| Internet-Draft | MLS | October 2021 |
| Barnes, et al. | Expires 14 April 2022 | [Page] |
Messaging applications are increasingly making use of end-to-end security mechanisms to ensure that messages are only accessible to the communicating endpoints, and not to any servers involved in delivering messages. Establishing keys to provide such protections is challenging for group chat settings, in which more than two clients need to agree on a key but may not be online at the same time. In this document, we specify a key establishment protocol that provides efficient asynchronous group key establishment with forward secrecy and post-compromise security for groups in size ranging from two to thousands.¶
This note is to be removed before publishing as an RFC.¶
Source for this draft and an issue tracker can be found at https://github.com/mlswg/mls-protocol.¶
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 14 April 2022.¶
Copyright (c) 2021 IETF Trust and the persons identified as the document authors. All rights reserved.¶
This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.¶
DISCLAIMER: This is a work-in-progress draft of MLS and has not yet seen significant security analysis. It should not be used as a basis for building production systems.¶
RFC EDITOR: PLEASE REMOVE THE FOLLOWING PARAGRAPH The source for this draft is maintained in GitHub. Suggested changes should be submitted as pull requests at https://github.com/mlswg/mls-protocol. Instructions are on that page as well. Editorial changes can be managed in GitHub, but any substantive change should be discussed on the MLS mailing list.¶
A group of users who want to send each other encrypted messages needs a way to derive shared symmetric encryption keys. For two parties, this problem has been studied thoroughly, with the Double Ratchet emerging as a common solution [doubleratchet] [signal]. Channels implementing the Double Ratchet enjoy fine-grained forward secrecy as well as post-compromise security, but are nonetheless efficient enough for heavy use over low-bandwidth networks.¶
For a group of size greater than two, a common strategy is to unilaterally broadcast symmetric "sender" keys over existing shared symmetric channels, and then for each member to send messages to the group encrypted with their own sender key. Unfortunately, while this improves efficiency over pairwise broadcast of individual messages and provides forward secrecy (with the addition of a hash ratchet), it is difficult to achieve post-compromise security with sender keys. An adversary who learns a sender key can often indefinitely and passively eavesdrop on that member's messages. Generating and distributing a new sender key provides a form of post-compromise security with regard to that sender. However, it requires computation and communications resources that scale linearly with the size of the group.¶
In this document, we describe a protocol based on tree structures that enable asynchronous group keying with forward secrecy and post-compromise security. Based on earlier work on "asynchronous ratcheting trees" [art], the protocol presented here uses an asynchronous key-encapsulation mechanism for tree structures. This mechanism allows the members of the group to derive and update shared keys with costs that scale as the log of the group size.¶
RFC EDITOR PLEASE DELETE THIS SECTION.¶
draft-12¶
draft-11¶
draft-10¶
draft-09¶
draft-08¶
draft-07¶
draft-06¶
draft-05¶
draft-04¶
draft-03¶
draft-02¶
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draft-00¶
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.¶
An agent that uses this protocol to establish shared cryptographic state with other clients. A client is defined by the cryptographic keys it holds.¶
A collection of clients with shared cryptographic state.¶
A client that is included in the shared state of a group, hence has access to the group's secrets.¶
A signed object describing a client's identity and capabilities, and including a hybrid public-key encryption (HPKE [I-D.irtf-cfrg-hpke]) public key that can be used to encrypt to that client.¶
A key package that is prepublished by a client, which other clients can use to introduce the client to a new group.¶
A 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.¶
This protocol is designed to execute in the context of a Service Provider (SP) as described in [I-D.ietf-mls-architecture]. In particular, we assume the SP provides the following services:¶
The goal of this protocol is to allow a group of clients to exchange confidential and authenticated messages. It does so by deriving a sequence of secrets and keys known only to members. Those should be secret against an active network adversary and should have both forward secrecy and post-compromise security with respect to compromise of any members.¶
We describe the information stored by each client as state, which includes both public and private data. An initial state is set up by a group creator, which is a group containing only itself. The creator then sends Add proposals for each client in the initial set of members, followed by a Commit message which incorporates all of the Adds into the group state. Finally, the group creator generates a Welcome message corresponding to the Commit and sends this directly to all the new members, who can use the information it contains to set up their own group state and derive a shared secret. Members exchange Commit messages for post-compromise security, to add new members, and to remove existing members. These messages produce new shared secrets which are causally linked to their predecessors, forming a logical Directed Acyclic Graph (DAG) of states.¶
The protocol algorithms we specify here follow. Each algorithm specifies both (i) how a client performs the operation and (ii) how other clients update their state based on it.¶
There are three major operations in the lifecycle of a group:¶
Each of these operations is "proposed" by sending a message of the corresponding type (Add / Update / Remove). The state of the group is not changed, however, until a Commit message is sent to provide the group with fresh entropy. In this section, we show each proposal being committed immediately, but in more advanced deployment cases an application might gather several proposals before committing them all at once.¶
Before the initialization of a group, clients publish InitKeys (as KeyPackage objects) to a directory provided by the Service Provider.¶
Group
A B C Directory Channel
| | | | |
| KeyPackageA | | | |
|------------------------------------------------->| |
| | | | |
| | KeyPackageB | | |
| |-------------------------------->| |
| | | | |
| | | KeyPackageC | |
| | |--------------->| |
| | | | |
¶
When a client A wants to establish a group with B and C, it first initializes a group state containing only itself and downloads KeyPackages for B and C. For each member, A generates an Add and Commit message adding that member, and broadcasts them to the group. It also generates a Welcome message and sends this directly to the new member (there's no need to send it to the group). Only after A has received its Commit message back from the server does it update its state to reflect the new member's addition.¶
Upon receiving the Welcome message, the new member will be able to read and send new messages to the group. Messages received before the client has joined the group are ignored.¶
Group
A B C Directory Channel
| | | | |
| KeyPackageB, KeyPackageC | |
|<-------------------------------------------| |
|state.init() | | | |
| | | | |
| | | | Add(A->AB) |
| | | | Commit(Add) |
|--------------------------------------------------------------->|
| | | | |
| Welcome(B) | | | |
|------------->|state.join() | | |
| | | | |
| | | | Add(A->AB) |
| | | | Commit(Add) |
|<---------------------------------------------------------------|
|state.add(B) | | | |
| | | | |
| | | | |
| | | | Add(AB->ABC) |
| | | | Commit(Add) |
|--------------------------------------------------------------->|
| | | | |
| | Welcome(C) | | |
|---------------------------->|state.join() | |
| | | | |
| | | | Add(AB->ABC) |
| | | | Commit(Add) |
|<---------------------------------------------------------------|
|state.add(C) |<------------------------------------------------|
| |state.add(C) | | |
| | | | |
¶
Subsequent additions of group members proceed in the same way. Any member of the group can download a KeyPackage for a new client and broadcast an Add message that the current group can use to update their state, and a Welcome message that the new client can use to initialize its state and join the group.¶
To enforce the forward secrecy and post-compromise security of messages, each member periodically updates their leaf secret. Any member can update this information at any time by generating a fresh KeyPackage and sending an Update message followed by a Commit message. Once all members have processed both, the group's secrets will be unknown to an attacker that had compromised the sender's prior leaf secret.¶
Update messages should be sent at regular intervals of time as long as the group is active, and members that don't update should eventually be removed from the group. It's left to the application to determine an appropriate amount of time between Updates.¶
Group
A B ... Z Directory Channel
| | | | |
| | Update(B) | | |
| |------------------------------------------->|
| Commit(Upd) | | | |
|---------------------------------------------------------->|
| | | | |
| | | | Update(B) |
| | | | Commit(Upd) |
|<----------------------------------------------------------|
|state.upd(B) |<-------------------------------------------|
| |state.upd(B) |<----------------------------|
| | |state.upd(B) | |
| | | | |
¶
Members are removed from the group in a similar way. Any member of the group can send a Remove proposal followed by a Commit message, which adds new entropy to the group state that's known to all except the removed member. Note that this does not necessarily imply that any member is actually allowed to evict other members; groups can enforce access control policies on top of these basic mechanism.¶
Group
A B ... Z Directory Channel
| | | | |
| | | Remove(B) | |
| | | Commit(Rem) | |
| | |---------------------------->|
| | | | |
| | | | Remove(B) |
| | | | Commit(Rem) |
|<----------------------------------------------------------|
|state.rem(B) | |<----------------------------|
| | |state.rem(B) | |
| | | | |
| | | | |
¶
The protocol uses "ratchet trees" for deriving shared secrets among a group of clients.¶
Trees consist of nodes. A node is a leaf if it has no children, and a parent otherwise; note that all parents in our trees have precisely two children, a left child and a right child. A node is the root of a tree if it has no parents, and intermediate if it has both children and parents. The descendants of a node are that node, its children, and the descendants of its children, and we say a tree contains a node if that node is a descendant of the root of the tree. Nodes are siblings if they share the same parent.¶
A subtree of a tree is the tree given by the descendants of any node, the head of the subtree. The size of a tree or subtree is the number of leaf nodes it contains. For a given parent node, its left subtree is the subtree with its left child as head (respectively right subtree).¶
All trees used in this protocol are left-balanced binary trees. A binary tree is full (and balanced) if its size is a power of two and for any parent node in the tree, its left and right subtrees have the same size.¶
A binary tree is left-balanced if for every
parent, either the parent is balanced, or the left subtree of that
parent is the largest full subtree that could be constructed from
the leaves present in the parent's own subtree.
