared by the group,
   each Participant creates an initial Participant Application Secret to
   be used for its own sending chain:









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              application_secret
                        |
                        V
              Derive-Secret(., "app sender", [sender])
                        |
                        V
              application_secret_[sender]_[0]

   Note that [sender] represent the uint32 value encoding the index of
   the participant in the ratchet tree.

   Updating the Application secret and deriving the associated AEAD key
   and nonce can be summarized as the following Application key schedule
   where each participant's Application secret chain looks as follows
   after the initial derivation:

           application_secret_[sender]_[N-1]
                     |
                     +--> HKDF-Expand-Label(.,"nonce", "", nonce_length)
                     |    = write_nonce_[sender]_[N-1]
                     |
                     +--> HKDF-Expand-Label(.,"key", "", key_length)
                     |    = write_key_[sender]_[N-1]
                     V
           Derive-Secret(., "app upd","")
                     |
                     V
           application_secret_[sender]_[N]

   The Application context provided together with the previous
   Application secret is used to bind the Application messages with the
   next key and add some freshness.

   [[OPEN ISSUE: The HKDF context field is left empty for now.  A proper
   security study is needed to make sure that we do not need more
   information in the context to achieve the security goals.]]

   [[ 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. ]]

9.1.1.  Updating the Application Secret

   The following rules apply to an Application Secret:





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   o  Senders MUST only use the Application Secret once and
      monotonically increment the generation of their secret.  This is
      important to provide Forward Secrecy at the level of Application
      messages.  An attacker getting hold of a Participant's Application
      Secret at generation [N+1] will not be able to derive the
      Participant's Application Secret [N] nor the associated AEAD key
      and nonce.

   o  Receivers MUST delete an Application Secret once it has been used
      to derive the corresponding AEAD key and nonce as well as the next
      Application Secret.  Receivers MAY keep the AEAD key and nonce
      around for some reasonable period.

   o  Receivers MUST delete AEAD keys and nonces once they have been
      used to successfully decrypt a message.

9.1.2.  Application AEAD Key Calculation

   The Application AEAD keying material is generated from the following
   input values:

   o  The Application Secret value;

   o  A purpose value indicating the specific value being generated;

   o  The length of the key being generated.

   Note, that because the identity of the participant using the keys to
   send data is included in the initial Application Secret, all
   successive updates to the Application secret will implicitly inherit
   this ownership.

   All the traffic keying material is recomputed whenever the underlying
   Application Secret changes.

9.2.  Message Encryption and Decryption

   The Group participants MUST use the AEAD algorithm associated with
   the negotiated MLS ciphersuite to AEAD encrypt and decrypt their
   Application messages and sign them as follows:











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       struct {
           opaque content<0..2^32-1>;
           opaque signature<0..2^16-1>;
           uint8 zeros[length_of_padding];
       } ApplicationPlaintext;

       struct {
           uint8  group[32];
           uint32 epoch;
           uint32 generation;
           uint32 sender;
           opaque encrypted_content<0..2^32-1>;
       } Application;

   The Group identifier and epoch allow a device to know which Group
   secrets should be used and from which Epoch secret to start computing
   other secrets and keys.  The participant identifier is used to derive
   the participant Application secret chain from the initial shared
   Application secret.  The application generation field is used to
   determine which Application secret should be used from the chain to
   compute the correct AEAD keys before performing decryption.

   The signature field allows strong authentication of messages:

       struct {
           uint8  group[32];
           uint32 epoch;
           uint32 generation;
           uint32 sender;
           opaque content<0..2^32-1>;
       } MLSSignatureContent;

   The signature used in the MLSPlaintext is computed over the
   MLSSignatureContent which covers the metadata information about the
   current state of the group (group identifier, epoch, generation and
   sender's Leaf index) to prevent Group participants from impersonating
   other participants.  It is also necessary in order to prevent cross-
   group attacks.

   [[ 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 GroupState instead, if more information is
   required to achieve the security goals regarding cross-group attacks.
   ]]




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   [[ 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 ? ]]

   Application messages SHOULD be padded to provide some resistance
   against traffic analysis techniques over encrypted traffic.  [CLINIC]
   [HCJ16] While MLS might deliver the same payload less frequently
   across a lot of ciphertexts than traditional web servers, it might
   still provide the attacker enough information to mount an attack.  If
   Alice asks Bob: "When are we going to the movie ?" the answer
   "Wednesday" might be leaked to an adversary by the ciphertext length.
   An attacker expecting Alice to answer Bob with a day of the week
   might find out the plaintext by correlation between the question and
   the length.

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

9.2.1.  Delayed and Reordered Application messages

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

   For usability, MLS Participants 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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10.  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.

10.1.  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 parties to
   authenticate their legitimate peers.

10.2.  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 participant 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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10.3.  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.

10.4.  Init Key Reuse

   Initialization keys are intended to be used only once and then
   deleted.  Reuse of init keys is not believed to be inherently
   insecure [dhreuse], although it can complicate protocol analyses.

11.  IANA Considerations

   TODO: Registries for protocol parameters, e.g., ciphersuites

12.  Contributors

   o  Benjamin Beurdouche
      INRIA
      benjamin.beurdouche@ens.fr

   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



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      ekr@rtfm.com

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

13.  References

13.1.  Normative References

   [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>.

   [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>.

   [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.

13.2.  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-29 (work in progress), October
              2018.

   [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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   [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
   # 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:



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           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
       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.



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   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 from a node to the root, 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 is the list of full subtrees, from left to right.  A
   # balance 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.
   def frontier(n):
       st = [1 << k for k in range(log2(n) + 1) if n & (1 << k) != 0]
       st = reversed(st)




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       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


   Jon Millican
   Facebook

   Email: jmillican@fb.com


   Emad Omara
   Google

   Email: emadomara@google.com








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   Katriel Cohn-Gordon
   University of Oxford

   Email: me@katriel.co.uk


   Raphael Robert
   Wire

   Email: raphael@wire.com









































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