Internet DRAFT - draft-barnes-mls-protocol
draft-barnes-mls-protocol
Network Working Group R. Barnes
Internet-Draft Cisco
Intended status: Informational J. Millican
Expires: January 3, 2019 Facebook
E. Omara
Google
K. Cohn-Gordon
University of Oxford
R. Robert
Wire
July 02, 2018
The Messaging Layer Security (MLS) Protocol
draft-barnes-mls-protocol-01
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 January 3, 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
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the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Basic Assumptions . . . . . . . . . . . . . . . . . . . . . . 5
4. Protocol Overview . . . . . . . . . . . . . . . . . . . . . . 5
5. Binary Trees . . . . . . . . . . . . . . . . . . . . . . . . 9
5.1. Terminology . . . . . . . . . . . . . . . . . . . . . . . 9
5.2. Merkle Trees . . . . . . . . . . . . . . . . . . . . . . 11
5.2.1. Merkle Proofs . . . . . . . . . . . . . . . . . . . . 12
5.3. Ratchet Trees . . . . . . . . . . . . . . . . . . . . . . 12
5.3.1. Ratchet Trees for ART . . . . . . . . . . . . . . . . 13
5.3.2. Ratchet Trees for TreeKEM . . . . . . . . . . . . . . 13
5.3.3. Ratchet Tree Updates . . . . . . . . . . . . . . . . 14
5.3.4. Blank Ratchet Tree Nodes . . . . . . . . . . . . . . 15
6. Group State . . . . . . . . . . . . . . . . . . . . . . . . . 16
6.1. Cryptographic Objects . . . . . . . . . . . . . . . . . . 17
6.1.1. ART with Curve25519 and SHA-256 . . . . . . . . . . . 18
6.1.2. ART with P-256 and SHA-256 . . . . . . . . . . . . . 18
6.1.3. TreeKEM with Curve25519, SHA-256, and AES-128-GCM . . 19
6.1.4. TreeKEM with P-256, SHA-256, and AES-128-GCM . . . . 19
6.2. Direct Paths . . . . . . . . . . . . . . . . . . . . . . 20
6.3. Key Schedule . . . . . . . . . . . . . . . . . . . . . . 21
7. Initialization Keys . . . . . . . . . . . . . . . . . . . . . 22
7.1. UserInitKey . . . . . . . . . . . . . . . . . . . . . . . 23
7.2. GroupInitKey . . . . . . . . . . . . . . . . . . . . . . 23
8. Handshake Messages . . . . . . . . . . . . . . . . . . . . . 24
8.1. Init . . . . . . . . . . . . . . . . . . . . . . . . . . 26
8.2. GroupAdd . . . . . . . . . . . . . . . . . . . . . . . . 26
8.3. UserAdd . . . . . . . . . . . . . . . . . . . . . . . . . 27
8.4. Update . . . . . . . . . . . . . . . . . . . . . . . . . 28
8.5. Remove . . . . . . . . . . . . . . . . . . . . . . . . . 29
9. Sequencing of State Changes . . . . . . . . . . . . . . . . . 29
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9.1. Server-Enforced Ordering . . . . . . . . . . . . . . . . 30
9.2. Client-Enforced Ordering . . . . . . . . . . . . . . . . 31
9.3. Merging Updates . . . . . . . . . . . . . . . . . . . . . 31
10. Message Protection . . . . . . . . . . . . . . . . . . . . . 32
11. Security Considerations . . . . . . . . . . . . . . . . . . . 33
11.1. Confidentiality of the Group Secrets . . . . . . . . . . 33
11.2. Authentication . . . . . . . . . . . . . . . . . . . . . 34
11.3. Forward and post-compromise security . . . . . . . . . . 34
11.4. Init Key Reuse . . . . . . . . . . . . . . . . . . . . . 34
12. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 35
13. Contributors . . . . . . . . . . . . . . . . . . . . . . . . 35
14. References . . . . . . . . . . . . . . . . . . . . . . . . . 35
14.1. Normative References . . . . . . . . . . . . . . . . . . 35
14.2. Informative References . . . . . . . . . . . . . . . . . 36
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 37
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/ekr/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. This document describes two candidate
approaches, one using "asynchronous ratcheting trees" [art], the
other using an asynchronous key-encapsulation mechanism for tree
structures called TreeKEM. Both mechanisms allow the members of the
group to derive and update shared keys with costs that scale as the
log of the group size. The use of Merkle trees to store identity
information allows strong authentication of group membership, again
with logarithmic cost.