Given a list of n items, there is a unique left-balanced
binary tree structure with these elements as leaves.¶
(Note that left-balanced binary trees are the same structure that is used for the Merkle trees in the Certificate Transparency protocol [I-D.ietf-trans-rfc6962-bis].)¶
The direct path of a root is the empty list, and of any other node is the concatenation of that node's parent along with the parent's direct path. The copath of a node is the node's sibling concatenated with the list of siblings of all the nodes in its direct path, excluding the root.¶
For example, in the below tree:¶
7 = root
______|______
/ \
3 11
__|__ __|
/ \ / \
1 5 9 |
/ \ / \ / \ |
A B C D E F G
1 1 1
0 1 2 3 4 5 6 7 8 9 0 1 2
¶
Each node in the tree is assigned an index, starting at zero and running from left to right. A node is a leaf node if and only if it has an even index. The node indices for the nodes in the above tree are as follows:¶
A tree with n leaves has 2*n - 1 nodes. For example, the above tree has 7
leaves (A, B, C, D, E, F, G) and 13 nodes. The root of a tree with n leaves
is always the node with index 2^k - 1, where k is the largest number such
that 2^k < n.¶
A particular instance of a ratchet tree is defined by the same parameters that define an instance of HPKE, namely:¶
DeriveKeyPair function that
creates a key pair for the KEM from a symmetric secret¶
Extract and Expand functions¶
Each node in a ratchet tree contains up to five values:¶
The conditions under which each of these values must or must not be present are laid out in Section 5.3.¶
A node in the tree may also be blank, indicating that no value is present at that node. The resolution of a node is an ordered list of non-blank nodes that collectively cover all non-blank descendants of the node.¶
For example, consider the following tree, where the "_" character represents a blank node and unmerged leaves are indicated in square brackets:¶
_
__|__
/ \
_ 5[C]
/ \ / \
A _ C D
0 1 2 3 4 5 6
¶
In this tree, we can see all of the above rules in play:¶
Every node, regardless of whether the node is blank or populated, has a corresponding hash that summarizes the contents of the subtree below that node. The rules for computing these hashes are described in Section 7.6.¶
We generally assume that each participant maintains a complete and up-to-date view of the public state of the group's ratchet tree, including the public keys for all nodes and the credentials associated with the leaf nodes.¶
No participant in an MLS group knows the private key associated with every node in the tree. Instead, each member is assigned to a leaf of the tree, which determines the subset of private keys it knows. The credential stored at that leaf is one provided by the member.¶
In particular, MLS maintains the members' views of the tree in such a way as to maintain the tree invariant:¶
The private key for a node in the tree is known to a member of the group only if that member's leaf is a descendant of the node.¶
In other words, if a node is not blank, then it holds a public key. The corresponding private key is known only to members occupying leaves below that node.¶
The reverse implication is not true: A member may not know the private keys of all the intermediate nodes they're below. Such a member has an unmerged leaf. Encrypting to an intermediate node requires encrypting to the node's public key, as well as the public keys of all the unmerged leaves below it. A leaf is unmerged when it is first added, because the process of adding the leaf does not give it access to all of the nodes above it in the tree. Leaves are "merged" as they receive the private keys for nodes, as described in Section 5.4.¶
A member of an MLS group advances the key schedule to provide forward secrecy and post-compromise security by providing the group with fresh key material to be added into the group's shared secret. To do so, one member of the group generates fresh key material, applies it to their local tree state, and then sends this key material to other members in the group via an UpdatePath message (see Section 7.8) . All other group members then apply the key material in the UpdatePath to their own local tree state to derive the group's now-updated shared secret.¶
To begin, the generator of the UpdatePath updates its leaf KeyPackage and its direct path to the root with new secret values. The HPKE leaf public key within the KeyPackage MUST be derived from a freshly generated HPKE secret key to provide post-compromise security.¶
The generator of the UpdatePath starts by sampling a fresh random value called "leaf_secret", and uses the leaf_secret to generate their leaf HPKE key pair (see Section 7) and to seed a sequence of "path secrets", one for each ancestor of its leaf. In this setting, path_secret[0] refers to the node directly above the leaf, path_secret[1] for its parent, and so on. At each step, the path secret is used to derive a new secret value for the corresponding node, from which the node's key pair is derived.¶
leaf_node_secret = DeriveSecret(leaf_secret, "node") path_secret[0] = DeriveSecret(leaf_secret, "path") path_secret[n] = DeriveSecret(path_secret[n-1], "path") node_secret[n] = DeriveSecret(path_secret[n], "node") leaf_priv, leaf_pub = KEM.DeriveKeyPair(leaf_node_secret) node_priv[n], node_pub[n] = KEM.DeriveKeyPair(node_secret[n])¶
For example, suppose there is a group with four members, with C an unmerged leaf at node 5:¶
3
__|__
/ \
1 5[C]
/ \ / \
A B C D
0 1 2 3 4 5 6
¶
If member B subsequently generates an UpdatePath based on a secret "leaf_secret", then it would generate the following sequence of path secrets:¶
path_secret[1] --> node_secret[1] --> node_priv[1], node_pub[1]
^
|
path_secret[0] --> node_secret[0] --> node_priv[0], node_pub[0]
^
|
leaf_secret --> leaf_node_secret --> leaf_priv, leaf_pub
~> leaf_key_package
¶
After applying the UpdatePath, the tree will have the following structure, where
lp and np[i] represent the leaf_priv and node_priv values generated as
described above:¶
np[1] -> 3
__|__
/ \
np[0] -> 1 5[C]
/ \ / \
A B C D
^
|
lp
0 1 2 3 4 5 6
¶
After performing these operations, the generator of the UpdatePath MUST delete the leaf_secret.¶
After generating fresh key material and applying it to ratchet forward their local tree state as described in the prior section, the generator must broadcast this update to other members of the group in a Commit message, who apply it to keep their local views of the tree in sync with the sender's. More specifically, when a member commits a change to the tree (e.g., to add or remove a member), it transmits an UpdatePath containing a set of public keys and encrypted path secrets for intermediate nodes in the direct path of its leaf. The other members of the group use these values to update their view of the tree, aligning their copy of the tree to the sender's.¶
An UpdatePath contains the following information for each node in the direct path of the sender's leaf, including the root:¶
The path secret value for a given node is encrypted for the subtree corresponding to the parent's non-updated child, that is, the child on the copath of the sender's leaf node. There is one encryption of the path secret to each public key in the resolution of the non-updated child.¶
The recipient of an UpdatePath processes it with the following steps:¶
Compute the updated path secrets.¶
Merge the updated path secrets into the tree.¶
For all updated nodes,¶
For example, in order to communicate the example update described in the previous section, the sender would transmit the following values:¶
| Public Key | Ciphertext(s) |
|---|---|
| node_pub[1] | E(pk(5), path_secret[1]), E(pk(C), path_secret[1]) |
| node_pub[0] | E(pk(A), path_secret[0]) |
In this table, the value pk(ns[X]) represents the public key derived from the node secret X, whereas pk(X) represents the public leaf key for user X. The value E(K, S) represents the public-key encryption of the path secret S to the public key K (using HPKE).¶
After processing the update, each recipient MUST delete outdated key material, specifically:¶
Each MLS session uses a single ciphersuite that specifies the following primitives to be used in group key computations:¶
MLS uses draft-08 of HPKE [I-D.irtf-cfrg-hpke] for public-key encryption.
The DeriveKeyPair function associated to the KEM for the ciphersuite maps
octet strings to HPKE key pairs.¶
Ciphersuites are represented with the CipherSuite type. HPKE public keys are opaque values in a format defined by the underlying protocol (see the Cryptographic Dependencies section of the HPKE specification for more information).¶
opaque HPKEPublicKey<1..2^16-1>;¶
The signature algorithm specified in the ciphersuite is the mandatory algorithm to be used for signatures in MLSPlaintext and the tree signatures. It MUST be the same as the signature algorithm specified in the credential field of the KeyPackage objects in the leaves of the tree (including the InitKeys used to add new members).¶
The ciphersuites are defined in section Section 16.1.¶
A member of a group authenticates the identities of other participants by means of credentials issued by some authentication system, like a PKI. Each type of credential MUST express the following data in the context of the group it is used with:¶
Credentials MAY also include information that allows a relying party to verify the identity / signing key binding.¶
Additionally, Credentials SHOULD specify the signature scheme corresponding to each contained public key.¶
// See RFC 8446 and the IANA TLS SignatureScheme registry
uint16 SignatureScheme;
// See IANA registry for registered values
uint16 CredentialType;
struct {
opaque identity<0..2^16-1>;
SignatureScheme signature_scheme;
opaque signature_key<0..2^16-1>;
} BasicCredential;
struct {
opaque cert_data<0..2^16-1>;
} Certificate;
struct {
CredentialType credential_type;
select (Credential.credential_type) {
case basic:
BasicCredential;
case x509:
Certificate chain<1..2^32-1>;
};
} Credential;
¶
A BasicCredential is a raw, unauthenticated assertion of an identity/key
binding. The format of the key in the public_key field is defined by the
relevant ciphersuite: the group ciphersuite for a credential in a ratchet tree,
the KeyPackage ciphersuite for a credential in a KeyPackage object.¶
For X509Credential, each entry in the chain represents a single DER-encoded
X509 certificate. The chain is ordered such that the first entry (chain[0])
is the end-entity certificate and each subsequent certificate in the chain
MUST be the issuer of the previous certificate. The algorithm for the
public_key in the end-entity certificate MUST match the relevant
ciphersuite.¶
For ciphersuites using Ed25519 or Ed448 signature schemes, the public key is in the format specified [RFC8032]. For ciphersuites using ECDSA with the NIST curves P-256 or P-521, the public key is the output of the uncompressed Elliptic-Curve-Point-to-Octet-String conversion according to [SECG].¶
The signatures used throughout this document are encoded as specified in
[RFC8446]. In particular, ECDSA signatures are DER-encoded and EdDSA signatures
are defined as the concatenation of r and s as specified in [RFC8032].¶
Note that each new credential that has not already been validated by the application MUST be validated against the Authentication Service.¶
In order to facilitate asynchronous addition of clients to a group, it is possible to pre-publish key packages that provide some public information about a user. KeyPackage structures provide information about a client that any existing member can use to add this client to the group asynchronously.¶
A KeyPackage object specifies a ciphersuite that the client supports, as well as providing a public key that others can use for key agreement.¶
The identity arising from the credential, together with the endpoint_id in
the KeyPackage serve to uniquely identify a client in a group.¶
When used as InitKeys, KeyPackages are intended to be used only once and SHOULD NOT be reused except in case of last resort. (See Section 15.4). Clients MAY generate and publish multiple InitKeys to support multiple ciphersuites.¶
KeyPackages contain a public key chosen by the client, which the client MUST ensure uniquely identifies a given KeyPackage object among the set of KeyPackages created by this client.¶
The value for hpke_init_key MUST be a public key for the asymmetric encryption scheme defined by cipher_suite. The whole structure is signed using the client's signature key. A KeyPackage object with an invalid signature field MUST be considered malformed. The input to the signature computation comprises all of the fields except for the signature field.¶
enum {
reserved(0),
mls10(1),
(255)
} ProtocolVersion;
// See IANA registry for registered values
uint16 ExtensionType;
struct {
ExtensionType extension_type;
opaque extension_data<0..2^32-1>;
} Extension;
struct {
ProtocolVersion version;
CipherSuite cipher_suite;
HPKEPublicKey hpke_init_key;
opaque endpoint_id<0..255>;
Credential credential;
Extension extensions<8..2^32-1>;
opaque signature<0..2^16-1>;
} KeyPackage;
¶
KeyPackage objects MUST contain at least two extensions, one of type
capabilities, and one of
type lifetime. The capabilities extension
allow MLS session establishment to be safe from downgrade attacks on the
parameters described (as discussed in Section 10), while still only advertising
one version / ciphersuite per KeyPackage.¶
As the KeyPackage is a structure which is stored in the Ratchet
Tree and updated depending on the evolution of this tree, each
modification of its content MUST be reflected by a change of its
signature. This allow other members to control the validity of the KeyPackage
at any time and in particular in the case of a newcomer joining the group.¶
When it is necessary to refer to a specific KeyPackage, protocol messages incorporate a KeyPackageID:¶
struct {
opaque key_package_hash<0..255>;
} KeyPackageID
¶
This value is the hash of the KeyPackage, using the hash indicated by the
cipher_suite field. KeyPackage hashes are used in a Welcome message to
indicate which KeyPackage is being used to include the new member. Since members
of a group are uniquely identified by their leaf KeyPackages, messages within a
group use the hash of this key package to refer to group members, e.g., to
specify the target of a Remove proposal or the signer of an MLSPlaintext.¶
The capabilities extension indicates what protocol versions, ciphersuites,
protocol extensions, and non-default proposal types are supported by a client.
Proposal types defined in this document are considered "default" and thus need
not be listed.¶
struct {
ProtocolVersion versions<0..255>;
CipherSuite ciphersuites<0..255>;
ExtensionType extensions<0..255>;
ProposalType proposals<0..255>;
} Capabilities;
¶
This extension MUST be always present in a KeyPackage. Extensions that appear
in the extensions field of a KeyPackage MUST be included in the extensions
field of the capabilities extension.¶
The lifetime extension represents the times between which clients will
consider a KeyPackage valid. This time is represented as an absolute time,
measured in seconds since the Unix epoch (1970-01-01T00:00:00Z). A client MUST
NOT use the data in a KeyPackage for any processing before the not_before
date, or after the not_after date.¶
uint64 not_before; uint64 not_after;¶
Applications MUST define a maximum total lifetime that is acceptable for a KeyPackage, and reject any KeyPackage where the total lifetime is longer than this duration.¶
This extension MUST always be present in a KeyPackage.¶
Within MLS, a KeyPackage is identified by its hash (see, e.g.,
Section 11.2.2). The external_key_id extension allows applications to add
an explicit, application-defined identifier to a KeyPackage.¶
opaque external_key_id<0..2^16-1>;¶
The parent_hash extension carries information to authenticate the structure of
the tree, as described below.¶
opaque parent_hash<0..255>;¶
Consider a ratchet tree with a parent node P and children V and S. The parent hash
of P changes whenever an UpdatePath object is applied to the ratchet tree along
a path traversing node V (and hence also P). The new "Parent Hash of P (with Co-Path
Child S)" is obtained by hashing P's ParentHashInput struct using the resolution
of S to populate the original_child_resolution field. This way, P's Parent Hash
fixes the new HPKE public keys of all nodes on the path from P to the root.
Furthermore, for each such key PK the hash also binds the set of HPKE public keys
to which PK's secret key was encrypted in the commit packet that anounced the
UpdatePath object.¶
struct {
HPKEPublicKey public_key;
opaque parent_hash<0..255>;
HPKEPublicKey original_child_resolution<0..2^32-1>;
} ParentHashInput;
¶
The Parent Hash of P with Co-Path Child S is the hash of a ParentHashInput object
populated as follows. The field public_key contains the HPKE public key of P. If P
is the root, then parent_hash is set to a zero-length octet string.
