| Internet-Draft | MLS | March 2022 |
| Barnes, et al. | Expires 8 September 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 8 September 2022.¶
Copyright (c) 2022 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 Revised BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Revised 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.¶
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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 group represents a logical collection of clents that share a common secret value at any given time. Its state is represented as a linear sequence of epochs in which each epoch depends on its predecessor.¶
A state of a group in which a specific set of authenticated clients hold 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 [RFC9180]) public key that can be used to encrypt to that client, and 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.¶
An MLSPlaintext or MLSCiphertext message carrying an MLS Proposal or Commit object, as opposed to application data.¶
An MLSCiphertext message carrying application data.¶
Terminology specific to tree computations is described in Section 5.1.¶
We use the TLS presentation language [RFC8446] to describe the structure of protocol messages. In addition to the base syntax, we add two additional features, the ability for fields to be optional and the ability for vectors to have variable-size length headers.¶
An optional value is encoded with a presence-signaling octet, followed by the value itself if present. When decoding, a presence octet with a value other than 0 or 1 MUST be rejected as malformed.¶
struct {
uint8 present;
select (present) {
case 0: struct{};
case 1: T value;
}
} optional<T>;
¶
In the TLS presentation language, vectors are encoded as a sequence of encoded elements prefixed with a length. The length field has a fixed size set by specifying the minimum and maximum lengths of the encoded sequence of elements.¶
In MLS, there are several vectors whose sizes vary over significant ranges. So
instead of using a fixed-size length field, we use a variable-size length using
a variable-length integer encoding based on the one in Section 16 of
[RFC9000]. (They differ only in that the one here requires a minimum-size
encoding.) Instead of presenting min and max values, the vector description
simply includes a V. For example:¶
struct {
uint32 fixed<0..255>;
opaque variable<V>;
} StructWithVectors;
¶
Such a vector can represent values with length from 0 bytes to 2^30 bytes. The variable-length integer encoding reserves the two most significant bits of the first byte to encode the base 2 logarithm of the integer encoding length in bytes. The integer value is encoded on the remaining bits, in network byte order. The encoded value MUST use the smallest number of bits required to represent the value. When decoding, values using more bits than necessary MUST be treated as malformed.¶
This means that integers are encoded on 1, 2, or 4 bytes and can encode 6-, 14-, or 30-bit values respectively.¶
| Prefix | Length | Usable Bits | Min | Max |
|---|---|---|---|---|
| 00 | 1 | 6 | 0 | 63 |
| 01 | 2 | 14 | 64 | 16383 |
| 10 | 4 | 30 | 16384 | 1073741823 |
| 11 | invalid | - | - | - |
Vectors that start with "11" prefix are invalid and MUST be rejected.¶
For example, the four byte sequence 0x9d7f3e7d decodes to 494878333; the two byte sequence 0x7bbd decodes to 15293; and the single byte 0x25 decodes to 37.¶
The following figure adapts the pseudocode provided in [RFC9000] to add a check for minimum-length encoding:¶
ReadVarint(data):
// The length of variable-length integers is encoded in the
// first two bits of the first byte.
v = data.next_byte()
prefix = v >> 6
length = 1 << prefix
// Once the length is known, remove these bits and read any
// remaining bytes.
v = v & 0x3f
repeat length-1 times:
v = (v << 8) + data.next_byte()
return v
// Check that the encoder used the minimum bits required
if length > 1 && v < (1 << (length - 1)):
raise an exception
¶
The use of variable-size integers for vector lengths allows vectors to grow very large, up to 2^30 bytes. Implementations should take care not to allow vectors to overflow available storage. To facilitate debugging of potential interoperatbility problems, implementations should provide a clear error when such an overflow condition occurs.¶
MLS is designed to operate in the context described in [I-D.ietf-mls-architecture]. In particular, we assume that the following services are provided:¶
The core functionality of MLS is continuous group authenticated key exchange (AKE). As with other authenticated key exchange protocols (such as TLS), the participants in the protocol agree on a common secret value, and each participant can verify the identity of the other participants. MLS provides group AKE in the sense that there can be more than two participants in the protocol, and continuous group AKE in the sense that the set of participants in the protocol can change over time.¶
The core organizing principles of MLS are groups and epochs. A group represents a logical collection of clients that share a common secret value at any given time. The history of a group is divided into a linear sequence of epochs. In each epoch, a set of authenticated members agree on an epoch secret that is known only to the members of the group in that epoch. The set of members involved in the group can change from one epoch to the next, and MLS ensures that only the members in the current epoch have access to the epoch secret. From the epoch secret, members derive further shared secrets for message encryption, group membership authentication, etc.¶
The creator of an MLS group creates the group's first epoch unilaterally, with no protocol interactions. Thereafter, the members of the group advance their shared cryptographic state from one epoch to another by exchanging MLS messages:¶
KeyPackage and Welcome messages are used to initiate a group or introduce new members, so they are exchanged between group members and clients not yet in the group.¶
Proposal and Commit messages are sent from one member of a group to the others. MLS provides a common framing layer for sending messages within a group: An MLSPlaintext message provides sender authentication for unencrypted Proposal and Commit messages. An MLSCiphertext message provides encryption and authentication for both Proposal/Commit messages as well as any application data.¶
The cryptographic state at the core of MLS is divided into three areas of responsibility:¶
epoch_secret
_ | _
|\ Ratchet / ... \ Secret /|
| \ Tree : | : Tree / |
| \ : | : / |
| \ : V : / |
| --> commit_secret --> epoch_secret --> encryption_secret --> |
| / : | : \ |
| / : ... > Key Schedule \ |
| / : | : \ |
|/ \_ | _/ \|
V
epoch_secret
Each member of the group maintains a view of these facets of the group's state. MLS messages are used to initialize these views and keep them in sync as the group transitions between epochs.¶
Each new epoch is initiated with a Commit message. The Commit instructs existing members of the group to update their views of the ratchet tree by applying a set of Proposals, and uses the updated ratchet tree to distribute fresh entropy to the group. This fresh entropy is provided only to members in the new epoch, not to members who have been removed, so it maintains the confidentiality of the epoch secret (in other words, it provides post-compromise security with respect to those members).¶
For each Commit that adds member(s) to the group, there is a single corresponding Welcome message. The Welcome message provides all the new members with the information they need to initialize their views of the key schedule and ratchet tree, so that these views are equivalent to the views held by other members of the group in this epoch.¶
In addition to defining how one epoch secret leads to the next, the key schedule also defines a collection of secrets that are derived from the epoch secret. For example:¶
Finally, an init secret is derived that is used to initialize the next epoch.¶
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. In the illustrations below, we show the Proposal and Commit messages directly, while in reality they would be sent encapsulated in MLSPlaintext or MLSCiphertext objects.¶
Before the initialization of a group, clients publish KeyPackages 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. However, messages sent before they were added to the group will not be accessible.¶
Group
A B C Directory Channel
| | | | |
| KeyPackageB, KeyPackageC | |
|<-------------------------------------------| |
| | | | |
| | | | Add(A->AB) |
| | | | Commit(Add) |
|--------------------------------------------------------------->|
| | | | |
| Welcome(B) | | | |
|------------->| | | |
| | | | |
| | | | Add(A->AB) |
| | | | Commit(Add) |
|<---------------------------------------------------------------|
| | | | |
| | | | |
| | | | Add(AB->ABC) |
| | | | Commit(Add) |
|--------------------------------------------------------------->|
| | | | |
| | Welcome(C) | | |
|---------------------------->| | |
| | | | |
| | | | Add(AB->ABC) |
| | | | Commit(Add) |
|<---------------------------------------------------------------|
| |<------------------------------------------------|
| | | | |
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 Add and Commit messages that the current group will 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 the keys that represent them to the group. A member does this by sending a Commit (possibly with no proposals), or by sending an Update message that is committed by another member. Once the other members of the group have processed these messages, 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) |
|<----------------------------------------------------------|
| |<-------------------------------------------|
| | |<----------------------------|
| | | | |
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. The Commit message provides new entropy to all members of the group except the removed member. This new entropy is added to the epoch secret for the new epoch, so that it is not known to 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) |
|<----------------------------------------------------------|
| | |<----------------------------|
| | | | |
A group has a single linear sequence of epochs. Groups and epochs are generally independent of one-another. However, it can sometimes be useful to link epochs cryptographically, either within a group or across groups. MLS derives a resumption pre-shared key (PSK) from each epoch to allow entropy extracted from one epoch to be injected into a future epoch. This link guarantees that members entering the new epoch agree on a key if and only if they were members of the group during the epoch from which the resumption key was extracted.¶
MLS supports two ways to tie a new group to an existing group. Re-initialization closes one group and creates a new group comprising the same members with different parameters. Branching starts a new group with a subset of the original group's participants (with no effect on the original group). In both cases, the new group is linked to the old group via a resumption PSK.¶
epoch_A_[n-1]
|
|
|<-- ReInit
|
V
epoch_A_[n] epoch_B_[0]
. |
. PSK(usage=reinit) |
.....................>|
|
V
epoch_B_[1]
epoch_A_[n-1]
|
|
|<-- ReInit
|
V
epoch_A_[n] epoch_B_[0]
| |
| PSK(usage=branch) |
|....................>|
| |
V V
epoch_A_[n+1] epoch_B_[1]
Applications may also choose to use resumption PSKs to link epochs in other
ways. For example, the following figure shows a case where a resumption PSK
from epoch n is injected into epoch n+k. This demonstrates that the members
of the group at epoch n+k were also members at epoch n, irrespective of any
changes to these members' keys due to Updates or Commits.¶
epoch_A_[n-1]
|
|
|<-- ReInit
|
V
epoch_A_[n]
|
| PSK(usage=application)
|.....................