2. Terminology
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119].
[TODO: The architecture document uses "Client" instead of
"Participant". Harmonize terminology.]
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 can be
published for both individual participants (UserInitKey) and
groups (GroupInitKey).
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.
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Terminology specific to tree computations is described in Section 5.
We use the TLS presentation language [I-D.ietf-tls-tls13] 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.omara-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 9 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 keys known only to group members. Keys 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 key. 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.
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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:
o Adding a member, initiated by a current member
o Adding a member, initiated by the new member
o Key update
o Removal of 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
GroupAdd 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 GroupAdd 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 | |
|<-------------------------------------------| |
| | | | |
| | | | GroupAdd(A->AB) |
|--------------------------------------------------------------->|
| | | | |
| | | | GroupAdd(AB->ABC) |
|--------------------------------------------------------------->|
| | | | |
| | | | GroupAdd(A->AB) |
|<---------------------------------------------------------------|
|state.add(B) |<------------------------------------------------|
| |state.init() |x---------------------------------|
| | | | |
| | | | GroupAdd(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 a GroupAdd which the current group can use to update their
state and the new participant can use to initialize its state.
It is sometimes necessary for a new participant to join without an
explicit invitation from a current member. For example, if a user
that is authorized to be in the group logs in on a new device, that
device will need to join the group as a new participant, but will not
have been invited.
In these "user-initiated join" cases, the "InitKey + Add message"
flow is reversed. We assume that at some previous point, a group
member has published a GroupInitKey reflecting the current state of
the group (A, B, C). The new participant Z downloads that
GroupInitKey from the directory, generates a UserAdd message, and
broadcasts it to the group. Once current members process this
message, they will have a shared state that also includes Z.
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Group
A B ... Z Directory Channel
| GroupInitKey | | | |
|------------------------------------------->| |
| | | | |
~ ~ ~ ~ ~
| | | | |
| | | GroupInitKey | |
| | |<-------------| |
| | | | |
| | | UserAdd(.->D)| |
| | |---------------------------->|
| | | | |
| | | | UserAdd(.->D)|
|<----------------------------------------------------------|
|state.add(D) |<-------------------------------------------|
| |state.add(D) |<----------------------------|
| | |state.init() | |
| | | | |
To enforce forward secrecy and post-compromise security of messages,
each participant periodically updates its leaf key, the DH key pair
that represents its contribution to the group key. Any member of the
group can send an Update at any time by generating a fresh leaf key
pair and sending an Update message that describes how to update the
group key with that new key pair. 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 private key.
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) | | | |
|---------------------------------------------------------->|
| | | | |
| | | | Update(A) |
|<----------------------------------------------------------|
|state.upd(D) |<-------------------------------------------|
| |state.upd(D) |<----------------------------|
| | |state.upd(A) | |
| | | | |
Users are deleted from the group in a similar way, as a key update is
effectively removing the old leaf from the group. Any member of the
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group can generate a Delete message that adds new entropy to the
group state that is known to all members except the deleted member.
After other participants have processed this message, the group's
secrets will be unknown to the deleted 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
| | | | |
| | | Delete(B) | |
| | |---------------------------->|
| | | | |
| | | | Delete(B) |
|<----------------------------------------------------------|
|state.del(B) | |<----------------------------|
| | |state.del(B) | |
| | | | |
| | | | |
5. Binary Trees
The protocol uses two types of binary tree structures:
o Merkle trees for efficiently committing to a set of group
participants.
o Ratchet trees for deriving shared secrets among this group of
participants.
The two trees in the protocol share a common structure, allowing us
to maintain a direct mapping between their nodes when manipulating
group membership. The "nth" leaf in each tree is owned by the "nth"
group participant.
5.1. Terminology
We use a common set of terminology to refer to both types of binary
tree.