Otherwise parent_hash is the Parent Hash of P's parent with P's sibling as the
co-path child.¶
Finally, original_child_resolution is the array of HPKEPublicKey values of the
nodes in the resolution of S but with the unmerged_leaves of P omitted. For
example, in the ratchet tree depicted in Section 5.2 the
ParentHashInput of node 5 with co-path child 4 would contain an empty
original_child_resolution since 4's resolution includes only itself but 4 is also
an unmerged leaf of 5. Meanwhile, the ParentHashInput of node 5 with co-path child
6 has an array with one element in it: the HPKE public key of 6.¶
The Parent Hash of P appears in three types of structs. If V is itself a parent node
then P's Parent Hash is stored in the parent_hash fields of both V's
ParentHashInput struct and V's ParentNode struct. (The ParentNode struct is
used to encapsulate all public information about V that must be conveyed to a new
member joining the group as well as to define the Tree Hash of node V.)¶
If, on the other hand, V is a leaf and its KeyPackage contains the parent_hash
extension then the Parent Hash of P (with V's sibling as co-path child) is stored in
that field. In particular, the extension MUST be present in the leaf_key_package
field of an UpdatePath object. (This way, the signature of such a KeyPackage also
serves to attest to which keys the group member introduced into the ratchet tree and
to whom the corresponding secret keys were sent. This helps prevent malicious insiders
from constructing artificial ratchet trees with a node V whose HPKE secret key is
known to the insider yet where the insider isn't assigned a leaf in the subtree rooted
at V. Indeed, such a ratchet tree would violate the tree invariant.)¶
To this end, when processing a Commit message clients MUST recompute the
expected value of parent_hash for the committer's new leaf and verify that it
matches the parent_hash value in the supplied leaf_key_package. Moreover, when
joining a group, new members MUST authenticate each non-blank parent node P. A parent
node P is authenticated by performing the following check:¶
The left-child recursion under the right child of P is necessary because the expansion of the tree to the right due to Add proposals can cause blank nodes to be interposed between a parent node and its right child.¶
To allow group members to verify that they agree on the public cryptographic state of the group, this section defines a scheme for generating a hash value (called the "tree hash") that represents the contents of the group's ratchet tree and the members' KeyPackages. The tree hash of a tree is the tree hash of its root node, which we define recursively, starting with the leaves.¶
As some nodes may be blank while others contain data we use the following struct to include data if present.¶
struct {
uint8 present;
select (present) {
case 0: struct{};
case 1: T value;
}
} optional<T>;
¶
The tree hash of a leaf node is the hash of leaf's LeafNodeHashInput object which
might include a Key Package depending on whether or not it is blank.¶
struct {
uint32 node_index;
optional<KeyPackage> key_package;
} LeafNodeHashInput;
¶
Now the tree hash of any non-leaf node is recursively defined to be the hash of
its ParentNodeTreeHashInput. This includes an optional ParentNode
object depending on whether the node is blank or not.¶
struct {
HPKEPublicKey public_key;
opaque parent_hash<0..255>;
uint32 unmerged_leaves<0..2^32-1>;
} ParentNode;
struct {
uint32 node_index;
optional<ParentNode> parent_node;
opaque left_hash<0..255>;
opaque right_hash<0..255>;
} ParentNodeTreeHashInput;
¶
The left_hash and right_hash fields hold the tree hashes of the node's
left and right children, respectively.¶
Each member of the group maintains a GroupContext object that summarizes the state of the group:¶
struct {
opaque group_id<0..255>;
uint64 epoch;
opaque tree_hash<0..255>;
opaque confirmed_transcript_hash<0..255>;
Extension extensions<0..2^32-1>;
} GroupContext;
¶
The fields in this state have the following semantics:¶
group_id field is an application-defined identifier for the
group.¶
epoch field represents the current version of the group key.¶
tree_hash field contains a commitment to the contents of the
group's ratchet tree and the credentials for the members of the
group, as described in Section 7.6.¶
confirmed_transcript_hash field contains a running hash over
the messages that led to this state.¶
When a new member is added to the group, an existing member of the group provides the new member with a Welcome message. The Welcome message provides the information the new member needs to initialize its GroupContext.¶
Different changes to the group will have different effects on the group state. These effects are described in their respective subsections of Section 11.1. The following general rules apply:¶
group_id field is constant¶
epoch field increments by one for each Commit message that
is processed¶
tree_hash is updated to represent the current tree and
credentials¶
confirmed_transcript_hash is updated with the data for an
MLSPlaintext message encoding a Commit message in two parts:¶
struct {
WireFormat wire_format;
opaque group_id<0..255>;
uint64 epoch;
Sender sender;
opaque authenticated_data<0..2^32-1>;
ContentType content_type = commit;
Commit commit;
opaque signature<0..2^16-1>;
} MLSPlaintextCommitContent;
struct {
optional<MAC> confirmation_tag;
} MLSPlaintextCommitAuthData;
interim_transcript_hash_[0] = ""; // zero-length octet string
confirmed_transcript_hash_[n] =
Hash(interim_transcript_hash_[n] ||
MLSPlaintextCommitContent_[n]);
interim_transcript_hash_[n+1] =
Hash(confirmed_transcript_hash_[n] ||
MLSPlaintextCommitAuthData_[n]);
¶
Thus the confirmed_transcript_hash field in a GroupContext object represents a
transcript over the whole history of MLSPlaintext Commit messages, up to the
confirmation tag field in the current MLSPlaintext message. The confirmation
tag is then included in the transcript for the next epoch. The interim
transcript hash is computed by new members using the confirmation tag in the
GroupInfo struct, and enables existing members to incorporate a Commit message
into the transcript without having to store the whole MLSPlaintextCommitAuthData
structure.¶
As shown above, when a new group is created, the interim_transcript_hash field
is set to the zero-length octet string.¶
As described in Section 11.2, each MLS Commit message may optionally transmit a KeyPackage leaf and node values along its direct path. The path contains a public key and encrypted secret value for all intermediate nodes in the path above the leaf. The path is ordered from the closest node to the leaf to the root; each node MUST be the parent of its predecessor.¶
struct {
opaque kem_output<0..2^16-1>;
opaque ciphertext<0..2^16-1>;
} HPKECiphertext;
struct {
HPKEPublicKey public_key;
HPKECiphertext encrypted_path_secret<0..2^32-1>;
} UpdatePathNode;
struct {
KeyPackage leaf_key_package;
UpdatePathNode nodes<0..2^32-1>;
} UpdatePath;
¶
For each UpdatePathNode, the resolution of the corresponding copath node MUST
be filtered by removing all new leaf nodes added as part of this MLS Commit
message. The number of ciphertexts in the encrypted_path_secret vector MUST be
equal to the length of the filtered resolution, with each ciphertext being the
encryption to the respective resolution node.¶
The HPKECiphertext values are computed as¶
kem_output, context = SetupBaseS(node_public_key, group_context)
ciphertext = context.Seal("", path_secret)
¶
where node_public_key is the public key of the node that the path
secret is being encrypted for, group_context is the current GroupContext object
for the group, and the functions SetupBaseS and
Seal are defined according to [I-D.irtf-cfrg-hpke].¶
Decryption is performed in the corresponding way, using the private key of the resolution node and the ephemeral public key transmitted in the message.¶
Group keys are derived using the Extract and Expand functions from the KDF
for the group's ciphersuite, as well as the functions defined below:¶
ExpandWithLabel(Secret, Label, Context, Length) =
KDF.Expand(Secret, KDFLabel, Length)
Where KDFLabel is specified as:
struct {
uint16 length = Length;
opaque label<7..255> = "mls10 " + Label;
opaque context<0..2^32-1> = Context;
} KDFLabel;
DeriveSecret(Secret, Label) =
ExpandWithLabel(Secret, Label, "", KDF.Nh)
¶
The value KDF.Nh is the size of an output from KDF.Extract, in bytes. In
the below diagram:¶
0 represents an all-zero byte string of length KDF.Nh.¶
When processing a handshake message, a client combines the following information to derive new epoch secrets:¶
Given these inputs, the derivation of secrets for an epoch proceeds as shown in the following diagram:¶
init_secret_[n-1]
|
V
commit_secret -> KDF.Extract
|
V
ExpandWithLabel(., "joiner", GroupContext_[n], KDF.Nh)
|
V
joiner_secret
|
V
psk_secret (or 0) -> KDF.Extract
|
+--> DeriveSecret(., "welcome")
| = welcome_secret
|
V
ExpandWithLabel(., "epoch", GroupContext_[n], KDF.Nh)
|
V
epoch_secret
|
+--> DeriveSecret(., <label>)
| = <secret>
|
V
DeriveSecret(., "init")
|
V
init_secret_[n]
¶
A number of secrets are derived from the epoch secret for different purposes:¶
| Secret | Label |
|---|---|
sender_data_secret
|
"sender data" |
encryption_secret
|
"encryption" |
exporter_secret
|
"exporter" |
authentication_secret
|
"authentication" |
external_secret
|
"external" |
confirmation_key
|
"confirm" |
membership_key
|
"membership" |
resumption_secret
|
"resumption" |
The "external secret" is used to derive an HPKE key pair whose private key is held by the entire group:¶
external_priv, external_pub = KEM.DeriveKeyPair(external_secret)¶
The public key external_pub can be published as part of the PublicGroupState
struct in order to allow non-members to join the group using an external commit.¶
In addition to initializing a new epoch via KDF invocations as described above, an MLS group can also initialize a new epoch via an asymmetric interaction using the external key pair for the previous epoch. This is done when an new member is joining via an external commit.¶
In this process, the joiner sends a new init_secret value to the group using
the HPKE export method. The joiner then uses that init_secret with
information provided in the PublicGroupState and an external Commit to initialize
their copy of the key schedule for the new epoch.¶
kem_output, context = SetupBaseS(external_pub, "")
init_secret = context.export("MLS 1.0 external init secret", KDF.Nh)
¶
Members of the group receive the kem_output in an ExternalInit proposal and
preform the corresponding calculation to retrieve the init_secret value.¶
context = SetupBaseR(kem_output, external_priv, "")
init_secret = context.export("MLS 1.0 external init secret", KDF.Nh)
¶
In both cases, the info input to HPKE is set to the PublicGroupState for the
previous epoch, encoded using the TLS serialization.¶
For the generation of encryption keys and nonces, the key schedule begins with
the encryption_secret at the root and derives a tree of secrets with the same
structure as the group's ratchet tree. Each leaf in the Secret Tree is
associated with the same group member as the corresponding leaf in the ratchet
tree. Nodes are also assigned an index according to their position in the array
representation of the tree (described in Appendix A). If N is a node index in
the Secret Tree then left(N) and right(N) denote the children of N (if they
exist).¶
The secret of any other node in the tree is derived from its parent's secret using a call to DeriveTreeSecret:¶
DeriveTreeSecret(Secret, Label, Node, Generation, Length) =
ExpandWithLabel(Secret, Label, TreeContext, Length)
Where TreeContext is specified as:
struct {
uint32 node = Node;
uint32 generation = Generation;
} TreeContext;
¶
If N is a node index in the Secret Tree then the secrets of the children of N are defined to be:¶
tree_node_[N]_secret
|
|
+--> DeriveTreeSecret(., "tree", left(N), 0, KDF.Nh)
| = tree_node_[left(N)]_secret
|
+--> DeriveTreeSecret(., "tree", right(N), 0, KDF.Nh)
= tree_node_[right(N)]_secret
¶
The secret in the leaf of the Secret Tree is used to initiate two symmetric hash ratchets, from which a sequence of single-use keys and nonces are derived, as described in Section 8.4. The root of each ratchet is computed as:¶
tree_node_[N]_secret
|
|
+--> DeriveTreeSecret(., "handshake", N, 0, KDF.Nh)
| = handshake_ratchet_secret_[N]_[0]
|
+--> DeriveTreeSecret(., "application", N, 0, KDF.Nh)
= application_ratchet_secret_[N]_[0]
¶
As described in Section 9, MLS encrypts three different types of information:¶
The sender information used to look up the key for content encryption is
encrypted with an AEAD where the key and nonce are derived from both
sender_data_secret and a sample of the encrypted message content.¶
For handshake and application messages, a sequence of keys is derived via a "sender ratchet". Each sender has their own sender ratchet, and each step along the ratchet is called a "generation".¶
A sender ratchet starts from a per-sender base secret derived from a Secret Tree, as described in Section 8.3. The base secret initiates a symmetric hash ratchet which generates a sequence of keys and nonces. The sender uses the j-th key/nonce pair in the sequence to encrypt (using the AEAD) the j-th message they send during that epoch. Each key/nonce pair MUST NOT be used to encrypt more than one message.¶
Keys, nonces, and the secrets in ratchets are derived using DeriveTreeSecret. The context in a given call consists of the index of the sender's leaf in the ratchet tree and the current position in the ratchet. In particular, the node index of the sender's leaf in the ratchet tree is the same as the node index of the leaf in the Secret Tree used to initialize the sender's ratchet.¶
ratchet_secret_[N]_[j]
|
+--> DeriveTreeSecret(., "nonce", N, j, AEAD.Nn)
| = ratchet_nonce_[N]_[j]
|
+--> DeriveTreeSecret(., "key", N, j, AEAD.Nk)
| = ratchet_key_[N]_[j]
|
V
DeriveTreeSecret(., "secret", N, j, KDF.Nh)
= ratchet_secret_[N]_[j+1]
¶
Here, AEAD.Nn and AEAD.Nk denote the lengths in bytes of the nonce and key for the AEAD scheme defined by the ciphersuite.¶
It is important to delete all security-sensitive values as soon as they are consumed. A sensitive value S is said to be consumed if¶
Here, S may be the init_secret, commit_secret, epoch_secret,
encryption_secret as well as any secret in a Secret Tree or one of the
ratchets.¶
As soon as a group member consumes a value they MUST immediately delete (all representations of) that value. This is crucial to ensuring forward secrecy for past messages. Members MAY keep unconsumed values around for some reasonable amount of time to handle out-of-order message delivery.¶
For example, suppose a group member encrypts or (successfully) decrypts an application message using the j-th key and nonce in the ratchet of node index N in some epoch n. Then, for that member, at least the following values have been consumed and MUST be deleted:¶
commit_secret, joiner_secret, epoch_secret, encryption_secret of
that epoch n as well as the init_secret of the previous epoch n-1,¶
application_ratchet_nonce_[N]_[j] and application_ratchet_key_[N]_[j].¶
Concretely, suppose we have the following Secret Tree and ratchet for participant D:¶
G
/ \
/ \
E F
/ \ / \
A B C D
/ \
HR0 AR0 -+- K0
| |
| +- N0
|
AR1 -+- K1
| |
| +- N1
|
AR2
¶
Then if a client uses key K1 and nonce N1 during epoch n then it must consume
(at least) values G, F, D, AR0, AR1, K1, N1 as well as the key schedule secrets
used to derive G (the encryption_secret), namely init_secret of epoch n-1
and commit_secret, joiner_secret, epoch_secret of epoch n. The client MAY
retain (not consume) the values K0 and N0 to allow for out-of-order delivery,
and SHOULD retain AR2 for processing future messages.¶
The main MLS key schedule provides an exporter_secret which can
be used by an application as the basis to derive new secrets called
exported_value outside the MLS layer.¶
MLS-Exporter(Label, Context, key_length) =
ExpandWithLabel(DeriveSecret(exporter_secret, Label),
"exporter", Hash(Context), key_length)
¶
Each application SHOULD provide a unique label to MLS-Exporter that
identifies its use case. This is to prevent two
exported outputs from being generated with the same values and used
for different functionalities.¶
The exported values are bound to the group epoch from which the
exporter_secret is derived, hence reflects a particular state of
the group.¶
It is RECOMMENDED for the application generating exported values to refresh those values after a Commit is processed.¶
The main MLS key schedule provides a resumption_secret which can provide extra
security in some cross-group operations.¶
The application SHOULD specify an upper limit on the number of past
epochs for which the resumption_secret may be stored.¶
There are two ways in which a resumption_secret can be used: to re-initialize
the group with different parameters, or to create a
sub-group of an existing group as detailed in Section 8.2.¶
Resumption keys are distinguished from exporter keys in that they have specific use inside the MLS protocol, whereas the use of exporter secrets may be decided by an external application. They are thus derived separately to avoid key material reuse.¶
The main MLS key schedule provides a per-epoch authentication_secret.