| .
| .
... ...
| .
| .
V .
epoch_A_[n+k-1] .
| .
| .
|<....................
|
V
epoch_A_[n+k]
The protocol uses "ratchet trees" for deriving shared secrets among a group of clients. A ratchet tree is an arrangement of secrets and key pairs among the members of a group in a way that allows for secrets to be efficiently updated to reflect changes in the group.¶
Ratchet trees allow a group to efficiently remove any member by encrypting new entropy to a subset of the group. A ratchet tree assigns shared keys to subgroups of the overall group, so that, for example, encrypting to all but one member of the group requires only log(N) encryptions, instead of the N-1 encryptions that would be needed to encrypt to each participant individually (where N is the number of members in the group).¶
This remove operation allows MLS to efficiently achieve post-compromise security. In an Update proposal or a full Commit message, an old (possibly compromised) representation of a member is efficiently removed from the group and replaced with a freshly generated instance.¶
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's 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, or if the node itself is the root of the tree. Nodes are siblings if they share the same parent.¶
A subtree of a tree is the tree given by any node (the head of the subtree) and its descendants. 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:¶
X = root
______|______
/ \
V Z
__|__ __|
/ \ / \
U W Y |
/ \ / \ / \ |
A B C D E F G
0 1 2 3 4 5 6
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.¶
Each leaf is given an index (or leaf index), starting at 0 from the left to
n-1 at the right.¶
Finally, a node in the tree may also be blank, indicating that no value is present at that node (i.e. no keying material). This is often the case when a leaf was recently removed from the tree.¶
There are multiple ways that an implementation might represent a ratchet tree in memory. For example, left-balanced binary trees can be represented as an array of nodes, with node relationships computed based on nodes' indices in the array. Or a more traditional representation of linked node objects may be used. Appendix B and Appendix C provide some details on how to implement the tree operations required for MLS in these representations. MLS places no requirements on implementations' internal representations of ratchet trees. An implementation MAY use any tree representation and associated algorithms, as long as they produce correct protocol messages.¶
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 the node's subtree contains that member's leaf.¶
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 8.4.¶
For example, consider a four-member group (A, B, C, D) where the node above the
right two members is blank. (This is what it would look like if A created a
group with B, C, and D.) Then the public state of the tree and the views of the
private keys of the tree held by each participant would be as follows, where _
represents a blank node, ? represents an unknown private key, and pk(X)
represents the public key corresponding to the private key X:¶
Public Tree
============================
pk(ABCD)
/ \
pk(AB) _
/ \ / \
pk(A) pk(B) pk(C) pk(D)
Private @ A Private @ B Private @ C Private @ D
============= ============= ============= =============
ABCD ABCD ABCD ABCD
/ \ / \ / \ / \
AB _ AB _ ? _ ? _
/ \ / \ / \ / \ / \ / \ / \ / \
A ? ? ? ? B ? ? ? ? C ? ? ? ? D
¶
Note how the tree invariant applies: Each member knows only their own leaf, and the private key AB is known only to A and B.¶
A particular instance of a ratchet tree includes 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 non-blank node in a ratchet tree contains up to five values:¶
The resolution of a node is an ordered list of non-blank nodes that collectively cover all non-blank descendants of the node. The resolution of a non-blank node with no unmerged leaves is just the node itself. More generally, the resolution of a node is effectively a depth-first, left-first enumeration of the nearest non-blank nodes below the node:¶
For example, consider the following subtree, where the _ character
represents a blank node and unmerged leaves are indicated in square
brackets:¶
...
/
_
__|__
/ \
_ Z[C]
/ \ / \
A _ C D
0 1 2 3
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 8.7.¶
Each MLS session uses a single ciphersuite that specifies the following primitives to be used in group key computations:¶
MLS uses HPKE for public-key encryption [RFC9180]. The
DeriveKeyPair function associated to the KEM for the ciphersuite maps octet
strings to HPKE key pairs. As in HPKE, MLS assumes that an AEAD algorithm
produces a single ciphertext output from AEAD encryption (aligning with
[RFC5116]), as opposed to a separate ciphertext and tag.¶
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<V>;¶
The signature algorithm specified in the ciphersuite is the mandatory algorithm to be used for signatures in MLSMessageAuth and the tree signatures. It MUST be the same as the signature algorithm specified in the credentials in the leaves of the tree (including the leaf node information in KeyPackages used to add new members).¶
To disambiguate different signatures used in MLS, each signed value is prefixed by a label as shown below:¶
SignWithLabel(SignatureKey, Label, Content) =
Signature.Sign(SignatureKey, SignContent)
VerifyWithLabel(VerificationKey, Label, Content) =
Signature.Verify(VerificationKey, SignContent)
Where SignContent is specified as:
struct {
opaque label<V> = "MLS 1.0 " + Label;
opaque content<V> = Content;
} SignContent;
¶
Here, the functions Signature.Sign and Signature.Verify are defined
by the signature algorithm.¶
The ciphersuites are defined in section Section 18.1.¶
Some MLS messages refer to other MLS objects by hash. For example, Welcome messages refer to KeyPackages for the members being welcomed, and Commits refer to Proposals they cover. These identifiers are computed as follows:¶
opaque HashReference[16];
MakeKeyPackageRef(value) = KDF.expand(
KDF.extract("", value), "MLS 1.0 KeyPackage Reference", 16)
MakeLeafNodeRef(value) = KDF.expand(
KDF.extract("", value), "MLS 1.0 Leaf Node Reference", 16)
MakeProposalRef(value) = KDF.expand(
KDF.extract("", value), "MLS 1.0 Proposal Reference", 16)
HashReference KeyPackageRef;
HashReference LeafNodeRef;
HashReference ProposalRef;
¶
For a KeyPackageRef, the value input is the encoded KeyPackage, and the
ciphersuite specified in the KeyPackage determines the KDF used. For a
LeafNodeRef, the value input is the LeafNode object for the leaf node in
question. For a ProposalRef, the value input is the MLSMessageContentAuth carrying the
proposal. In the latter two cases, the KDF is determined by the group's
ciphersuite.¶
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:¶
Note that a Credential can provide multiple identifiers for the client. If an application wishes to decided whether a credential represents the correct identifier for a participant in a given context, it is up to the application to decide what the correct value is and compare it to the credential. For example, a certificate in an X509Credential may attest to several domain names or email addresses in its subjectAltName extension. An application may decide to present all of these to a user, or if it knows a "desired" domain name or email address, it can check that the desired identifier is among those attested. Using the terminology from [RFC6125], a Credential provides "presented identifiers", and it is up to the application to supply a "reference identifier" for the authenticated client, if any.¶
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<V>;
SignatureScheme signature_scheme;
opaque signature_key<V>;
} BasicCredential;
struct {
opaque cert_data<V>;
} Certificate;
struct {
CredentialType credential_type;
select (Credential.credential_type) {
case basic:
BasicCredential;
case x509:
Certificate chain<V>;
};
} 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 leaf node of a
ratchet tree or the KeyPackage ciphersuite for a credential in a KeyPackage
object. For ciphersuites using Ed25519 or Ed448 signature schemes, the public