Trees consist of various different types of _nodes_. A node is a
_leaf_ if it has no children, and a _parent_ otherwise; note that all
parents in our Merkle or 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 that node, its children,
and the descendants of its children, and we say a tree _contains_ a
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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, which has no sibling. 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
We extend both types of tree to include a concept of "blank" nodes;
which are used to replace group members who have been removed. We
expand on how these are used and implemented in the sections below.
(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].)
5.2. Merkle Trees
Merkle trees are used to efficiently commit to a collection of group
members. We require a hash function, denoted H, to construct this
tree.
Each node in a Merkle tree is the output of the hash function,
computed as follows:
o Leaf nodes: "H( 0x01 || leaf-value )"
o Parent nodes: "H( 0x02 || left-value || right-value)"
o Blank leaf nodes: "H( 0x00 )"
The below tree provides an example of a size 2 tree, containing
identity keys "A" and "B".
* H(2 || H(1 || A) || H(1 || B))
/ \
/ \
H(1 || A) * * H(1 || B)
In Merkle trees, blank nodes appear only at the leaves. In
computation of intermediate nodes, they are treated in the same way
as other nodes.
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5.2.1. Merkle Proofs
A proof of a given leaf being a member of the Merkle tree consists of
the value of the leaf node, as well as the values of each node in its
copath. From these values, its path to the root can be verified;
proving the inclusion of the leaf in the Merkle tree.
In the below tree, we denote with a star the Merkle proof of
membership for leaf node "A". For brevity, we notate "Hash(0x02 ||
A || B)" as "AB".
ABCD
/ \
AB CD*
/ \ / \
A B* C D
5.3. Ratchet Trees
Ratchet trees are used for generating shared group secrets. In this
section, we describe the structure of a ratchet tree, along with two
ways to manage a ratchet tree, called ART and TreeKEM.
To construct these trees, we require:
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 (TreeKEM only)
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 relationships between nodes are different for ART and TreeKEM.
In either case, the ratchet tree structure ensures the following
property: A party can compute the secret value for the root of the
tree if and only if that party holds the secret value for another
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node lower in the tree (together with public information). Each
participant holds one leaf secret; each participant can update the
root secret by changing their leaf secret.
5.3.1. Ratchet Trees for ART
In ART the contents of a parent node are computed from its children
as follows:
o parent_secret = DH(left_child, right_child)
o parent_private, parent_public = Derive-Key-Pair(parent_secret)
Ratchet trees are constructed as left-balanced trees, defined such
that each parent node's key pair is derived from the Diffie-Hellman
shared secret of its two child nodes. To compute the root secret and
private key, a participant must know the public keys of nodes in its
copath, as well as its own leaf private key.
For example, the ratchet tree consisting of the private keys (A, B,
C, D) is constructed as follows:
DH(DH(AB), DH(CD))
/ \
DH(AB) DH(CD)
/ \ / \
A B C D
5.3.2. Ratchet Trees for TreeKEM
In TreeKEM, the contents of a parent node are computed from one of
its children as follows:
o parent_secret = Hash(child_secret)
o 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
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If the first participant subsequently changes its leaf secret to be
X, then the tree will have the following structure.
H(H(X))
/ \
H(X) H(D)
/ \ / \
X B C D
5.3.3. 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. While the details of update processing differ between
ART and TreeKEM (as described below), in both cases the participant
proposing an update to the tree 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.
In ART, the transmitted nodes are represented by their public keys.
Receivers process an update with the following steps:
1. Replace the public keys in the cached tree with the received
values
2. Whenever a public key is updated for a node whose sibling has a
private key populated:
* Perform a DH operation and update the node's parent
* Repeat the prior step until reaching the root
In TreeKEM, the sender transmits a node by sending the public key for
the node and an encrypted version of the secret value for the node.
The secret value is encrypted in such a way that it can be decrypted
only by holders of the private key for one of its children, namely
the child that is not in the direct path being transmitted. (That
is, each node in the direct path is encrypted for holders of the
private key for a node in the corresponding copath.) For leaf nodes,
no encrypted secret is transmitted.