If one of the parties is being actively impersonated by an attacker, their
authentication_secret will differ from that of the other group members.
Thus, members of a group MAY use their authentication_secrets within
an out-of-band authentication protocol to ensure that they
share the same view of the group.¶
Handshake and application messages use a common framing structure. This framing provides encryption to ensure confidentiality within the group, as well as signing to authenticate the sender within the group.¶
The two main structures involved are MLSPlaintext and MLSCiphertext. MLSCiphertext represents a signed and encrypted message, with protections for both the content of the message and related metadata. MLSPlaintext represents a message that is only signed, and not encrypted. Applications MUST use MLSCiphertext to encrypt application messages and SHOULD use MLSCiphertext to encode handshake messages, but MAY transmit handshake messages encoded as MLSPlaintext objects in cases where it is necessary for the Delivery Service to examine such messages.¶
enum {
reserved(0),
application(1),
proposal(2),
commit(3),
(255)
} ContentType;
enum {
reserved(0),
member(1),
preconfigured(2),
new_member(3),
(255)
} SenderType;
struct {
SenderType sender_type;
switch (sender_type) {
case member: KeyPackageID member;
case preconfigured: opaque external_key_id<0..255>;
case new_member: struct{};
}
} Sender;
struct {
opaque mac_value<0..255>;
} MAC;
enum {
reserved(0),
mls_plaintext(1),
mls_ciphertext(2),
(255)
} WireFormat;
struct {
WireFormat wire_format;
opaque group_id<0..255>;
uint64 epoch;
Sender sender;
opaque authenticated_data<0..2^32-1>;
ContentType content_type;
select (MLSPlaintext.content_type) {
case application:
opaque application_data<0..2^32-1>;
case proposal:
Proposal proposal;
case commit:
Commit commit;
}
opaque signature<0..2^16-1>;
optional<MAC> confirmation_tag;
optional<MAC> membership_tag;
} MLSPlaintext;
struct {
WireFormat wire_format = mls_ciphertext;
opaque group_id<0..255>;
uint64 epoch;
ContentType content_type;
opaque authenticated_data<0..2^32-1>;
opaque encrypted_sender_data<0..255>;
opaque ciphertext<0..2^32-1>;
} MLSCiphertext;
¶
The field confirmation_tag MUST be present if content_type equals commit.
Otherwise, it MUST NOT be present.¶
External sender types are sent as MLSPlaintext, see Section 11.1.9 for their use.¶
The remainder of this section describes how to compute the signature of an
MLSPlaintext object and how to convert it to an MLSCiphertext object for
member sender types. The steps are:¶
group_id, epoch, content_type and authenticated_data fields from the
MLSPlaintext object directly¶
sender_data_secret for the epoch and a sample of the encrypted
MLSCiphertextContent.¶
Decryption is done by decrypting the sender data, then the message, and then verifying the content signature.¶
The following sections describe the encryption and signing processes in detail.¶
The signature field in an MLSPlaintext object is computed using the signing
private key corresponding to the public key, which was authenticated by the
credential at the leaf of the tree indicated by the sender field. The signature
covers the plaintext metadata and message content, which is all of MLSPlaintext
except for the signature, the confirmation_tag and membership_tag fields.
If the sender is a member of the group, the signature also covers the
GroupContext for the current epoch, so that signatures are specific to a given
group and epoch.¶
struct {
select (MLSPlaintextTBS.sender.sender_type) {
case member:
GroupContext context;
case preconfigured:
case new_member:
struct{};
}
WireFormat wire_format;
opaque group_id<0..255>;
uint64 epoch;
Sender sender;
opaque authenticated_data<0..2^32-1>;
ContentType content_type;
select (MLSPlaintextTBS.content_type) {
case application:
opaque application_data<0..2^32-1>;
case proposal:
Proposal proposal;
case commit:
Commit commit;
}
} MLSPlaintextTBS;
¶
The membership_tag field in the MLSPlaintext object authenticates the sender's
membership in the group. For an MLSPlaintext with a sender type other than
member, this field MUST be omitted. For messages sent by members, it MUST be
present and set to the following value:¶
struct {
MLSPlaintextTBS tbs;
opaque signature<0..2^16-1>;
optional<MAC> confirmation_tag;
} MLSPlaintextTBM;
membership_tag = MAC(membership_key, MLSPlaintextTBM);
¶
Note that the membership_tag only needs to be computed for MLSPlaintext
messages that will be sent over the wire (wire_format == mls_plaintext). It
isn't needed for messages that will be encrypted and transmitted as
MLSCiphertext messages (wire_format == mls_ciphertext).¶
The ciphertext field of the MLSCiphertext object is produced by supplying the
inputs described below to the AEAD function specified by the ciphersuite in use.
The plaintext input contains the content and signature of the MLSPlaintext, plus
optional padding. These values are encoded in the following form:¶
struct {
select (MLSCiphertext.content_type) {
case application:
opaque application_data<0..2^32-1>;
case proposal:
Proposal proposal;
case commit:
Commit commit;
}
opaque signature<0..2^16-1>;
optional<MAC> confirmation_tag;
opaque padding<0..2^16-1>;
} MLSCiphertextContent;
¶
In the MLS key schedule, the sender creates two distinct key ratchets for handshake and application messages for each member of the group. When encrypting a message, the sender looks at the ratchets it derived for its own member and chooses an unused generation from either the handshake or application ratchet depending on the content type of the message. This generation of the ratchet is used to derive a provisional nonce and key.¶
Before use in the encryption operation, the nonce is XORed with a fresh random value to guard against reuse. Because the key schedule generates nonces deterministically, a client must keep persistent state as to where in the key schedule it is; if this persistent state is lost or corrupted, a client might reuse a generation that has already been used, causing reuse of a key/nonce pair.¶
To avoid this situation, the sender of a message MUST generate a fresh random
4-byte "reuse guard" value and XOR it with the first four bytes of the nonce
from the key schedule before using the nonce for encryption. The sender MUST
include the reuse guard in the reuse_guard field of the sender data object, so
that the recipient of the message can use it to compute the nonce to be used for
decryption.¶
+-+-+-+-+---------...---+
| Key Schedule Nonce |
+-+-+-+-+---------...---+
XOR
+-+-+-+-+---------...---+
| Guard | 0 |
+-+-+-+-+---------...---+
===
+-+-+-+-+---------...---+
| Encrypt/Decrypt Nonce |
+-+-+-+-+---------...---+
¶
The Additional Authenticated Data (AAD) input to the encryption contains an object of the following form, with the values used to identify the key and nonce:¶
struct {
opaque group_id<0..255>;
uint64 epoch;
ContentType content_type;
opaque authenticated_data<0..2^32-1>;
} MLSCiphertextContentAAD;
¶
The "sender data" used to look up the key for the content encryption is
encrypted with the ciphersuite's AEAD with a key and nonce derived from both the
sender_data_secret and a sample of the encrypted content. Before being
encrypted, the sender data is encoded as an object of the following form:¶
struct {
KeyPackageID sender;
uint32 generation;
opaque reuse_guard[4];
} MLSSenderData;
¶
MLSSenderData.sender is assumed to be a member sender type. When constructing
an MLSSenderData from a Sender object, the sender MUST verify Sender.sender_type
is member and use Sender.sender for MLSSenderData.sender.¶
The reuse_guard field contains a fresh random value used to avoid nonce reuse
in the case of state loss or corruption, as described in Section 9.2.¶
The key and nonce provided to the AEAD are computed as the KDF of the first
KDF.Nh bytes of the ciphertext generated in the previous section. If the
length of the ciphertext is less than KDF.Nh, the whole ciphertext is used
without padding. In pseudocode, the key and nonce are derived as:¶
ciphertext_sample = ciphertext[0..KDF.Nh-1] sender_data_key = ExpandWithLabel(sender_data_secret, "key", ciphertext_sample, AEAD.Nk) sender_data_nonce = ExpandWithLabel(sender_data_secret, "nonce", ciphertext_sample, AEAD.Nn)¶
The Additional Authenticated Data (AAD) for the SenderData ciphertext is all the
fields of MLSCiphertext excluding encrypted_sender_data:¶
struct {
opaque group_id<0..255>;
uint64 epoch;
ContentType content_type;
} MLSSenderDataAAD;
¶
When parsing a SenderData struct as part of message decryption, the recipient
MUST verify that the KeyPackageID indicated in the sender field identifies a
member of the group.¶
A group is always created with a single member, the "creator". The other members are added when the creator effectively sends itself an Add proposal and commits it, then sends the corresponding Welcome message to the new participants. These processes are described in detail in Section 11.1.1, Section 11.2, and Section 11.2.2.¶
The creator of a group MUST take the following steps to initialize the group:¶
capabilities extensions
in these KeyPackages to verify that the
chosen version and ciphersuite is the best option supported by all members.¶
Initialize a one-member group with the following initial values:¶
KDF.Nh¶
The recipient of a Welcome message processes it as described in Section 11.2.2.¶
In principle, the above process could be streamlined by having the creator directly create a tree and choose a random value for first epoch's epoch secret. We follow the steps above because it removes unnecessary choices, by which, for example, bad randomness could be introduced. The only choices the creator makes here are its own KeyPackage, the leaf secret from which the Commit is built, and the intermediate key pairs along the direct path to the root.¶
The configuration of a group imposes certain requirements on clients in the
group. At a minimum, all members of the group need to support the ciphersuite
and protocol version in use. Additional requirements can be imposed by
including a required_capabilities extension in the GroupContext.¶
struct {
ExtensionType extensions<0..255>;
ProposalType proposals<0..255>;
} RequiredCapabilities;
¶
This extension lists the extensions and proposal types that must be supported by
all members of the group. For new members, it is enforced by existing members during the
application of Add commits. Existing members should of course be in compliance
already. In order to ensure this continues to be the case even as the group's
extensions can be updated, a GroupContextExtensions proposal is invalid if it
contains a required_capabilities extension that requires capabililities not
supported by all current members.¶
A new group may be tied to an already existing group for the purpose of re-initializing the existing group, or to branch into a sub-group. Re-initializing an existing group may be used, for example, to restart the group with a different ciphersuite or protocol version. Branching may be used to bootstrap a new group consisting of a subset of current group members, based on the current group state.¶
In both cases, the psk_nonce included in the PreSharedKeyID object must be a
randomly sampled nonce of length KDF.Nh to avoid key re-use.¶
If a client wants to create a subgroup of an existing group, they MAY choose to
include a PreSharedKeyID in the GroupSecrets object of the Welcome message choosing
the psktype branch, the group_id of the group from which a subgroup is to
be branched, as well as an epoch within the number of epochs for which a
resumption_secret is kept.¶
Over the lifetime of a group, its membership can change, and existing members might want to change their keys in order to achieve post-compromise security. In MLS, each such change is accomplished by a two-step process:¶
The group thus evolves from one cryptographic state to another each time a Commit message is sent and processed. These states are referred to as "epochs" and are uniquely identified among states of the group by eight-octet epoch values. When a new group is initialized, its initial state epoch is 0x0000000000000000. Each time a state transition occurs, the epoch number is incremented by one.¶
Proposals are included in an MLSPlaintext by way of a Proposal structure that indicates their type:¶
// See IANA registry for registered values
uint16 ProposalType;
struct {
ProposalType msg_type;
select (Proposal.msg_type) {
case add: Add;
case update: Update;
case remove: Remove;
case psk: PreSharedKey;
case reinit: ReInit;
case external_init: ExternalInit;
case app_ack: AppAck;
case group_context_extensions: GroupContextExtensions;
};
} Proposal;
¶
On receiving an MLSPlaintext containing a Proposal, a client MUST verify the signature on the enclosing MLSPlaintext. If the signature verifies successfully, then the Proposal should be cached in such a way that it can be retrieved by hash (as a ProposalOrRef object) in a later Commit message.¶
An Add proposal requests that a client with a specified KeyPackage be added to the group. The proposer of the Add MUST validate the KeyPackage in the same way as receipients are required to do below.¶
struct {
KeyPackage key_package;
} Add;
¶
The proposer of the Add does not control where in the group's ratchet tree the new member is added. Instead, the sender of the Commit message chooses a location for each added member and states it in the Commit message.¶
An Add is applied after being included in a Commit message. The position of the
Add in the list of proposals determines the node index index of the leaf node
where the new member will be added. For the first Add in the Commit, index is