key is in the format specified in [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].¶
For an X.509 credential, each entry in the chain represents a single DER-encoded
X.509 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.¶
The signatures used in 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].¶
Each new credential that has not already been validated by the application MUST be validated against the Authentication Service. Applications SHOULD require that a client present the same set of identifiers throughout its presence in the group, even if its Credential is changed in a Commit or Update. If an application allows clients to change identifiers over time, then each time the client presents a new credential, the application MUST verify that the set of identifiers in the credential is acceptable to the application for this client.¶
MLS implementations will presumably provide applications with a way to request protocol operations with regard to other clients (e.g., removing clients). Such functions will need to refer to the other clients using some identifier. MLS clients have a few types of identifiers, with different operational properties.¶
The Credentials presented by the clients in a group authenticate application-level identifiers for the clients. These identifiers may not uniquely identify clients. For example, if a user has multiple devices that are all present in an MLS group, then those devices' clients could all present the user's application-layer identifiers.¶
Internally to the protocol, group members are uniquely identified by their leaves, expressed as LeafNodeRef objects. These identifiers are unstable: They change whenever the member sends a Commit, or whenever an Update proposal from the member is committed.¶
MLS provides two unique client identifiers that are stable across epochs:¶
The application may also provide application-specific unique identifiers in the
extensions field of KeyPackage or LeafNode objects.¶
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 main structure is MLSMessageContent, which contains the content of the message. This structure is authenticated using MLSMessageAuth (see Section 7.1). The two structures are combined in MLSMessageContentAuth, which can then be encoded/decoded from/to MLSPlaintext or MLSCiphertext, which are then included in the MLSMessage structure.¶
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),
mls10(1),
(255)
} ProtocolVersion;
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:
LeafNodeRef member_ref;
case preconfigured:
opaque sender_id<V>;
case new_member:
struct{};
}
} Sender;
enum {
reserved(0),
mls_plaintext(1),
mls_ciphertext(2),
mls_welcome(3),
mls_group_info(4),
mls_key_package(5),
(255)
} WireFormat;
struct {
opaque group_id<V>;
uint64 epoch;
Sender sender;
opaque authenticated_data<V>;
ContentType content_type;
select (MLSMessageContent.content_type) {
case application:
opaque application_data<V>;
case proposal:
Proposal proposal;
case commit:
Commit commit;
}
} MLSMessageContent;
struct {
ProtocolVersion version = mls10;
WireFormat wire_format;
select (MLSMessage.wire_format) {
case mls_plaintext:
MLSPlaintext plaintext;
case mls_ciphertext:
MLSCiphertext ciphertext;
case mls_welcome:
Welcome welcome;
case mls_group_info:
GroupInfo group_info;
case mls_key_package:
KeyPackage key_package;
}
} MLSMessage;
¶
External sender types are sent as MLSPlaintext, see Section 13.1.9 for their use.¶
The following structure is used to fully describe the data transmitted in plaintexts or ciphertexts.¶
struct {
WireFormat wire_format;
MLSMessageContent content;
MLSMessageAuth auth;
} MLSMessageContentAuth;
¶
MLSMessageContent is authenticated using the MLSMessageAuth structure.¶
struct {
opaque mac_value<V>;
} MAC;
struct {
// SignWithLabel(., "MLSMessageContentTBS", MLSMessageContentTBS)
opaque signature<V>;
select (MLSMessageContent.content_type) {
case commit:
// MAC(confirmation_key, GroupContext.confirmed_transcript_hash)
MAC confirmation_tag;
case application:
case proposal:
struct{};
}
} MLSMessageAuth;
¶
The signature field in an MLSMessageAuth 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
is computed using SignWithLabel with label "MLSMessageContentTBS" and with a content
that covers the message content and the wire format that will be used for this message.
If the sender is a member of the group, the content also covers the
GroupContext for the current epoch, so that signatures are specific to a given
group and epoch.¶
struct {
ProtocolVersion version = mls10;
WireFormat wire_format;
MLSMessageContent content;
select (MLSMessageContentTBS.content.sender.sender_type) {
case member:
case new_member:
GroupContext context;
case preconfigured:
struct{};
}
} MLSMessageContentTBS;
¶
The confirmation tag value confirms that the members of the group have arrived at the same state of the group.¶
A MLSMessageAuth is said to be valid when both the signature and
confirmation_tag fields are valid.¶
Plaintexts are encoded using the MLSPlaintext structure.¶
struct {
MLSMessageContent content;
MLSMessageAuth auth;
select(MLSPlaintext.content.sender.sender_type) {
case member:
MAC membership_tag;
case preconfigured:
case new_member:
struct{};
}
} MLSPlaintext;
¶
The membership_tag field in the MLSPlaintext object authenticates the sender's
membership in the group. For messages sent by members, it MUST be set to the
following value:¶
struct {
MLSMessageContentTBS content_tbs;
MLSMessageAuth auth;
} MLSMessageContentTBM;
membership_tag = MAC(membership_key, MLSMessageContentTBM);
¶
When decoding a MLSPlaintext into a MLSMessageContentAuth,
the application MUST check membership_tag, and MUST check that the
MLSMessageAuth is valid.¶
Ciphertexts are encoded using the MLSCiphertext structure.¶
struct {
opaque group_id<V>;
uint64 epoch;
ContentType content_type;
opaque authenticated_data<V>;
opaque encrypted_sender_data<V>;
opaque ciphertext<V>;
} MLSCiphertext;
¶
encrypted_sender_data and ciphertext are encrypted using the AEAD function
specified by the ciphersuite in use, using as input the structures MLSSenderData
and MLSCiphertextContent.¶
The ciphertext content is encoded using the MLSCiphertextContent structure.¶
struct {
select (MLSCiphertext.content_type) {
case application:
opaque application_data<V>;
case proposal:
Proposal proposal;
case commit:
Commit commit;
}
MLSMessageAuth auth;
opaque padding<V>;
} 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<V>;
uint64 epoch;
ContentType content_type;
opaque authenticated_data<V>;
} MLSCiphertextContentAAD;
¶
When decoding a MLSCiphertextContent, the application MUST check that the MLSMessageAuth is valid.¶
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 {
LeafNodeRef 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 7.3.1.¶
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 the first three fields of MLSCiphertext:¶
struct {
opaque group_id<V>;
uint64 epoch;
ContentType content_type;
} MLSSenderDataAAD;
¶
When parsing a SenderData struct as part of message decryption, the recipient
MUST verify that the LeafNodeRef indicated in the sender field identifies a
member of the group.¶
The ratchet tree for an epoch describes the membership of a group in that epoch, providing public-key encryption (HPKE) keys that can be used to encrypt to subsets of the group as well as information to authenticate the members. In order to reflect changes to the membership of the group from one epoch to the next, corresponding changes are made to the ratchet tree. In this section, we describe the content of the tree and the required operations.¶
As discussed in Section 5.3, the nodes of a ratchet tree contain several types of data describing individual members (for leaf nodes) or subgroups of the group (for parent nodes). Parent nodes are simpler:¶
struct {
HPKEPublicKey public_key;
opaque parent_hash<V>;
uint32 unmerged_leaves<V>;
} ParentNode;
¶
The public_key field contains an HPKE public key whose private key is held only
by the members at the leaves among its descendants. The parent_hash field
contains a hash of this node's parent node, as described in Section 8.8.