A TreeKEM update is processed with the following steps:
1. Compute the updated secret values * Identify a node in the direct
path for which the local participant has the private key *
Decrypt the secret value for that node * Compute secret values
for ancestors of that node by hashing the decrypted secret
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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 F
/ \ / \
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):
+------------+-------------+
| Public Key | Ciphertext |
+------------+-------------+
| pk(G) | E(pk(F), G) |
| | |
| pk(E) | E(pk(A), E) |
| | |
| pk(B) | |
+------------+-------------+
5.3.4. Blank Ratchet Tree Nodes
Nodes in a ratchet tree can have a special value "_", used to
indicate that the node should be ignored during path computations.
Such nodes are used to replace leaves when participants are deleted
from the group.
If any node in the copath of a leaf is _, it should be ignored during
the computation of the path. For example, the tree consisting of the
private keys (A, _, C, D) is constructed as follows for ART:
DH(A, DH(CD))
/ \
A DH(CD)
/ \ / \
A _ C D
Replacing a node by _ in TreeKEM, means performing an update on any
leaf without sending the new key to the the blanked leaf. In the
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following example, participant A update its key to A' and derive the
new sequence of keys up-to the path. Here A only send H(H(A')) to
the parent node of C and D but does not send H(A') to B which evicts
it from the Group. ~~~~~ H(H(A')) / \ H(A') H(C) / \ / \ A' _ C D
~~~~~
If two sibling nodes are both _, their parent value also becomes _.
Blank nodes effectively result in an unbalanced tree, but allow the
tree management to behave as for a balanced tree for programming
simplicity.
6. Group State
The state of an MLS group at a given time comprises:
o A group identifier (GID)
o A ciphersuite used for cryptographic computations
o A Merkle tree over the participants' identity keys
o A ratchet tree over the participants' leaf key pairs
o A message master secret (known only to participants)
o An add key pair (private key known only to participants)
o An init secret (known only to participants)
Since a group can evolve over time, a session logically comprises a
sequence of states. The time in which each individual state is used
is called an "epoch", and each state is assigned an epoch number that
increments when the state changes.
MLS handshake messages provide each node with enough information
about the trees to authenticate messages within the group and compute
the group secrets.
Thus, each participant will need to store the following information
about each state of the group:
1. The participant's index in the identity/ratchet trees
2. The private key associated with the participant's leaf public
key
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3. The private key associated with the participant's identity
public key
4. The current epoch number
5. The group identifier (GID)
6. A subset of the identity tree comprising at least the copath for
the participant's leaf
7. A subset of the ratchet tree comprising at least the copath for
the participant's leaf
8. The current message encryption shared secret, called the master
secret
9. The current add key pair
10. The current init secret
6.1. 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 (TreeKEM only) [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 and Merkle tree nodes used in the protocol are opaque
values in a format defined by the ciphersuite, using the following
four types:
uint16 CipherSuite;
opaque DHPublicKey<1..2^16-1>;
opaque SignaturePublicKey<1..2^16-1>;
opaque MerkleNode<1..255>
[[OPEN ISSUE: In some cases we will want to include a raw key when we
sign and in others we may want to include an identity or a
certificate containing the key. This type needs to be extended to
accommodate that.]]
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6.1.1. ART with Curve25519 and SHA-256
This ciphersuite uses the following primitives:
o Hash function: SHA-256
o Diffie-Hellman group: Curve25519 [RFC7748]
o AEAD: N/A
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. ART with P-256 and SHA-256
This ciphersuite uses the following primitives:
o Hash function: SHA-256
o Diffie-Hellman group: secp256r1 (NIST P-256)
o AEAD: N/A
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.
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(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.
6.1.3. TreeKEM with Curve25519, SHA-256, and AES-128-GCM
This ciphersuite uses the following primities:
o Hash function: SHA-256
o Diffie-Hellman group: Curve25519 [RFC7748]
o AEAD: AES-128-GCM
DH and Derive-Key-Pair operations are performed in the same way as
the corresponding ART ciphersuite.
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.