the leftmost empty leaf in the tree, for the second Add, the next empty leaf to
the right, etc.¶
Validate the KeyPackage:¶
Verify that the following fields in the KeyPackage are unique among the members of the group (including any other members added in the same Commit):¶
required_capabilities
extension, then the required extensions and proposals MUST be listed in
the KeyPackage's capabilities extension.¶
index to the root, add index to the unmerged_leaves list for the node.¶
index to a new node containing the
public key from the KeyPackage in the Add, as well as the credential under
which the KeyPackage was signed¶
An Update proposal is a similar mechanism to Add with the distinction that it is the sender's leaf KeyPackage in the tree which would be updated with a new KeyPackage.¶
struct {
KeyPackage key_package;
} Update;
¶
The values in the following fields of the KeyPackage contained in an Update
proposal MUST be the same as those of the KeyPackage it replaces in the tree.
version, cipher_suite, credential.identity, endpoint_id. However, the
value of the credential.signature_key field of the new KeyPackage MUST be
different from that of all other KeyPackages in the tree. Furthermore, the value
of the hpke_init_key field of the new KeyPackage MUST be different from that
of the KeyPackage it replaces.¶
A member of the group applies an Update message by taking the following steps:¶
A Remove proposal requests that the member with KeyPackageID removed be removed
from the group.¶
struct {
KeyPackageID removed;
} Remove;
¶
A member of the group applies a Remove message by taking the following steps:¶
removed. This
lookup MUST be done on the tree before any non-Remove proposals have
been applied (the "old" tree in the terminology of Section 11.2), since
proposals such as Update can change the KeyPackage stored at a leaf.
Let removed_index be the node index of this leaf node.¶
removed_index with a blank node¶
removed_index to the root¶
A ReInit proposal represents a request to re-initialize the group with different parameters, for example, to increase the version number or to change the ciphersuite. The re-initialization is done by creating a completely new group and shutting down the old one.¶
struct {
opaque group_id<0..255>;
ProtocolVersion version;
CipherSuite cipher_suite;
Extension extensions<0..2^32-1>;
} ReInit;
¶
A member of the group applies a ReInit proposal by waiting for the committer to
send the Welcome message and by checking that the group_id and the parameters
of the new group corresponds to the ones specified in the proposal. The Welcome
message MUST specify exactly one pre-shared key with psktype = reinit, and with
psk_group_id and psk_epoch equal to the group_id and epoch of the
existing group after the Commit containing the reinit Proposal was processed.
The Welcome message may specify the inclusion of other pre-shared keys with a
psktype different from reinit.¶
If a ReInit proposal is included in a Commit, it MUST be the only proposal
referenced by the Commit. If other non-ReInit proposals have been sent during
the epoch, the committer SHOULD prefer them over the ReInit proposal, allowing
the ReInit to be resent and applied in a subsequent epoch. The version field
in the ReInit proposal MUST be no less than the version for the current group.¶
An ExternalInit proposal is used by new members that want to join a group by using an external commit. This propsal can only be used in that context.¶
struct {
opaque kem_output<0..2^16-1>;
} ExternalInit;
¶
A member of the group applies an ExternalInit message by initializing the next
epoch using an init secret computed as described in Section 8.1.
The kem_output field contains the required KEM output.¶
An AppAck proposal is used to acknowledge receipt of application messages. Though this information implies no change to the group, it is structured as a Proposal message so that it is included in the group's transcript by being included in Commit messages.¶
struct {
KeyPackageID sender;
uint32 first_generation;
uint32 last_generation;
} MessageRange;
struct {
MessageRange received_ranges<0..2^32-1>;
} AppAck;
¶
An AppAck proposal represents a set of messages received by the sender in the
current epoch. Messages are represented by the sender and generation values
in the MLSCiphertext for the message. Each MessageRange represents receipt of a
span of messages whose generation values form a continuous range from
first_generation to last_generation, inclusive.¶
AppAck proposals are sent as a guard against the Delivery Service dropping
application messages. The sequential nature of the generation field provides
a degree of loss detection, since gaps in the generation sequence indicate
dropped messages. AppAck completes this story by addressing the scenario where
the Delivery Service drops all messages after a certain point, so that a later
generation is never observed. Obviously, there is a risk that AppAck messages
could be suppressed as well, but their inclusion in the transcript means that if
they are suppressed then the group cannot advance at all.¶
The schedule on which sending AppAck proposals are sent is up to the application, and determines which cases of loss/suppression are detected. For example:¶
An application using AppAck proposals to guard against loss/suppression of application messages also needs to ensure that AppAck messages and the Commits that reference them are not dropped. One way to do this is to always encrypt Proposal and Commit messages, to make it more difficult for the Delivery Service to recognize which messages conatain AppAcks. The application can also have clients enforce an AppAck schedule, reporting loss if an AppAck is not received at the expected time.¶
A GroupContextExtensions proposal is used to update the list of extensions in the GroupContext for the group.¶
struct {
Extension extensions<0..2^32-1>;
} GroupContextExtensions;
¶
A member of the group applies a GroupContextExtensions proposal with the following steps:¶
required_capabilities extension, verify that
all members of the group support the required capabilities (including those
added in the same commit, and excluding those removed).¶
Note that once the GroupContext is updated, its inclusion in the confirmation_tag by way of the key schedule will confirm that all members of the group agree on the extensions in use.¶
Add and Remove proposals can be constructed and sent to the group by a party
that is outside the group. For example, a Delivery Service might propose to
remove a member of a group who has been inactive for a long time, or propose adding
a newly-hired staff member to a group representing a real-world team. Proposals
originating outside the group are identified by a preconfigured or
new_member SenderType in MLSPlaintext.¶
ReInit proposals can also be sent to the group by a preconfigured sender, for
example to enforce a changed policy regarding MLS version or ciphersuite.¶
The new_member SenderType is used for clients proposing that they themselves
be added. For this ID type the sender value MUST be zero and the Proposal type
MUST be Add. The MLSPlaintext MUST be signed with the private key corresponding
to the KeyPackage in the Add message. Recipients MUST verify that the
MLSPlaintext carrying the Proposal message is validly signed with this key.¶
The preconfigured SenderType is reserved for signers that are pre-provisioned
to the clients within a group. If proposals with these sender IDs are to be
accepted within a group, the members of the group MUST be provisioned by the
application with a mapping between these IDs and authorized signing keys.
Recipients MUST verify that the MLSPlaintext carrying the Proposal message is
validly signed with the corresponding key. To ensure consistent handling of
external proposals, the application MUST ensure that the members of a group
have the same mapping and apply the same policies to external proposals.¶
An external proposal MUST be sent as an MLSPlaintext object, since the sender will not have the keys necessary to construct an MLSCiphertext object.¶
A Commit message initiates a new epoch for the group, based on a collection of Proposals. It instructs group members to update their representation of the state of the group by applying the proposals and advancing the key schedule.¶
Each proposal covered by the Commit is included by a ProposalOrRef value, which identifies the proposal to be applied by value or by reference. Proposals supplied by value are included directly in the Commit object. Proposals supplied by reference are specified by including the hash of the MLSPlaintext in which the Proposal was sent, using the hash function from the group's ciphersuite. For proposals supplied by value, the sender of the proposal is the same as the sender of the Commit. Conversely, proposals sent by people other than the committer MUST be included by reference.¶
enum {
reserved(0),
proposal(1)
reference(2),
(255)
} ProposalOrRefType;
struct {
ProposalOrRefType type;
select (ProposalOrRef.type) {
case proposal: Proposal proposal;
case reference: opaque hash<0..255>;
}
} ProposalOrRef;
struct {
ProposalOrRef proposals<0..2^32-1>;
optional<UpdatePath> path;
} Commit;
¶
A group member that has observed one or more proposals within an epoch MUST send a Commit message before sending application data. This ensures, for example, that any members whose removal was proposed during the epoch are actually removed before any application data is transmitted.¶
The sender of a Commit MUST include all valid proposals that it has received during the current epoch. Invalid proposals include, for example, proposals with an invalid signature or proposals that are semantically invalid, such as an Add when the sender does not have the application-level permission to add new users. Proposals with a non-default proposal type MUST NOT be included in a commit unless the proposal type is supported by all the members of the group that will process the Commit (i.e., not including any members being added or removed by the Commit).¶
If there are multiple proposals that apply to the same leaf, the committer
chooses one and includes only that one in the Commit, considering the rest
invalid. The committer MUST prefer any Remove received, or the most recent
Update for the leaf if there are no Removes. If there are multiple Add proposals
containing KeyPackages with the same tuple (credential.identity, endpoint_id)
the committer again chooses one to include and considers the rest invalid. Add
proposals that contain KeyPackages with an (credential.identity, endpoint_id)
tuple that matches that of an existing KeyPackage in the group MUST be
considered invalid. The comitter MUST consider invalid any Add or Update
proposal if the Credential in the contained KeyPackage shares the same signature
key with a Credential in any leaf of the group, or indeed if the KeyPackage
shares the same hpke_init_key with another KeyPackage in the group.¶
The Commit MUST NOT combine proposals sent within different epochs. In the event that a valid proposal is omitted from the next Commit, the sender of the proposal SHOULD retransmit it in the new epoch.¶
A member of the group MAY send a Commit that references no proposals at all,
which would thus have an empty proposals vector. Such
a Commit resets the sender's leaf and the nodes along its direct path, and
provides forward secrecy and post-compromise security with regard to the sender
of the Commit. An Update proposal can be regarded as a "lazy" version of this
operation, where only the leaf changes and intermediate nodes are blanked out.¶
The path field of a Commit message MUST be populated if the Commit covers at
least one Update or Remove proposal. The path field MUST also be populated
if the Commit covers no proposals at all (i.e., if the proposals vector
is empty). The path field MAY be omitted if the Commit covers only Add
proposals. In pseudocode, the logic for validating a Commit is as follows:¶
hasUpdates = false
hasRemoves = false
for i, id in commit.proposals:
proposal = proposalCache[id]
assert(proposal != null)
hasUpdates = hasUpdates || proposal.msg_type == update
hasRemoves = hasRemoves || proposal.msg_type == remove
if len(commit.proposals) == 0 || hasUpdates || hasRemoves:
assert(commit.path != null)
¶
To summarize, a Commit can have three different configurations, with different uses:¶
When creating or processing a Commit, three different ratchet trees and their associated GroupContexts are used:¶
A member of the group creates a Commit message and the corresponding Welcome message at the same time, by taking the following steps:¶
proposals
field populated from Proposals received during the current epoch, and an empty
path field.¶
Generate the provisional ratchet tree and GroupContext by applying the proposals
referenced in the initial Commit object, as described in Section 11.1. Update
proposals are applied first, followed by Remove proposals, and then finally
Add proposals. Add proposals are applied in the order listed in the
proposals vector, and always to the leftmost unoccupied leaf in the tree, or
the right edge of the tree if all leaves are occupied.¶
path field: If the path field is required
based on the proposals that are in the commit (see above), then it MUST be
populated. Otherwise, the sender MAY omit the path field at its discretion.¶
If populating the path field: Create an UpdatePath using the provisional
ratchet tree and GroupContext. Any new member (from an add proposal) MUST be
exluded from the resolution during the computation of the UpdatePath. The
leaf_key_package for this UpdatePath must have a parent_hash extension.