The unmerged_leaves field lists the leaves under this parent node that are
unmerged, according to their indices among all the leaves in the tree.¶
A leaf node in the tree describes all the details of an individual client's appearance in the group, signed by that client. It is also used in client KeyPackage objects to store the information that will be needed to add a client to a group.¶
enum {
reserved(0),
key_package(1),
update(2),
commit(3),
(255)
} LeafNodeSource;
struct {
ProtocolVersion versions<V>;
CipherSuite ciphersuites<V>;
ExtensionType extensions<V>;
ProposalType proposals<V>;
} Capabilities;
struct {
uint64 not_before;
uint64 not_after;
} Lifetime;
// See IANA registry for registered values
uint16 ExtensionType;
struct {
ExtensionType extension_type;
opaque extension_data<V>;
} Extension;
struct {
HPKEPublicKey public_key;
Credential credential;
Capabilities capabilities;
LeafNodeSource leaf_node_source;
select (leaf_node_source) {
case add:
Lifetime lifetime;
case update:
struct {}
case commit:
opaque parent_hash<V>;
}
Extension extensions<V>;
// SignWithLabel(., "LeafNodeTBS", LeafNodeTBS)
opaque signature<V>;
} LeafNode;
struct {
HPKEPublicKey public_key;
Credential credential;
Capabilities capabilities;
LeafNodeSource leaf_node_source;
select (leaf_node_source) {
case key_package:
Lifetime lifetime;
case update:
struct{};
case commit:
opaque parent_hash<V>;
}
Extension extensions<V>;
select (leaf_node_source) {
case key_package:
struct{};
case update:
opaque group_id<V>;
case commit:
opaque group_id<V>;
}
} LeafNodeTBS;
¶
The public_key field conains an HPKE public key whose private key is held only
by the member occupying this leaf (or in the case of a LeafNode in a KeyPackage
object, the issuer of the KeyPackage). The credential contains authentication
information for this member, as described in Section 6.3.¶
The capabilities field 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. Extensions that appear in the extensions field of a LeafNode
MUST be included in the extensions field of the capabilities field.¶
The leaf_node_source field indicates how this LeafNode came to be added to the
tree. This signal tells other members of the group whether the leaf node is
required to have a lifetime or parent_hash, and whether the group_id is
added as context to the signature. Whether these fields can be computed by the
client represented by the LeafNode depends on when the LeafNode was created.
For example, a KeyPackage is created before the client knows which group it will
be used with, so its signature can't bind to a group_id.¶
In the case where the leaf was added to the tree based on a pre-published
KeyPackage, the lifetime field represents the times between which clients will
consider a LeafNode valid. These times are represented as absolute times,
measured in seconds since the Unix epoch (1970-01-01T00:00:00Z). Applications
MUST define a maximum total lifetime that is acceptable for a LeafNode, and
reject any LeafNode where the total lifetime is longer than this duration.¶
In the case where the leaf node was inserted into the tree via a Commit message,
the parent_hash field contains the parent hash for this leaf node (see
Section 8.8).¶
The LeafNodeTBS structure covers the fields above the signature in the LeafNode. In addition, when the leaf node was created in the context of a group (the update and commit cases), the group ID of the group is added as context to the signature.¶
LeafNode objects stored in the group's ratchet tree are updated according to the evolution of the tree. Each modification of LeafNode content MUST be reflected by a change in its signature. This allows other members to verify the validity of the LeafNode at any time, particularly in the case of a newcomer joining the group.¶
The validity of a LeafNode needs to be verified at a few stages:¶
The client verifies the validity of a LeafNode using the following steps:¶
required_capabilities extension, then the required
extensions and proposals MUST be listed in the LeafNode's capabilities
field.¶
Verify the lifetime field:¶
lifetime range. A KeyPackage
containing a LeafNode that is expired or not yet valid MUST NOT be sent in
an Add proposal.¶
lifetime is
RECOMMENDED, if it is feasible in a given application context. Because of
the asynchronous nature of MLS, the lifetime may have been valid when the
leaf node was proposed for addition, even if it is expired at these later
points in the protocol.¶
leaf_node_source field has the appropriate value for the
context in which the LeafNode is being validated (as defined in
Section 8.2).¶
Verify that the following fields in the LeafNode are unique among the members of the group (including any other members added in the same Commit):¶
extensions field MUST be listed in the field
capabilities.extensions of the LeafNode.¶
In order to provide forward secrecy and post-compromise security, whenever a member initiates an epoch change (i.e., commits; see Section 13.2), they refresh the key pairs of their leaf and of all nodes on their leaf's direct path (all nodes for which they know the secret key).¶
The member initiating the epoch change generates the fresh key pairs using the following procedure. The procedure is designed in a way that allows group members to efficiently communicate the fresh secret keys to other group members, as described in Section 8.9.¶
Recall the definition of resolution from Section 5.3. To begin with, the generator of the UpdatePath updates its leaf and its leaf's filtered direct path with new key pairs. The filtered direct path of a node is obtained from the node's direct path by removing all nodes whose child on the nodes's copath has an empty resolution (any unmerged leaves of the copath child count towards its resolution). Such a removed node does not need a key pair, since after blanking it, its resolution consists of a single node on the filtered direct path. Using the key pair of the node in the resolution is equivalent to using the key pair of the removed node.¶
Generate a sequence of path secrets, one for each node on the leaf's filtered direct
path, as follows. In this setting, path_secret[0] refers to the first parent node
in the filtered direct path, path_secret[1] to the second parent node, and so on.¶
path_secret[0] is sampled at random path_secret[n] = DeriveSecret(path_secret[n-1], "path")¶
Compute the sequence of HPKE key pairs (node_priv,node_pub), one for each
node on the leaf's direct path, as follows.¶
node_secret[n] = DeriveSecret(path_secret[n], "node") node_priv[n], node_pub[n] = KEM.DeriveKeyPair(node_secret[n])¶
The node secret is derived as a temporary intermediate secret so that each secret is only used with one algorithm: The path secret is used as an input to DeriveSecret and the node secret is used as an input to DeriveKeyPair.¶
For example, suppose there is a group with four members, with C an unmerged leaf at Z:¶
Y
__|__
/ \
X Z[C]
/ \ / \
A B C D
0 1 2 3
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_node
¶
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] -> Y'
__|__
/ \
np[0] -> X' Z[C]
/ \ / \
A B C D
^
|
lp
0 1 2 3
¶
In addition to the path-based updates to the tree described above, it is also necessary to add and remove leaves of the tree in order to reflect changes to the membership of the group (see Section 13.1.1 and Section 13.1.3). Leaves are always added and removed at the right edge of the tree: Either a new rightmost leaf is added, or the rightmost leaf is removed. Nodes' parent/child node relationships are then updated to maintain the tree's left-balanced structure. These operations are also known as extending and truncating the tree.¶
To add a new leaf: Add leaf L as the new rightmost leaf of the tree. Add a blank parent node P whose right child is L. P is attached to the tree as the right child of the only appropriate node to make the updated tree left-balanced (or set it as a new root). The former right child of P's parent becomes P's left child (or the old root becomes P's left child if P is the new root).¶
_ <-- new parent _
__|_ __|__
/ \ / \