6.1.4. TreeKEM with P-256, SHA-256, and AES-128-GCM
This ciphersuite uses the following primities:
o Hash function: P-256
o Diffie-Hellman group: secp256r1 (NIST P-256)
o AEAD: AES-128-GCM
DH and Derive-Key-Pair operations are performed in the same way as
the corresponding ART ciphersuite.
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.
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6.2. Direct Paths
As described in Section 5.3.3, each MLS message needs to transmit
node values along the direct path from a leaf to the root. In ART,
this simply entails sending the public key for each node. In
TreeKEM, 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.
DHPublicKey ARTPath<0..2^16-1>;
struct {
DHPublicKey ephemeral_key;
opaque nonce<0..255>;
opaque ciphertext<0..255>;
} ECIESCiphertext;
struct {
DHPublicKey public_key;
ECIESCiphertext ciphertext;
} TreeKEMNode;
struct {
DHPublicKey leaf;
TreeKEMNode intermediates<0..2^16-1>;
} TreeKEMPath;
struct {
select (mode) {
case ART: ARTPath;
case TreeKEM: TreeKEMPath;
};
} DirectPath;
When using TreeKEM, 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
o Compute the shared secret Z with the node's other child
o Generate a fresh nonce N
o Encrypt the node's secret value using the AEAD algorithm specified
by the ciphersuite in use, with the following inputs:
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* Key: A key derived from Z as specified by the ciphersuite
* Nonce: A random nonce N of the size required by the algorithm
* 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
* nonce: The random nonce N
* ciphertext: The AEAD output
Decryption is performed in the corresponding way, using the private
key of the non-updated child and the ephemeral public key transmitted
in the message.
6.3. 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:
Derive-Secret(Secret, Label, ID, Epoch, Msg) =
HKDF-Expand(Secret, HkdfLabel, Length)
Where HkdfLabel is specified as:
struct {
uint16 length = Length;
opaque label<7..255> = "mls10 " + Label;
opaque group_id<0..2^16-1> = ID;
uint32 epoch = Epoch;
opaque message<1..2^16-1> = Msg
} 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
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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 handshake message that caused the epoch change
o The current group identifier (GID) and epoch
The derivation of the update secret depends on the change being made,
as described below.
For UserAdd or GroupAdd, the new user does not know the prior epoch
init secret. Instead, entropy from the prior epoch is added via the
update secret, and an all-zero vector with the same length as a hash
output is used in the place of the init secret.
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(., "msg", ID, Epoch, Msg)
| = message_master_secret
|
+--> Derive-Secret(., "add", ID, Epoch, Msg)
| |
| V
| Derive-Key-Pair(.) = Add Key Pair
|
V
Derive-Secret(., "init", ID, Epoch, Msg)
|
V
Init Secret [n]
7. 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 or group. UserInitKey messages
provide information about a potential group member, that a group
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member can use to add this user to a group asynchronously.
GroupInitKey messages provide information about a group that a new
user can use to join the group without any of the existing members of
the group being online.
7.1. UserInitKey
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 11.4).
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 or KEM 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;
7.2. GroupInitKey
A GroupInitKey object specifies the aspects of a group's state that a
new member needs to initialize its state (together with an identity
key and a fresh leaf key pair).
o The current epoch number
o The number of participants currently in the group
o The group ID
o The cipher suite used by the group
o The public key of the current update key pair for the group
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o The frontier of the identity tree, as a sequence of hash values
o The frontier of the ratchet tree, as a sequence of public keys
GroupInitKey messages are not themselves signed. A GroupInitKey
should not be published "bare"; instead, it should be published by
constructing a handshake message with type "none", which will include
a signature by a member of the group and a proof of membership in the
group.
struct {
uint32 epoch;
uint32 group_size;
opaque group_id<0..2^16-1>;
CipherSuite cipher_suite;
DHPublicKey add_key;
MerkleNode identity_frontier<0..2^16-1>;
TreeNode ratchet_frontier<0..2^16-1>;
} GroupInitKey;
8. 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 new participant adding themselves
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
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 message that
accomplishes a change to the group state. It also includes two other
important features:
o A GroupInitKey so that a new participant can observe the latest
state of the handshake and initialize itself
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o A signature by a member of the group, together with a Merkle
inclusion proof that demonstrates that the signer is a legitimate
member of the group.