Note that the KeyPackage in the UpdatePath effectively updates an existing
KeyPackage in the group and thus MUST adhere to the same restrictions as
KeyPackages used in Update proposals.¶
path field in the Commit.¶
commit_secret as the value path_secret[n+1] derived from the
path_secret[n] value assigned to the root node.¶
path field: Set the path field in the Commit to the
null optional. Define commit_secret as the all-zero vector of length
KDF.Nh (the same length as a path_secret value would be). In this case,
the new ratchet tree is the same as the provisional ratchet tree.¶
psk_secret as specified in Section 8.2, where the order
of PSKs in the derivation corresponds to the order of PreSharedKey proposals
in the proposals vector.¶
Construct an MLSPlaintext object containing the Commit object. Sign the MLSPlaintext using the old GroupContext as context.¶
init_secret from the previous epoch, the commit_secret and the
psk_secret as defined in the previous steps, and the new GroupContext to
compute the new joiner_secret, welcome_secret, epoch_secret, and
derived secrets for the new epoch.¶
confirmation_key for the new epoch to compute the
confirmation_tag value, and the membership_key for the old epoch to
compute the membership_tag value in the MLSPlaintext.¶
confirmation_tag from the MLSPlaintext.¶
Construct a GroupInfo reflecting the new state:¶
joiner_secret
for the new epoch (see Section 11.2.2)¶
For each new member in the group:¶
path field was populated above: Compute the path secret
corresponding to the common ancestor node¶
init_secret
for the current epoch and the path secret (if present).¶
psks MUST be the same as the order of PreSharedKey proposals in the
proposals vector.¶
PreSharedKeyID with psktype
reinit and with psk_group_id and psk_epoch corresponding to the current
group and the epoch after the commit was processed.¶
A member of the group applies a Commit message by taking the following steps:¶
epoch field of the enclosing MLSPlaintext message is equal
to the epoch field of the current GroupContext object¶
sender field.¶
proposals vector
are available.¶
Generate the provisional ratchet tree and GroupContext by applying the proposals
referenced in the initial Commit object, as described in Section 11.1. Update
proposals are applied first, followed by Remove proposals, and then finally
Add proposals. Add proposals are applied in the order listed in the
proposals vector, and always to the leftmost unoccupied leaf in the tree, or
the right edge of the tree if all leaves are occupied.¶
path value is populated if the proposals vector contains
any Update or Remove proposals, or if it's empty. Otherwise, the path value
MAY be omitted.¶
If the path value is populated: Process the path value using the
provisional ratchet tree and GroupContext, to generate the new ratchet tree
and the commit_secret:¶
leaf_key_package at the
Committer's leaf.¶
parent_hash extension and that its value
matches the new parent of the sender's leaf node.¶
commit_secret as the value path_secret[n+1] derived from the
path_secret[n] value assigned to the root node.¶
path value is not populated: Define commit_secret as the all-zero
vector of length KDF.Nh (the same length as a path_secret value would be).¶
psk_secret as specified in Section 8.2, where the order
of PSKs in the derivation corresponds to the order of PreSharedKey proposals
in the proposals vector.¶
init_secret from the previous epoch, the commit_secret and the
psk_secret as defined in the previous steps, and the new GroupContext to
compute the new joiner_secret, welcome_secret, epoch_secret, and
derived secrets for the new epoch.¶
confirmation_key for the new epoch to compute the confirmation tag
for this message, as described below, and verify that it is the same as the
confirmation_tag field in the MLSPlaintext object.¶
If the Commit included a ReInit proposal, the client MUST NOT use the group to send messages anymore. Instead, it MUST wait for a Welcome message from the committer and check that¶
version, cipher_suite and extensions fields of the new group
corresponds to the ones in the ReInit proposal, and that the version
is greater than or equal to that of the original group.¶
psks field in the Welcome message includes a PreSharedKeyID with
psktype = reinit, and psk_epoch and psk_group_id equal to the epoch
and group ID of the original group after processing the Commit.¶
The confirmation tag value confirms that the members of the group have arrived at the same state of the group:¶
MLSPlaintext.confirmation_tag =
MAC(confirmation_key, GroupContext.confirmed_transcript_hash)
¶
External Commits are a mechanism for new members (external parties that want to become members of the group) to add themselves to a group, without requiring that an existing member has to come online to issue a Commit that references an Add Proposal.¶
Whether existing members of the group will accept or reject an External Commit follows the same rules that are applied to other handshake messages.¶
New members can create and issue an External Commit if they have access to the following information for the group's current epoch:¶
This information is aggregated in a PublicGroupState object as follows:¶
struct {
CipherSuite cipher_suite;
opaque group_id<0..255>;
uint64 epoch;
opaque tree_hash<0..255>;
opaque interim_transcript_hash<0..255>;
Extension group_context_extensions<0..2^32-1>;
Extension other_extensions<0..2^32-1>;
HPKEPublicKey external_pub;
KeyPackageID signer;
opaque signature<0..2^16-1>;
} PublicGroupState;
¶
Note that the tree_hash field is used the same way as in the Welcome message.
The full tree can be included via the ratchet_tree extension
Section 11.3.¶
The signature MUST verify using the public key taken from the credential in the
leaf node of the member with KeyPackageID signer. The signature covers the
following structure, comprising all the fields in the PublicGroupState above
signature:¶
struct {
opaque group_id<0..255>;
uint64 epoch;
opaque tree_hash<0..255>;
opaque interim_transcript_hash<0..255>;
Extension group_context_extensions<0..2^32-1>;
Extension other_extensions<0..2^32-1>;
HPKEPublicKey external_pub;
KeyPackageID signer;
} PublicGroupStateTBS;
¶
This signature authenticates the HPKE public key, so that the joiner knows that
the public key was provided by a member of the group. The fields that are not
signed are included in the key schedule via the GroupContext object. If the
joiner is provided an inaccurate data for these fields, then its external Commit
will have an incorrect confirmation_tag and thus be rejected.¶
The information in a PublicGroupState is not deemed public in general, but applications can choose to make it available to new members in order to allow External Commits.¶
External Commits work like regular Commits, with a few differences:¶
The proposals included by value in an External Commit MUST meet the following conditions:¶
credential and endpoint_id of
the removed leaf MUST be the same as the corresponding values in the Add
KeyPackage.¶
The proposals included by reference in an External Commit MUST meet the following conditions:¶
path field (and is therefore a "full"
Commit)¶
leaf_key_package of the path field.¶
new_member¶
In other words, External Commits come in two "flavors" -- a "join" commit that adds the sender to the group or a "resync" commit that replaces a member's prior appearance with a new one.¶
Note that the "resync" operation allows an attacker that has compromised a member's signature private key to introduce themselves into the group and remove the prior, legitimate member in a single Commit. Without resync, this can still be done, but requires two operations, the external Commit to join and a second Commit to remove the old appearance. Applications for whom this distinction is salient can choose to disallow external commits that contain a Remove, or to allow such resync commits only if they contain a "reinit" PSK proposal that demonstrates the joining member's presence in a prior epoch of the group. With the latter approach, the attacke would need to compromise the PSK as well as the signing key, but the application will need to ensure that continuing, non-resync'ing members have the required PSK.¶
The sender of a Commit message is responsible for sending a Welcome message to any new members added via Add proposals. The Welcome message provides the new members with the current state of the group, after the application of the Commit message. The new members will not be able to decrypt or verify the Commit message, but will have the secrets they need to participate in the epoch initiated by the Commit message.¶
In order to allow the same Welcome message to be sent to all new members,
information describing the group is encrypted with a symmetric key and nonce
derived from the joiner_secret for the new epoch. The joiner_secret is
then encrypted to each new member using HPKE. In the same encrypted package,
the committer transmits the path secret for the lowest node contained in the
direct paths of both the committer and the new member. This allows the new
member to compute private keys for nodes in its direct path that are being
reset by the corresponding Commit.¶
If the sender of the Welcome message wants the receiving member to include a PSK
in the derivation of the epoch_secret, they can populate the psks field indicating which
PSK to use.¶
struct {
opaque group_id<0..255>;
uint64 epoch;
opaque tree_hash<0..255>;
opaque confirmed_transcript_hash<0..255>;
Extension group_context_extensions<0..2^32-1>;
Extension other_extensions<0..2^32-1>;
MAC confirmation_tag;
KeyPackageID signer;
opaque signature<0..2^16-1>;
} GroupInfo;
struct {
opaque path_secret<1..255>;
} PathSecret;
struct {
opaque joiner_secret<1..255>;
optional<PathSecret> path_secret;
PreSharedKeys psks;
} GroupSecrets;
struct {
KeyPackageID new_member<1..255>;
HPKECiphertext encrypted_group_secrets;
} EncryptedGroupSecrets;
struct {
ProtocolVersion version = mls10;
CipherSuite cipher_suite;
EncryptedGroupSecrets secrets<0..2^32-1>;
opaque encrypted_group_info<1..2^32-1>;
} Welcome;
¶
The client processing a Welcome message will need to have a copy of the group's
ratchet tree. The tree can be provided in the Welcome message, in an extension
of type ratchet_tree. If it is sent otherwise (e.g., provided by a caching
service on the Delivery Service), then the client MUST download the tree before
processing the Welcome.¶
On receiving a Welcome message, a client processes it using the following steps:¶
secrets array where the new_member
value corresponds to one of this client's KeyPackages, using the hash
indicated by the cipher_suite field. If no such field exists, or if the
ciphersuite indicated in the KeyPackage does not match the one in the
Welcome message, return an error.¶
encrypted_group_secrets using HPKE with the algorithms indicated
by the ciphersuite and the HPKE private key corresponding to the GroupSecrets.