X ===> X | ===> X _ <-- new parent
/ \ / \ | / \ / \
A B A B C <-- new leaf A B C D <-- new leaf
¶
To remove the rightmost leaf: Remove the rightmost leaf node L and its parent node P. If P was the root of the tree, P's left child is now the root of the tree. Otherwise, set the right child of P's parent to be P's left child.¶
Y Y
__|__ __|_
/ \ / \
X Z <-- remove parent ===> X | <-- reassign child
/ \ / \ / \ |
A B C D <-- remove leaf A B C
Y <-- remove parent
__|_
/ \
X | ===> X <-- reassign root
/ \ | / \
A B C <-- remove leaf A B
¶
Note that in the rest of the protocol, the rightmost leaf will only be removed when it is blank.¶
Concrete algorithms for these operations on array-based and link-based trees are provided in Appendix B and Appendix C. The concrete algorithms are non-normative. An implementation MAY use any algorithm that produces the correct tree in its internal representation.¶
After generating fresh key material and applying it to ratchet forward their local tree state as described in the Section 8.4, 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 filtered 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 filtered 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 nodes on the filtered direct path of the sender's leaf,¶
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(Z), path_secret[1]), E(pk(C), path_secret[1]) |
| node_pub[0] | E(pk(A), path_secret[0]) |
In this table, the value node_pub[i] represents the public key derived from node_secret[i], pk(X) represents the current public key of node X, and 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:¶
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' leaf nodes. The tree hash of a tree is the tree hash of its root node, which we define recursively, starting with the leaves.¶
The tree hash of a leaf node is the hash of leaf's LeafNodeHashInput object which
might include a LeafNode object depending on whether or not it is blank.¶
struct {
uint32 leaf_index;
optional<LeafNode> leaf_node;
} LeafNodeHashInput;
¶
Now the tree hash of any non-leaf node is recursively defined to be the hash of
its ParentNodeHashInput. This includes an optional ParentNode
object depending on whether the node is blank or not.¶
struct {
optional<ParentNode> parent_node;
opaque left_hash<V>;
opaque right_hash<V>;
} ParentNodeHashInput;
¶
The left_hash and right_hash fields hold the tree hashes of the node's
left and right children, respectively.¶
The parent_hash field in ratchet tree nodes carries information to
authenticate the information in the ratchet tree. Parent hashes chain together
so that the signature on a leaf node, by covering the leaf node's parent hash,
indirectly includes information about the structure of the tree at the time the
leaf node was last updated.¶
Consider a ratchet tree with a non-blank parent node P and children V and S.¶
...
/
P
__|__
/ \
V S
/ \ / \
... ... ... ...
¶
The parent hash of P changes whenever an UpdatePath object is applied to
the ratchet tree along a path from a leaf U traversing node V (and hence also
P). The new "Parent hash of P (with copath child S)" is obtained by hashing P's
ParentHashInput struct.¶
struct {
HPKEPublicKey public_key;
opaque parent_hash<V>;
opaque original_sibling_tree_hash<V>;
} ParentHashInput;
¶
The field public_key contains the HPKE public key of P. If P is the root,
then the parent_hash field is set to a zero-length octet string. Otherwise,
parent_hash is the Parent Hash of the next node after P on the filtered
direct path of U. This way, P's Parent Hash fixes
the new HPKE public key of each node V on the path from P to the root. Note
that the path from P to the root may contain some blank nodes that are not
fixed by P's Parent Hash. However, for each node that has an HPKE key, this key
is fixed by P's Parent Hash.¶
Finally, original_sibling_tree_hash is the original tree hash of S. The
original tree hash corresponds to the tree hash of S the last time P was
updated. It can be computed as the tree hash of S in the ratchet tree modified
the following way:¶
For example, in the following tree:¶
W [D, H]
______|_____
/ \
U [D] Y [F, H]
__|__ __|__
/ \ / \
T _ X [F] _
/ \ / \ / \ / \
A B C D E F G H
With P = W and S = Y, original_sibling_tree_hash is the tree hash of the
following tree:¶
Y [F]
__|__
/ \
X [F] |
/ \ |
E F G
¶
Because W.unmerged_leaves = [H], H is removed from Y.unmerged_leaves,
then H is replaced with a blank leaf, then the tree is truncated removing the
last two nodes.¶
With P = W and S = U, original_sibling_tree_hash is the tree hash of the
following tree:¶
U
__|__
/ \
T _
/ \ / \
A B C _
¶
This time we have 4 leaf nodes because the truncation of the ratchet tree didn't remove the last leaf.¶
Note that no recomputation is needed if the tree hash of S is unchanged since
the last time P was updated. This is the case for computing or processing a
Commit whose UpdatePath traverses P, since the Commit itself resets P. (In
other words, it is only necessary to recompute the original sibling tree hash
when validating group's tree on joining.) More generally, if none of the entries
in P.unmerged_leaves is in the subtree under S (and thus no nodes were truncated),
then the original tree hash at S is the tree hash of S in the current tree.¶
If it is necessary to recompute the original tree hash of a node, the efficiency of recomputation can be improved by caching intermediate tree hashes, to avoid recomputing over the subtree when the subtree is included in multiple parent hashes. A subtree hash can be reused as long as the intersection of the parent's unmerged leaves with the subtree is the same as in the earlier computation.¶
Observe that original_child_resolution is equal to the resolution of S at the
time the UpdatePath was generated, since at that point P's set of unmerged
leaves was emptied. (Observe also that original_child_resolution contains all
unmerged leaves of S.) Therefore, P's Parent Hash fixes, for each node V on the
path from P to the root, not only the HPKE public key of V, but also the set of
HPKE public keys to which the corresponding HPKE secret key of V was encrypted by
the generator of the UpdatePath.¶
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 field of the structs
ParentHashInput and ParentNode of the node before P on the filtered direct
path of U. (The ParentNode struct is used to encapsulate all public
information about that node that must be conveyed to a new
member joining the group as well as to define its Tree Hash.)¶
If, on the other hand, V is the leaf U and its LeafNode has leaf_node_source set to commit,
then the Parent Hash of P (with V's sibling as copath child) is stored in
the parent_hash field. This is true in particular of the LeafNode object sent
in the leaf_node field of an UpdatePath. The signature of such a LeafNode thus also
attests 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.¶
Parent hashes are verified at two points in the protocol: When joining a group and when processing a Commit.¶
The parent hash in a node U is valid with respect to a parent node P if the following criteria hold:¶
parent_hash field of U is equal to the parent hash of P with copath
child S, where S is the child of P that is not on the path from U to P.¶
A parent node P is "parent-hash valid" if it can be chained back to a leaf node in this way. That is, if there is leaf node L and a sequence of parent nodes P_1, ..., P_N such that P_N = P and each step in the chain is authenticated by a parent hash: L's parent hash is valid with respect to P_1, P_1's parent hash is valid with respect to P_2, and so on.¶
When joining a group, the new member MUST authenticate that each non-blank parent node P is parent-hash valid. This can be done "bottom up" by building chains up from leaves and verifying that all non-blank parent nodes are covered by exactly one such chain, or "top down" by verifying that there is exactly one descendant of each non-blank parent node for which the parent node is parent-hash valid.¶
When processing a Commit message that includes an UpdatePath, 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_node.