Before considering a handshake message valid, the recipient MUST
verify both that the signature is valid, the Merkle inclusion proof
is valid, and the sender is authorized to make the change according
to group policy. The input to the signature computations comprises
the entire handshake message except for the signature field.
The Merkle tree head to be used for validating the inclusion proof
MUST be one that the recipient trusts to represent the current list
of participant identity keys.
enum {
none(0),
init(1),
user_add(2),
group_add(3),
update(4),
delete(5),
(255)
} HandshakeType;
struct {
HandshakeType msg_type;
uint24 inner_length;
select (Handshake.msg_type) {
case none: struct{};
case init: Init;
case user_add: UserAdd;
case group_add: GroupAdd;
case update: Update;
case delete: Delete;
};
uint32 prior_epoch;
GroupInitKey init_key;
uint32 signer_index;
MerkleNode identity_proof<1..2^16-1>;
SignaturePublicKey identity_key;
SignatureScheme algorithm;
opaque signature<1..2^16-1>;
} Handshake;
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[[ OPEN ISSUE: There will be a need to integrate credentials from an
authentication service that associate identities to the identity keys
used to sign messages. This integration will enable meaningful
authentication (of identities, rather than keys), and will need to be
done in such a way as to prevent unknown key share attacks. ]]
[[ OPEN ISSUE: The GroupAdd and Delete 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. ]]
8.1. 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
participants. This has computation and communication complexity O(N
log N) instead of the O(N) complexity of direct initialization. ]]
8.2. GroupAdd
A GroupAdd message is sent by a group member to add a new participant
to the group.
struct {
PublicKey ephemeral;
DirectPath add_path<1..2^16-1>;
} GroupAdd;
A group member generates this message using the following steps:
o Requesting from the directory a UserInitKey for the user to be
added
o Generate a fresh ephemeral DH key pair
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o Generate the leaf secret for the new node as the output of a DH
operation between the ephemeral key pair and the public key in the
UserInitKey
o Use the ratchet frontier and the new leaf secret to compute the
direct path between the new leaf and the new root
The public key of the ephemeral key pair is placed in the "ephemeral"
field of the GroupAdd message. The computed direct path is placed in
the "add_path" field.
The new participant processes the message and the private key
corresponding to the UserInitKey to initialize his state as follows:
o Compute the participant's leaf secret by combining the init key in
the UserInitKey with the prior epoch's add key pair
o Use the frontiers in the GroupInitKey of the Handshake message to
add its keys to the trees
An existing participant receiving a GroupAdd 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:
o Compute the new participant's leaf key pair by combining the leaf
key in the UserInitKey with the prior epoch add key pair
o Update the group's identity tree and ratchet tree with the new
participant's information
The update secret resulting from this change is the output of a DH
computation between the private key for the root of the ratchet tree
and the add public key from the previous epoch.
8.3. UserAdd
A UserAdd message is sent by a new group participant to add themself
to the group, based on having already had access to a GroupInitKey
for the group.
struct {
DirectPath add_path;
} UserAdd;
A new participant generates this message using the following steps:
o Fetch a GroupInitKey for the group
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o Use the frontiers in the GroupInitKey to add its keys to the trees
o Compute the direct path from the new participant's leaf in the new
ratchet tree (the add_path).
An existing participant receiving a UserAdd first verifies the
signature on the message, then verifies its identity inclusion proof
against the updated identity tree expressed in the GroupInitKey of
the Handshake message (since the signer is not included in the prior
group state held by the existing participant). The participant then
updates its state as follows:
o Update trees with the descriptions in the new GroupInitKey
o Update the local ratchet tree with the information in the UserAdd
message, replacing any common nodes with the values in the add
path
The update secret resulting from this change is the output of a DH
computation between the private key for the root of the ratchet tree
and the add public key from the previous epoch.
8.4. 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 update_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 verifies its identity proof against
the identity tree held by the participant. The participant 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
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The update secret resulting from this change is the secret for the
root node of the ratchet tree.