If a PreSharedKeyID is part of the GroupSecrets and the client is not in
possession of the corresponding PSK, return an error.¶
joiner_secret in the decrypted GroupSecrets object and the PSKs
specified in the GroupSecrets, derive the welcome_secret and using that
the welcome_key and welcome_nonce. Use the key and nonce to decrypt the
encrypted_group_info field.¶
welcome_nonce = KDF.Expand(welcome_secret, "nonce", AEAD.Nn) welcome_key = KDF.Expand(welcome_secret, "key", AEAD.Nk)¶
signer. If there is no matching leaf node, or if
signature verification fails, return an error.¶
Verify the integrity of the ratchet tree.¶
tree_hash field
in the GroupInfo.¶
parent_hash value (if the child is another parent) or has a parent_hash
extension in the KeyPackage containing the same value (if the child is a
leaf). If either of the node's children is empty, and in particular does not
have a parent hash, then its respective children's parent_hash values have
to be considered instead.¶
tree array (any even-numbered node) whose
key_package field is identical to the KeyPackage. If no such field
exists, return an error. Let index represent the index of this node in the
tree.¶
Construct a new group state using the information in the GroupInfo object.¶
group_id, epoch, tree_hash,
confirmed_transcript_hash, and group_context_extensions fields from
the GroupInfo object.¶
index, as defined above.¶
index with the private key corresponding to the
public key in the node.¶
path_secret value is set in the GroupSecrets object: Identify the
lowest common ancestor of the node index index and of the node index of
the member with KeyPackageID GroupInfo.signer. Set the private key for
this node to the private key derived from the path_secret.¶
joiner_secret from the GroupSecrets object to generate the epoch secret
and other derived secrets for the current epoch.¶
confirmed_transcript_hash in the GroupInfo.¶
confirmed_transcript_hash from the GroupInfo.¶
By default, a GroupInfo message only provides the joiner with a commitment to the group's ratchet tree. In order to process or generate handshake messages, the joiner will need to get a copy of the ratchet tree from some other source. (For example, the DS might provide a cached copy.) The inclusion of the tree hash in the GroupInfo message means that the source of the ratchet tree need not be trusted to maintain the integrity of tree.¶
In cases where the application does not wish to provide such an external source,
the whole public state of the ratchet tree can be provided in an extension of
type ratchet_tree, containing a ratchet_tree object of the following form:¶
enum {
reserved(0),
leaf(1),
parent(2),
(255)
} NodeType;
struct {
NodeType node_type;
select (Node.node_type) {
case leaf: KeyPackage key_package;
case parent: ParentNode node;
};
} Node;
optional<Node> ratchet_tree<1..2^32-1>;
¶
The presence of a ratchet_tree extension in a GroupInfo message does not
result in any changes to the GroupContext extensions for the group. The ratchet
tree provided is simply stored by the client and used for MLS operations.¶
If this extension is not provided in a Welcome message, then the client will need to fetch the ratchet tree over some other channel before it can generate or process Commit messages. Applications should ensure that this out-of-band channel is provided with security protections equivalent to the protections that are afforded to Proposal and Commit messages. For example, an application that encrypts Proposal and Commit messages might distribute ratchet trees encrypted using a key exchanged over the MLS channel.¶
This protocol includes a mechanism for negotiating extension parameters similar to the one in TLS [RFC8446]. In TLS, extension negotiation is one-to-one: The client offers extensions in its ClientHello message, and the server expresses its choices for the session with extensions in its ServerHello and EncryptedExtensions messages. In MLS, extensions appear in the following places:¶
In other words, an application can use GroupContext extensions to ensure that
all members of the group agree on a set of parameters. Clients indicate
their support for parameters in KeyPackage extensions. New members of a
group are informed of the group's GroupContext extensions via the
group_context_extensions field in the GroupInfo or PublicGroupState object.
The other_extensions field in a GroupInfo object can be used to provide
additional parameters to new joiners that are used to join the group.¶
This extension mechanism is designed to allow for secure and forward-compatible negotiation of extensions. For this to work, implementations MUST correctly handle extensible fields:¶
Note that the latter two requirements mean that all MLS extensions are mandatory, in the sense that an extension in use by the group MUST be supported by all members of the group.¶
This document does not define any way for the parameters of the group to change once it has been created; such a behavior could be implemented as an extension.¶
Each Commit message is premised on a given starting state,
indicated by the epoch field of the enclosing MLSPlaintext
message. If the changes implied by a Commit messages are made
starting from a different state, the results will be incorrect.¶
This need for sequencing is not a problem as long as each time a group member sends a Commit message, it is based on the most current state of the group. In practice, however, there is a risk that two members will generate Commit messages simultaneously, based on the same state.¶
When this happens, there is a need for the members of the group to deconflict the simultaneous Commit messages. There are two general approaches:¶
As long as Commit messages cannot be merged, there is a risk of starvation. In a sufficiently busy group, a given member may never be able to send a Commit message, because he always loses to other members. The degree to which this is a practical problem will depend on the dynamics of the application.¶
It might be possible, because of the non-contributivity of intermediate nodes, that Commit messages could be applied one after the other without the Delivery Service having to reject any Commit message, which would make MLS more resilient regarding the concurrency of Commit messages. The Messaging system can decide to choose the order for applying the state changes. Note that there are certain cases (if no total ordering is applied by the Delivery Service) where the ordering is important for security, ie. all updates must be executed before removes.¶
Regardless of how messages are kept in sequence, implementations MUST only update their cryptographic state when valid Commit messages are received. Generation of Commit messages MUST NOT modify a client's state, since the endpoint doesn't know at that time whether the changes implied by the Commit message will succeed or not.¶
With this approach, the Delivery Service ensures that incoming messages are added to an ordered queue and outgoing messages are dispatched in the same order. The server is trusted to break ties when two members send a Commit message at the same time.¶
Messages should have a counter field sent in clear-text that can be checked by the server and used for tie-breaking. The counter starts at 0 and is incremented for every new incoming message. If two group members send a message with the same counter, the first message to arrive will be accepted by the server and the second one will be rejected. The rejected message needs to be sent again with the correct counter number.¶
To prevent counter manipulation by the server, the counter's integrity can be ensured by including the counter in a signed message envelope.¶
This applies to all messages, not only state changing messages.¶
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.¶
The primary purpose of the Handshake protocol is to provide an authenticated group key exchange to clients. In order to protect Application messages sent among the members of a group, the Application secret provided by the Handshake key schedule is used to derive nonces and encryption keys for the Message Protection Layer according to the Application Key Schedule. That is, each epoch is equipped with a fresh Application Key Schedule which consist of a tree of Application Secrets as well as one symmetric ratchet per group member.¶
Each client maintains their own local copy of the Application Key Schedule for each epoch during which they are a group member. They derive new keys, nonces and secrets as needed while deleting old ones as soon as they have been used.¶
Application messages MUST be protected with the Authenticated-Encryption with Associated-Data (AEAD) encryption scheme associated with the MLS ciphersuite using the common framing mechanism. Note that "Authenticated" in this context does not mean messages are known to be sent by a specific client but only from a legitimate member of the group. To authenticate a message from a particular member, signatures are required. Handshake messages MUST use asymmetric signatures to strongly authenticate the sender of a message.¶
The group members MUST use the AEAD algorithm associated with the negotiated MLS ciphersuite to AEAD encrypt and decrypt their Application messages according to the Message Framing section.¶
The group identifier and epoch allow a recipient to know which group secrets should be used and from which Epoch secret to start computing other secrets and keys. The sender identifier is used to identify the member's symmetric ratchet from the initial group Application secret. The application generation field is used to determine how far into the ratchet to iterate in order to reproduce the required AEAD keys and nonce for performing decryption.¶
Application messages SHOULD be padded to provide some resistance against traffic analysis techniques over encrypted traffic. [CLINIC] [HCJ16] While MLS might deliver the same payload less frequently across a lot of ciphertexts than traditional web servers, it might still provide the attacker enough information to mount an attack. If Alice asks Bob: "When are we going to the movie ?" the answer "Wednesday" might be leaked to an adversary by the ciphertext length. An attacker expecting Alice to answer Bob with a day of the week might find out the plaintext by correlation between the question and the length.¶
Similarly to TLS 1.3, if padding is used, the MLS messages MUST be padded with zero-valued bytes before AEAD encryption. Upon AEAD decryption, the length field of the plaintext is used to compute the number of bytes to be removed from the plaintext to get the correct data. As the padding mechanism is used to improve protection against traffic analysis, removal of the padding SHOULD be implemented in a "constant-time" manner at the MLS layer and above layers to prevent timing side-channels that would provide attackers with information on the size of the plaintext. The padding length length_of_padding can be chosen at the time of the message encryption by the sender. Recipients can calculate the padding size from knowing the total size of the ApplicationPlaintext and the length of the content.¶
During each epoch senders MUST NOT encrypt more data than permitted by the security bounds of the AEAD scheme used.¶
Note that each change to the Group through a Handshake message will also set a
new encryption_secret. Hence this change MUST be applied before encrypting
any new application message. This is required both to ensure that any users
removed from the group can no longer receive messages and to (potentially)
recover confidentiality and authenticity for future messages despite a past
state compromise.¶
Since each Application message contains the group identifier, the epoch and a message counter, a client can receive messages out of order. If they are able to retrieve or recompute the correct AEAD decryption key from currently stored cryptographic material clients can decrypt these messages.¶
For usability, MLS clients might be required to keep the AEAD key and nonce for a certain amount of time to retain the ability to decrypt delayed or out of order messages, possibly still in transit while a decryption is being done.¶
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.¶
Group secrets are partly derived from the output of a ratchet tree. Ratchet trees work by assigning each member of the group to a leaf in the tree and maintaining the following property: the private key of a node in the tree is known only to members of the group that are assigned a leaf in the node's subtree. This is called the ratchet tree invariant and it makes it possible to encrypt to all group members except one, with a number of ciphertexts that's logarithmic in the number of group members.¶
The ability to efficiently encrypt to all members except one allows members to be securely removed from a group. It also allows a member to rotate their keypair such that the old private key can no longer be used to decrypt new messages.¶
The first form of authentication we provide is that group members can verify a
message originated from one of the members of the group. For encrypted messages,
this is guaranteed because messages are encrypted with an AEAD under a key
derived from the group secrets. For plaintext messages, this is guaranteed by
the use of a membership_tag which constitutes a MAC over the message, under a
key derived from the group secrets.¶
The second form of authentication is that group members can verify a message originated from a particular member of the group. This is guaranteed by a digital signature on each message from the sender's signature key.¶
The signature keys held by group members are critical to the security of MLS against active attacks. If a member's signature key is compromised, then an attacker can create KeyPackages impersonating the member; depending on the application, this can then allow the attacker to join the group with the compromised member's identity. For example, if a group has enabled external parties to join via external commits, then an attacker that has compromised a member's signature key could use an external commit to insert themselves into the group -- even using a "resync"-style external commit to replace the compromised member in the group.¶
Applications can mitigate the risks of signature key compromise using pre-shared keys. If a group requires joiners to know a PSK in addition to authenticating with a credential, then in order to mount an impersonation attack, the attacker would need to compromise the relevant PSK as well as the victim's signature key. The cost of this mitigation is that the application needs some external arrangement that ensures that the legitimate members of the group to have the required PSKs.¶
Post-compromise security is provided between epochs by members regularly updating their leaf key in the ratchet tree. Updating their leaf key prevents group secrets from continuing to be encrypted to previously compromised public keys.¶