After being merged into the tree, the nodes in the UpdatePath form a parent-hash
chain from the committer's leaf to the root.¶
As described in Section 13.2, each MLS Commit message may optionally transmit a LeafNode and parent node values along its direct path. The path contains a public key and encrypted secret value for all intermediate nodes in the filtered direct path from the leaf to the root. 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<V>;
opaque ciphertext<V>;
} HPKECiphertext;
struct {
HPKEPublicKey public_key;
HPKECiphertext encrypted_path_secret<V>;
} UpdatePathNode;
struct {
LeafNode leaf_node;
UpdatePathNode nodes<V>;
} 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 [RFC9180].¶
Decryption is performed in the corresponding way, using the private key of the resolution node.¶
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<V> = "MLS 1.0 " + Label;
opaque context<V> = 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 GroupInfo struct
in order to allow non-members to join the group using an external commit.¶
Each member of the group maintains a GroupContext object that summarizes the state of the group:¶
struct {
opaque group_id<V>;
uint64 epoch;
opaque tree_hash<V>;
opaque confirmed_transcript_hash<V>;
Extension extensions<V>;
} 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.¶
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 8.7.¶
confirmed_transcript_hash field contains a running hash over
the messages that led to this state.¶
extensions field contains the details of any protocol extensions that
apply to the group.¶
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 13.1. 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 field is updated with the data for an
MLSPlaintext message encoding a Commit message as described below.¶
extensions field changes when a GroupContextExtensions proposal is
committed.¶
The transcript hashes computed in MLS represent a running hash over all Proposal and Commit messages that have ever been sent in a group. Commit messages are included directly. Proposal messages are indirectly included via the Commit that applied them. Both types of message are included by hashing the MLSPlaintext in which they were sent.¶
The confirmed_transcript_hash is updated with an MLSMessageContent and
MLSMessageAuth containing a Commit in two steps:¶
struct {
WireFormat wire_format;
MLSMessageContent content; //with content.content_type == commit
opaque signature<V>;
} MLSMessageCommitContent;
struct {
MAC confirmation_tag;
} MLSMessageCommitAuthData;
interim_transcript_hash_[0] = ""; // zero-length octet string
confirmed_transcript_hash_[n] =
Hash(interim_transcript_hash_[n] ||
MLSMessageCommitContent_[n]);
interim_transcript_hash_[n+1] =
Hash(confirmed_transcript_hash_[n] ||
MLSMessageCommitAuthData_[n]);
¶
Thus the confirmed_transcript_hash field in a GroupContext object represents a
transcript over the whole history of MLSMessage Commit messages, up to the
confirmation_tag field of the most recent Commit. 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 of the
GroupInfo struct, while existing members can compute it directly.¶
As shown above, when a new group is created, the interim_transcript_hash field
is set to the zero-length octet string.¶
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 GroupInfo 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 GroupInfo for the
previous epoch, encoded using the TLS serialization.¶
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 that is used as a PSK
to inject entropy from one epoch into another. This functionality is used in the
reinitialization and branching processes described in Section 12.2 and
Section 12.3, but may be used by applications for other purposes.¶
Some uses of resumption PSKs might call for the use of PSKs from historical
epochs. The application SHOULD specify an upper limit on the number of past
epochs for which the resumption_secret may be stored.¶
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.¶
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.¶
If N is a parent node in the Secret Tree then the secrets of the children of N are defined as follows (where left(N) and right(N) denote the children of N):¶
tree_node_[N]_secret
|
|
+--> ExpandWithLabel(., "tree", "left", KDF.Nh)
| = tree_node_[left(N)]_secret
|
+--> ExpandWithLabel(., "tree", "right", 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 10.1. The root of each ratchet is computed as:¶
tree_node_[N]_secret
|
|
+--> ExpandWithLabel(., "handshake", "", KDF.Nh)
| = handshake_ratchet_secret_[N]_[0]
|
+--> ExpandWithLabel(., "application", "", KDF.Nh)
= application_ratchet_secret_[N]_[0]
¶
As described in Section 7, 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 10. 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 current position in the ratchet.¶
DeriveTreeSecret(Secret, Label, Generation, Length) =
ExpandWithLabel(Secret, Label, Generation, Length)
Where Generation is encoded as a uint32.
¶
ratchet_secret_[N]_[j]
|
+--> DeriveTreeSecret(., "nonce", j, AEAD.Nn)
| = ratchet_nonce_[N]_[j]
|
+--> DeriveTreeSecret(., "key", j, AEAD.Nk)
| = ratchet_key_[N]_[j]
|
V
DeriveTreeSecret(., "secret", 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 leaf node L 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_[L]_[j] and application_ratchet_key_[L]_[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.¶
In order to facilitate the asynchronous addition of clients to a group, key packages are pre-published that provide some public information about a user. A KeyPackage object specifies:¶
KeyPackages are intended to be used only once and SHOULD NOT be reused except in case of last resort. (See Section 17.4). Clients MAY generate and publish multiple KeyPackages to support multiple ciphersuites.¶
The value for init_key MUST be a public key for the asymmetric encryption
scheme defined by cipher_suite, and it MUST be unique among the set of
KeyPackages created by this client. Likewise, the leaf_node field MUST be
valid for the ciphersuite, including both the public_key and credential
fields. The whole structure is signed using the client's signature key. A
KeyPackage object with an invalid signature field MUST be considered malformed.¶
The signature is computed by the function SignWithLabel with a label
KeyPackage and a content comprising of all of the fields except for the
signature field.¶
struct {
ProtocolVersion version;
CipherSuite cipher_suite;
HPKEPublicKey init_key;
LeafNode leaf_node;
Extension extensions<V>;
// SignWithLabel(., "KeyPackageTBS", KeyPackageTBS)
opaque signature<V>;
} KeyPackage;
struct {
ProtocolVersion version;
CipherSuite cipher_suite;
HPKEPublicKey init_key;
LeafNode leaf_node;
Extension extensions<V>;
} KeyPackageTBS;
¶
If a client receives a KeyPackage carried within an MLSMessage object, then it
MUST verify that the version field of the KeyPackage has the same value as the
version field of the MLSMessage. The version field in the KeyPackage
provides an explicit signal of the intended version to the other members of
group when they receive the KeyPackage in an Add proposal.¶
The field leaf_node.capabilities indicates what protocol versions,
ciphersuites, protocol extensions, and non-default proposal types are supported
by the client. (Proposal types defined in this document are considered
"default" and not listed.) This information allows MLS session
establishment to be safe from downgrade attacks on the parameters described (as
discussed in Section 12), while still only advertising one version /
ciphersuite per KeyPackage.¶
The field leaf_node.leaf_node_source of the LeafNode in a KeyPackage MUST be
set to key_package.¶
Extension included in the extensions or leaf_node.extensions fields MUST be
included in the leaf_node.capabilities field.¶
The validity of a KeyPackage needs to be verified at a few stages:¶
The client verifies the validity of a KeyPackage using the following steps:¶
leaf_node field of the KeyPackage according to the process
defined in Section 8.3.¶
leaf_node.credential.¶
Within MLS, a KeyPackage is identified by its hash (see, e.g.,
Section 13.2.3.2). The external_key_id extension allows
applications to add an explicit, application-defined identifier to a KeyPackage.¶
opaque external_key_id<V>;¶
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 13.1.1, Section 13.2, and Section 13.2.3.2.¶
The creator of a group MUST take the following steps to initialize the group:¶
capabilities information
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 13.2.3.2. If application context informs the recipient that the Welcome should reflect the creation of a new group (for example, due to a branch or reinitialization), then the recipient MUST verify that the epoch value in the GroupInfo is equal to 1.¶
In principle, the above process could be streamlined by having the creator directly create a tree and choose a random value for first epoch's epoch secret. We follow the steps above because it removes unnecessary choices, by which, for example, bad randomness could be introduced. The only choices the creator makes here are its own KeyPackage and the leaf secret from which the Commit is built.¶
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 extension_types<V>;
ProposalType proposal_types<V>;
} RequiredCapabilities;
¶
This extension lists the extensions and proposal types that must be supported by all members of the group. The "default" proposal and extension types defined in this document are assumed to be implemented by all clients, and need not be listed in RequiredCapabilities in order to be safely used.¶
For new members, support for required capabilities 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 non-default capabilities not supported by all current members.¶