8.5. Remove
A Remove message is sent by a group member to remove one or more
participants from the group.
struct {
uint32 deleted;
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 deleted leaf (Note: In ART, this requires knowing the deleted
node's copath)
An existing participant receiving a Delete 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:
o Update the cached ratchet tree by replacing nodes in the direct
path from the deleted leaf using the information in the Delete
message
o Update the cached ratchet tree and identity tree by replacing the
deleted node's leaves with blank nodes
The update secret resulting from this change is the secret for the
root node of the ratchet tree after both updates.
9. 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
In ART, in either case, 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.
In TreeKEM, because of the non-contributivity of intermediate nodes
update messages can be applied one after the other without the
Delivery Service having to reject any handshake message which makes
TreeKEM 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
deletes.
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.
9.1. 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. In ART, if
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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. In TreeKEM, the message does not
necessarily need to be resent.
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.
9.2. 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.
9.3. Merging Updates
When TreeKEM is in use, it is possible 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 (as opposed
to both its children in ART), TreeKEM 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 a TreeKEM 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:
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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
10. Message Protection
[[ OPEN ISSUE: This section has initial considerations about message
protection. This issue clearly needs more specific recommendations,
possibly a protocol specification in this document or a separate one.
]]
The primary purpose of this protocol is to enable an authenticated
group key exchange among participants. In order to protect messages
sent among those participants, an application will need to specify
how messages are protected.
For every epoch, the root key of the ratcheting tree can be used to
derive key material for symmetric operations such as encryption/AEAD
and MAC; AEAD or MAC MUST be used to ensure that the message
originated from a member of the group.
In addition, asymmetric signatures SHOULD be used to authenticate the
sender of a message.
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In combination with server-side enforced ordering, data from previous
messages is used (as a salt when hashing) to:
o add freshness to derived symmetric keys
o cryptographically bind the transcript of all previous messages
with the current group shared secret
Possible candidates for that are:
o the key used for the previous message (hash ratcheting)
o the counter of the previous message (needs to be known to new
members of the group)
o the hash of the previous message (proof that other participants
saw the same history)
The requirement for this is that all participants know these values.
If additional clear-text fields are attached to messages (like the
counter), those fields MUST be protected by a signed message
envelope.
Alternatively, the hash of the previous message can also be included
as an additional field rather than change the encryption key. This
allows for a more flexible approach, because the receiving party can
choose to ignore it (if the value is not known, or if transcript
security is not required).
11. Security Considerations
The security goals of MLS are described in [[the architecture doc]].
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.
11.1. 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.]]
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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.
11.2. 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.]]
11.3. 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.
11.4. 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.
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12. IANA Considerations
TODO: Registries for protocol parameters, e.g., ciphersuites
13. 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
ekr@rtfm.com
o Thyla van der Merwe
Royal Holloway, University of London
thyla.van.der@merwe.tech
14. References
14.1. Normative References
[I-D.ietf-tls-tls13]
Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", draft-ietf-tls-tls13-28 (work in progress),
March 2018.
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[IEEE1363]
"IEEE Standard Specifications for Password-Based Public-
Key Cryptographic Techniques", IEEE standard,
DOI 10.1109/ieeestd.2009.4773330, n.d..
[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>.
[X962] ANSI, "Public Key Cryptography For The Financial Services
Industry: The Elliptic Curve Digital Signature Algorithm
(ECDSA)", ANSI X9.62, 1998.
14.2. 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>.
[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.
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[I-D.ietf-trans-rfc6962-bis]
Laurie, B., Langley, A., Kasper, E., Messeri, E., and R.
Stradling, "Certificate Transparency Version 2.0", draft-
ietf-trans-rfc6962-bis-28 (work in progress), March 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.
[signal] Perrin(ed), T. and M. Marlinspike, "The Double Ratchet
Algorithm", n.d.,
<https://www.signal.org/docs/specifications/
doubleratchet/>.
Authors' Addresses
Richard Barnes
Cisco
Email: rlb@ipv.sx
Jon Millican
Facebook
Email: jmillican@fb.com
Emad Omara
Google
Email: emadomara@google.com
Katriel Cohn-Gordon
University of Oxford
Email: me@katriel.co.uk
Raphael Robert
Wire
Email: raphael@wire.com
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