Forward-secrecy between epochs is provided by deleting private keys from past version of the ratchet tree, as this prevents old group secrets from being re-derived. Forward secrecy within an epoch is provided by deleting message encryption keys once they've been used to encrypt or decrypt a message.¶
Post-compromise security is also provided for new groups by members regularly generating new InitKeys and uploading them to the Delivery Service, such that compromised key material won't be used when the member is added to a new group.¶
InitKeys are intended to be used only once. That is, once an InitKey has been used to introduce the corresponding client to a group, it SHOULD be deleted from the InitKey publication system. Reuse of InitKeys can lead to replay attacks.¶
An application MAY allow for reuse of a "last resort" InitKey in order to prevent denial of service attacks. Since an InitKey is needed to add a client to a new group, an attacker could prevent a client being added to new groups by exhausting all available InitKeys.¶
It is possible for a malicious member of a group to "fragment" the group by crafting an invalid UpdatePath. Recall that an UpdatePath encrypts a sequence of path secrets to different subtrees of the group's ratchet trees. These path secrets should be derived in a sequence as described in Section 5.4, but the UpdatePath syntax allows the sender to encrypt arbitrary, unrelated secrets. The syntax also does not guarantee that the encrypted path secret encrypted for a given node corresponds to the public key provided for that node.¶
Both of these types of corruption will cause processing of a Commit to fail for some members of the group. If the public key for a node does not match the path secret, then the members that decrypt that path secret will reject the commit based on this mismatch. If the path secret sequence is incorrect at some point, then members that can decrypt nodes before that point will compute a different public key for the mismatched node than the one in the UpdatePath, which also causes the Commit to fail. Applications SHOULD provide mechanisms for failed commits to be reported, so that group members who were not able to recognize the error themselves can reject the commit and roll back to a previous state if necessary.¶
Even with such an error reporting mechanism in place, however, it is still possible for members to get locked out of the group by a malformed commit. Since malformed Commits can only be recognized by certain members of the group, in an asynchronous application, it may be the case that all members that could detect a fault in a Commit are offline. In such a case, the Commit will be accepted by the group, and the resulting state possibly used as the basis for further Commits. When the affected members come back online, they will reject the first commit, and thus be unable to catch up with the group.¶
Applications can address this risk by requiring certain members of the group to acknowledge successful processing of a Commit before the group regards the Commit as accepted. The minimum set of acknowledgements necessary to verify that a Commit is well-formed comprises an acknowledgement from one member per node in the UpdatePath, that is, one member from each subtree rooted in the copath node corresponding to the node in the UpdatePath.¶
This document requests the creation of the following new IANA registries:¶
All of these registries should be under a heading of "Messaging Layer Security", and assignments are made via the Specification Required policy [RFC8126]. See Section 16.5 for additional information about the MLS Designated Experts (DEs).¶
RFC EDITOR: Please replace XXXX throughout with the RFC number assigned to this document¶
A ciphersuite is a combination of a protocol version and the set of cryptographic algorithms that should be used.¶
Ciphersuite names follow the naming convention:¶
CipherSuite MLS_LVL_KEM_AEAD_HASH_SIG = VALUE;¶
Where VALUE is represented as a sixteen-bit integer:¶
uint16 CipherSuite;¶
| Component | Contents |
|---|---|
| MLS | The string "MLS" followed by the major and minor version, e.g. "MLS10" |
| LVL | The security level |
| KEM | The KEM algorithm used for HPKE in TreeKEM group operations |
| AEAD | The AEAD algorithm used for HPKE and message protection |
| HASH | The hash algorithm used for HPKE and the MLS transcript hash |
| SIG | The Signature algorithm used for message authentication |
The columns in the registry are as follows:¶
Initial contents:¶
| Value | Name | Recommended | Reference |
|---|---|---|---|
| 0x0000 | RESERVED | N/A | RFC XXXX |
| 0x0001 | MLS10_128_DHKEMX25519_AES128GCM_SHA256_Ed25519 | Y | RFC XXXX |
| 0x0002 | MLS10_128_DHKEMP256_AES128GCM_SHA256_P256 | Y | RFC XXXX |
| 0x0003 | MLS10_128_DHKEMX25519_CHACHA20POLY1305_SHA256_Ed25519 | Y | RFC XXXX |
| 0x0004 | MLS10_256_DHKEMX448_AES256GCM_SHA512_Ed448 | Y | RFC XXXX |
| 0x0005 | MLS10_256_DHKEMP521_AES256GCM_SHA512_P521 | Y | RFC XXXX |
| 0x0006 | MLS10_256_DHKEMX448_CHACHA20POLY1305_SHA512_Ed448 | Y | RFC XXXX |
| 0xff00 - 0xffff | Reserved for Private Use | N/A | RFC XXXX |
All of these ciphersuites use HMAC [RFC2104] as their MAC function, with different hashes per ciphersuite. The mapping of ciphersuites to HPKE primitives, HMAC hash functions, and TLS signature schemes is as follows [I-D.irtf-cfrg-hpke] [RFC8446]:¶
| Value | KEM | KDF | AEAD | Hash | Signature |
|---|---|---|---|---|---|
| 0x0001 | 0x0020 | 0x0001 | 0x0001 | SHA256 | ed25519 |
| 0x0002 | 0x0010 | 0x0001 | 0x0001 | SHA256 | ecdsa_secp256r1_sha256 |
| 0x0003 | 0x0020 | 0x0001 | 0x0003 | SHA256 | ed25519 |
| 0x0004 | 0x0021 | 0x0003 | 0x0002 | SHA512 | ed448 |
| 0x0005 | 0x0012 | 0x0003 | 0x0002 | SHA512 | ecdsa_secp521r1_sha512 |
| 0x0006 | 0x0021 | 0x0003 | 0x0003 | SHA512 | ed448 |
The hash used for the MLS transcript hash is the one referenced in the ciphersuite name. In the ciphersuites defined above, "SHA256" and "SHA512" refer to the SHA-256 and SHA-512 functions defined in [SHS].¶
It is advisable to keep the number of ciphersuites low to increase the chances clients can interoperate in a federated environment, therefore the ciphersuites only inlcude modern, yet well-established algorithms. Depending on their requirements, clients can choose between two security levels (roughly 128-bit and 256-bit). Within the security levels clients can choose between faster X25519/X448 curves and FIPS 140-2 compliant curves for Diffie-Hellman key negotiations. Additionally clients that run predominantly on mobile processors can choose ChaCha20Poly1305 over AES-GCM for performance reasons. Since ChaCha20Poly1305 is not listed by FIPS 140-2 it is not paired with FIPS 140-2 compliant curves. The security level of symmetric encryption algorithms and hash functions is paired with the security level of the curves.¶
The mandatory-to-implement ciphersuite for MLS 1.0 is
MLS10_128_DHKEMX25519_AES128GCM_SHA256_Ed25519 which uses
Curve25519 for key exchange, AES-128-GCM for HPKE, HKDF over SHA2-256, and
Ed25519 for signatures.¶
Values with the first byte 255 (decimal) are reserved for Private Use.¶
New ciphersuite values are assigned by IANA as described in Section 16.¶
This registry lists identifiers for extensions to the MLS protocol. The extension type field is two bytes wide, so valid extension type values are in the range 0x0000 to 0xffff.¶
Template:¶
Message(s): The messages in which the extension may appear, drawn from the following list:¶
Initial contents:¶
| Value | Name | Message(s) | Recommended | Reference |
|---|---|---|---|---|
| 0x0000 | RESERVED | N/A | N/A | RFC XXXX |
| 0x0001 | capabilities | KP | Y | RFC XXXX |
| 0x0002 | lifetime | KP | Y | RFC XXXX |
| 0x0003 | external_key_id | KP | Y | RFC XXXX |
| 0x0004 | parent_hash | KP | Y | RFC XXXX |
| 0x0005 | ratchet_tree | GI | Y | RFC XXXX |
| 0xff00 - 0xffff | Reserved for Private Use | N/A | N/A | RFC XXXX |
This registry lists identifiers for types of proposals that can be made for changes to an MLS group. The extension type field is two bytes wide, so valid extension type values are in the range 0x0000 to 0xffff.¶
Template:¶
Initial contents:¶
| Value | Name | Recommended | Reference |
|---|---|---|---|
| 0x0000 | RESERVED | N/A | RFC XXXX |
| 0x0001 | add | Y | RFC XXXX |
| 0x0002 | update | Y | RFC XXXX |
| 0x0003 | remove | Y | RFC XXXX |
| 0x0004 | psk | Y | RFC XXXX |
| 0x0005 | reinit | Y | RFC XXXX |
| 0x0006 | external_init | Y | RFC XXXX |
| 0x0007 | app_ack | Y | RFC XXXX |
| 0x0008 | group_context_extensions | Y | RFC XXXX |
| 0xff00 - 0xffff | Reserved for Private Use | N/A | RFC XXXX |
This registry lists identifiers for types of credentials that can be used for authentication in the MLS protocol. The credential type field is two bytes wide, so valid credential type values are in the range 0x0000 to 0xffff.¶
Template:¶
Initial contents:¶
| Value | Name | Recommended | Reference |
|---|---|---|---|
| 0x0000 | RESERVED | N/A | RFC XXXX |
| 0x0001 | basic | Y | RFC XXXX |
| 0x0002 | x509 | Y | RFC XXXX |
| 0xff00 - 0xffff | Reserved for Private Use | N/A | RFC XXXX |
Specification Required [RFC8126] registry requests are registered after a three-week review period on the MLS DEs' mailing list: mls-reg-review@ietf.org, on the advice of one or more of the MLS DEs. However, to allow for the allocation of values prior to publication, the MLS DEs may approve registration once they are satisfied that such a specification will be published.¶
Registration requests sent to the MLS DEs mailing list for review SHOULD use an appropriate subject (e.g., "Request to register value in MLS Bar registry").¶
Within the review period, the MLS DEs will either approve or deny the registration request, communicating this decision to the MLS DEs mailing list and IANA. Denials SHOULD include an explanation and, if applicable, suggestions as to how to make the request successful. Registration requests that are undetermined for a period longer than 21 days can be brought to the IESG's attention for resolution using the iesg@ietf.org mailing list.¶
Criteria that SHOULD be applied by the MLS DEs includes determining whether the proposed registration duplicates existing functionality, whether it is likely to be of general applicability or useful only for a single application, and whether the registration description is clear. For example, the MLS DEs will apply the ciphersuite-related advisory found in Section 6.1.¶
IANA MUST only accept registry updates from the MLS DEs and SHOULD direct all requests for registration to the MLS DEs' mailing list.¶
It is suggested that multiple MLS DEs be appointed who are able to represent the perspectives of different applications using this specification, in order to enable broadly informed review of registration decisions. In cases where a registration decision could be perceived as creating a conflict of interest for a particular MLS DE, that MLS DE SHOULD defer to the judgment of the other MLS DEs.¶
One benefit of using left-balanced trees is that they admit a simple flat array representation. In this representation, leaf nodes are even-numbered nodes, with the n-th leaf at 2*n. Intermediate nodes are held in odd-numbered nodes. For example, an 11-element tree has the following structure:¶
X
X
X X X
X X X X X
X X X X X X X X X X X
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
¶
This allows us to compute relationships between tree nodes simply by
manipulating indices, rather than having to maintain complicated
structures in memory, even for partial trees. The basic
rule is that the high-order bits of parent and child nodes have the
following relation (where x is an arbitrary bit string):¶
parent=01x => left=00x, right=10x¶
The following python code demonstrates the tree computations necessary for MLS. Test vectors can be derived from the diagram above.¶
# The exponent of the largest power of 2 less than x. Equivalent to:
# int(math.floor(math.log(x, 2)))
def log2(x):
if x == 0:
return 0
k = 0
while (x >> k) > 0:
k += 1
return k-1
# The level of a node in the tree. Leaves are level 0, their parents are
# level 1, etc. If a node's children are at different levels, then its
# level is the max level of its children plus one.
def level(x):
if x & 0x01 == 0:
return 0
k = 0
while ((x >> k) & 0x01) == 1:
k += 1
return k
# The number of nodes needed to represent a tree with n leaves.
def node_width(n):
if n == 0:
return 0
else:
return 2*(n - 1) + 1
# The index of the root node of a tree with n leaves.
def root(n):
w = node_width(n)
return (1 << log2(w)) - 1
# The left child of an intermediate node. Note that because the tree is
# left-balanced, there is no dependency on the size of the tree.
def left(x):
k = level(x)
if k == 0:
raise Exception('leaf node has no children')
return x ^ (0x01 << (k - 1))
# The right child of an intermediate node. Depends on the number of
# leaves because the straightforward calculation can take you beyond the
# edge of the tree.
def right(x, n):
k = level(x)
if k == 0:
raise Exception('leaf node has no children')
r = x ^ (0x03 << (k - 1))
while r >= node_width(n):
r = left(r)
return r
# The immediate parent of a node. May be beyond the right edge of the
# tree.
def parent_step(x):
k = level(x)
b = (x >> (k + 1)) & 0x01
return (x | (1 << k)) ^ (b << (k + 1))
# The parent of a node. As with the right child calculation, we have to
# walk back until the parent is within the range of the tree.
def parent(x, n):
if x == root(n):
raise Exception('root node has no parent')
p = parent_step(x)
while p >= node_width(n):
p = parent_step(p)
return p
# The other child of the node's parent.
def sibling(x, n):
p = parent(x, n)
if x < p:
return right(p, n)
else:
return left(p)
# The direct path of a node, ordered from leaf to root.
def direct_path(x, n):
r = root(n)
if x == r:
return []
d = []
while x != r:
x = parent(x, n)
d.append(x)
return d
# The copath of a node, ordered from leaf to root.
def copath(x, n):
if x == root(n):
return []
d = direct_path(x, n)
d.insert(0, x)
d.pop()
return [sibling(y, n) for y in d]
# The common ancestor of two nodes is the lowest node that is in the
# direct paths of both leaves.
def common_ancestor_semantic(x, y, n):
dx = set([x]) | set(direct_path(x, n))
dy = set([y]) | set(direct_path(y, n))
dxy = dx & dy
if len(dxy) == 0:
raise Exception('failed to find common ancestor')
return min(dxy, key=level)
# The common ancestor of two nodes is the lowest node that is in the
# direct paths of both leaves.
def common_ancestor_direct(x, y, _):
# Handle cases where one is an ancestor of the other
lx, ly = level(x)+1, level(y)+1
if (lx <= ly) and (x>>ly == y>>ly):
return y
elif (ly <= lx) and (x>>lx == y>>lx):
return x
# Handle other cases
xn, yn = x, y
k = 0
while xn != yn:
xn, yn = xn >> 1, yn >> 1
k += 1
return (xn << k) + (1 << (k-1)) - 1
¶