A group may be reinitialized by creating a new group with the same membership and different parameters, and linking it to the old group via a resumption PSK. The members of a group reinitialize it using the following steps:¶
A member of the old group sends a Welcome message for the new group that matches the ReInit¶
group_id, version, and cipher_suite fields in the Welcome
message MUST be the same as the corresponding fields in the ReInit
proposal.¶
epoch in the Welcome message MUST be 1¶
resumption with usage
reinit. The group_id must match the old group, and the epoch must
indicate the epoch after the Commit covering the ReInit.¶
psk_nonce included in the PreSharedKeyID of the resumption PSK
MUST be a randomly sampled nonce of length KDF.Nh, for the KDF defined
by the new group's ciphersuite.¶
Note that these three steps may be done by the same group member or different members. For example, if a group member sends a commit with an inline ReInit proposal (steps 1 and 2), but then goes offline, another group member may send the corresponding Welcome. This flexibility avoids situations where a group gets stuck between steps 2 and 3.¶
Resumption PSKs with usage reinit MUST NOT be used in other contexts. A
PreSharedKey proposal with type resumption and usage reinit MUST be
considered invalid.¶
A new group can be formed from a subset of an existing group's members, using
the same parameters as the old group. The creator of the group indicates this
situation by including a PreSharedKey of type resumption with usage branch
in the Welcome message that creates the branched subgroup.¶
A client receiving a Welcome including a PreSharedKey of type resumption with
usage branch MUST verify that the new group reflects a subgroup branched from
the referenced group.¶
version and ciphersuite values in the Welcome MUST be the same as
those used by the old group.¶
In addition, to avoid key re-use, the psk_nonce included in the
PreSharedKeyID object MUST be a randomly sampled nonce of length KDF.Nh.¶
Resumption PSKs with usage branch MUST NOT be used in other contexts. A
PreSharedKey proposal with type resumption and usage branch MUST be
considered invalid.¶
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:¶
In cases where the Proposal and Commit are sent by the same member, these two steps can be combined by sending the proposals in the commit.¶
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 MLSMessageContent 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 MLSMessageContent containing a Proposal, a client MUST verify the signature inside MLSMessageAuth. 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 verify the validity of the KeyPackage, as specified in Section 11.1.¶
struct {
KeyPackage key_package;
} Add;
¶
An Add is applied after being included in a Commit message. The position of the Add in the list of proposals determines the leaf node where the new member will be added. For the first Add in the Commit, the corresponding new member will be placed in the leftmost empty leaf in the tree, for the second Add, the next empty leaf to the right, etc. If no empty leaf exists, the tree is extended to the right.¶
leaf_node_source field in the LeafNode MUST be set to key_package.¶
unmerged_leaves list for the node.¶
leaf_node field of the KeyPackage in the Add.¶
An Update proposal is a similar mechanism to Add with the distinction that it replaces the sender's LeafNode in the tree instead of adding a new leaf to the tree.¶
struct {
LeafNode leaf_node;
} Update;
¶
A member of the group applies an Update message by taking the following steps:¶
leaf_node_source field MUST be set to update.¶
public_key value in the LeafNode is different from the
corresponding field in the LeafNode being replaced.¶
A Remove proposal requests that the member with LeafNodeRef removed be removed
from the group.¶
struct {
LeafNodeRef 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 13.2), since proposals such as Update can change the
LeafNode stored at a leaf. Let L be this leaf node.¶
A ReInit proposal represents a request to reinitialize the group with different parameters, for example, to increase the version number or to change the ciphersuite. The reinitialization is done by creating a completely new group and shutting down the old one.¶
struct {
opaque group_id<V>;
ProtocolVersion version;
CipherSuite cipher_suite;
Extension extensions<V>;
} ReInit;
¶
A member of the group applies a ReInit proposal by waiting for the committer to send the Welcome message that matches the ReInit, according to the criteria in Section 12.2.¶
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 proposal can only be used in that context.¶
struct {
opaque kem_output<V>;
} ExternalInit;
¶
A member of the group applies an ExternalInit message by initializing the next
epoch using an init secret computed as described in Section 9.3.
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 {
LeafNodeRef sender;
uint32 first_generation;
uint32 last_generation;
} MessageRange;
struct {
MessageRange received_ranges<V>;
} 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 contain 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<V>;
} 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. Commits that refer to new Proposals from the committer can be included by value. Commits for previously sent proposals from anyone (including the committer) can be sent by reference. Proposals sent by reference are specified by including the hash of the MLSPlaintext in which the proposal was sent (see Section 6.2).¶
enum {
reserved(0),
proposal(1)
reference(2),
(255)
} ProposalOrRefType;
struct {
ProposalOrRefType type;
select (ProposalOrRef.type) {
case proposal: Proposal proposal;
case reference: ProposalRef reference;
}
} ProposalOrRef;
struct {
ProposalOrRef proposals<V>;
optional<UpdatePath> path;
} Commit;
¶
A group member that has observed one or more valid 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, or multiple
PreSharedKey proposals that reference the same PreSharedKeyID, the committer
MUST choose one and include only that one in the Commit, considering the rest
invalid. The committer MUST NOT include any Update proposals generated by the
committer, since they would be duplicative with the path field in the Commit.
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 that the committer considers to represent the same
client or a client already in the group (for example, identical KeyPackages or
KeyPackages sharing the same Credential), the committer again chooses one to
include and considers the rest invalid. The committer 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 if the
LeafNode in the KeyPackage shares the same public_key with another LeafNode in
the group.¶
The Commit MUST NOT combine proposals sent within different epochs. Due to the asynchronous nature of proposals, receivers of a Commit SHOULD NOT enforce that all valid proposals sent within the current epoch are referenced by the next Commit. In the event that a valid proposal is omitted from the next Commit, and that proposal is still valid in the current epoch, the sender of the proposal MAY resend it after updating it to reflect the current 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.¶
By default, the path field of a Commit MUST be populated. The path field
MAY be omitted if (a) it covers at least one proposal and (b) none of the proposals
covered by the Commit are of "path required" types. A proposal type requires a
path if it cannot change the group membership in a way that requires the forward
secrecy and post-compromise security guarantees that an UpdatePath provides.
The only proposal types defined in this document that do not require a path are:¶
New proposal types MUST state whether they require a path. If any instance of a proposal type requires a path, then the proposal type requires a path. This attribute of a proposal type is reflected in the "Path Required" field of the proposal type registry defined in Section 18.3.¶
Update and Remove proposals are the clearest examples of proposals that require a path. An UpdatePath is required to evict the removed member or the old appearance of the updated member.¶
In pseudocode, the logic for validating the path field of a Commit is as
follows:¶
pathRequiredTypes = [
update,
remove,
external_init,
group_context_extensions
]
pathRequired = false
for i, id in commit.proposals:
proposal = proposalCache[id]
assert(proposal != null)
pathRequired = pathRequired ||
(proposal.msg_type in pathRequiredTypes)
if len(commit.proposals) == 0 || pathRequired:
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 13.1. 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
excluded from the resolution during the computation of the UpdatePath. The
leaf_node for this UpdatePath MUST have leaf_node_source set to commit.
Note that the LeafNode in the UpdatePath effectively updates an existing
LeafNode in the group and thus MUST adhere to the same restrictions as
LeafNodes used in Update proposals (aside from leaf_node_source).¶
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 9.4, where the order
of PSKs in the derivation corresponds to the order of PreSharedKey proposals
in the proposals vector.¶
Construct an MLSMessageContent object containing the Commit object. Sign the MLSMessageContent 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 MLSMessageAuth.¶
Construct a GroupInfo reflecting the new state:¶
joiner_secret
for the new epoch (see Section 13.2.3.2)¶
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.¶
If a ReInit proposal was part of the Commit, the committer MUST create a new
group with the parameters specified in the ReInit proposal,
and with the same members as the original group.
The Welcome message MUST include a PreSharedKeyID with the following
parameters:¶
A member of the group applies a Commit message by taking the following steps:¶
epoch field of the enclosing MLSMessageContent is equal
to the epoch field of the current GroupContext object¶
sender field.¶
proposals vector have unique
PreSharedKeyIDs and are available.¶
Generate the provisional ratchet tree and GroupContext by applying the proposals
referenced in the initial Commit object, as described in Section 13.1. 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_node_source field MUST be set to commit.¶
public_key value in the LeafNode is different from the
committer's current leaf node.¶
leaf_node at the
committer's leaf.¶
parent_hash field 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 9.4, 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 MLSMessageAuth object.¶
New members can join the group in two ways. Either by being added by a group member, or by adding themselves through an external Commit. In both cases, the new members need information to bootstrap their local group state.¶
struct {
CipherSuite cipher_suite;
opaque group_id<V>;
uint64 epoch;
opaque tree_hash<V>;
opaque confirmed_transcript_hash<V>;
Extension group_context_extensions<V>;
Extension other_extensions<V>;
MAC confirmation_tag;
LeafNodeRef signer;
// SignWithLabel(., "GroupInfoTBS", GroupInfoTBS)
opaque signature<V>;
} GroupInfo;
¶
New members MUST verify the signature using the public key taken from the
credential in the leaf node of the member with LeafNodeRef signer. The
signature covers the following structure, comprising all the fields in the
GroupInfo above signature:¶
struct {
CipherSuite cipher_suite;
opaque group_id<V>;
uint64 epoch;
opaque tree_hash<V>;
opaque confirmed_transcript_hash<V>;
Extension group_context_extensions<V>;
Extension other_extensions<V>;
MAC confirmation_tag;
LeafNodeRef signer;
} GroupInfoTBS;
¶
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:¶
In other words, to join a group via an External Commit, a new member needs a
GroupInfo with an ExternalPub extension present in the other_extensions.¶
struct {
HPKEPublicKey external_pub;
} ExternalPub;
¶
Thus, a member of the group can enable new clients to join by making a GroupInfo object available to them. Note that because a GroupInfo object is specific to an epoch, it will need to be updated as the group advances. In particular, each GroupInfo object can be used for one external join, since that external join will cause the epoch to change.¶
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 13.3.¶
The information in a GroupInfo is not generally public information, but applications can choose to make it available to new members in order to allow External Commits.¶
In principle, External Commits work like regular Commits. However, their content has to meet a specific set of requirements:¶
path field (and is therefore a "full"
Commit). The joiner is added at the leftmost free leaf node (just as if they
were added with an Add proposal), and the path is calculated relative to that
leaf node.¶
The proposals included by value in an External Commit MUST meet the following conditions:¶
path
field MUST meet the same criteria as the LeafNode in an Update for the
removed leaf (see Section 13.1.2). In particular, the credential in the
LeafNode MUST present a set of identifiers that is acceptable to the
application for the removed participant.¶
leaf_node of the path field.¶
new_member¶
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 attacker would need to compromise the PSK as well as the signing key, but the application will need to ensure that continuing, non-resynchronizing members have the required PSK.¶
The sender of a Commit message is responsible for sending a single Welcome message to all the 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 (closest to the leaf) node
which is 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 path_secret<V>;
} PathSecret;
struct {
opaque joiner_secret<V>;
optional<PathSecret> path_secret;
PreSharedKeys psks;
} GroupSecrets;
struct {
KeyPackageRef new_member;
HPKECiphertext encrypted_group_secrets;
} EncryptedGroupSecrets;
struct {
CipherSuite cipher_suite;
EncryptedGroupSecrets secrets<V>;
opaque encrypted_group_info<V>;
} 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
field in the LeafNode 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 LeafNode is
identical to the one in the KeyPackage. If no such field exists, return an
error. Let my_leaf represent this leaf 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.¶
my_leaf, as defined
above.¶
my_leaf 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 leaf node my_leaf and of the node of
the member with LeafNodeRef 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: LeafNode leaf_node;
case parent: ParentNode parent_node;
};
} Node;
optional<Node> ratchet_tree<V>;
¶
The nodes are listed in the order specified by a left-to-right in-order traversal of the rachet tree. Each node is listed between its left subtree and its right subtree. (This is the same ordering as specified for the array-based trees outlined in Appendix B.)¶
The leaves of the tree are stored in even-numbered entries in the array (the leaf with index L in array position 2*L). The root node of the tree is at position 2^k - 1 of the array, where k is the largest number such that 2^k is smaller than the length of the array. Intermediate parent nodes can be identified by performing the same calculation to the subarrays to the left and right of the root, following something like the following algorithm:¶
# Assuming a class Node that has left and right members
def subtree_root(nodes):
# If there is only one node in the array return it
if len(nodes) == 1:
return Node(nodes[0])
# Otherwise, the length of the array MUST be odd
if len(nodes) % 2 == 0:
raise Exception("Malformed node array {}", len(nodes))
# Identify the root of the subtree
k = 0
while (2**(k+1)) < len(nodes):
k += 1
R = 2**k - 1
root = Node(nodes[R])
root.left = subtree_root(nodes[:R])
root.right = subtree_root(nodes[(R+1):])
return root
¶
(Note that this is the same ordering of nodes as in the array-based tree representation described in Appendix B. The algorithms in that section may be used to simplify decoding this extension into other representations.)¶
The example tree in Section 5.1 would be represented as an array of nodes in the following form, where R represents the "subtree root" for a given subarray of the node array:¶
X
______|______
/ \
V Z
__|__ __|
/ \ / \
U W Y |
/ \ / \ / \ |
A B C D E F G
1 1 1
0 1 2 3 4 5 6 7 8 9 0 1 2
<-----------> R <------->
<---> R <---> <---> R -
- R - - R - - R -
¶
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.¶
Regardless of how the client obtains the tree, the client MUST verify that the
root hash of the ratchet tree matches the tree_hash of the GroupContext before
using the tree for MLS operations.¶
The base MLS protocol can be extended in a few ways. New ciphersuites can be added to enable the use of new cryptographic algorithms. New types of proposals can be used to perform new actions within an epoch. Extension fields can be used to add additional information to the protocol. In this section, we discuss some constraints on these extensibility mechanisms that are necessary to ensure broad interoperability.¶
As discussed in Section 6.1, MLS allows the participants in a group to negotiate the cryptographic algorithms used within the group. This extensibility is important for maintaining the security of the protocol over time [RFC7696]. It also creates a risk of interoperability failure due to clients not supporting a common ciphersuite.¶
The ciphersuite registry defined in Section 18.1 attempts to strike a balance on this point. On the one hand, the base policy for the registry is Specification Required, a fairly low bar designed to avoid the need for standards work in cases where different ciphers are needed for niche applications. There is a higher bar (Standards Action) for ciphers to set the Recommended field in the registry. This higher bar is there in part to ensure that the interoperability implications of new ciphersuites are considered.¶
MLS ciphersuites are defined independent of MLS versions, so that in principle the same ciphersuite can be used across versions. Standards work defining new versions of MLS should consider whether it is desirable for the new version to be compatible with existing ciphersuites, or whether the new version should rule out some ciphersuites. For example, a new version could follow the example of HTTP/2, which restricted the set of allowed TLS ciphers (see Section 9.2.2 of [RFC7540].¶
Commit messages do not have an extension field because the set of protocols is extensible. As discussed in Section 13.2, 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.¶
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 the capabilities field of their LeafNode. New
members of a group are informed of the group's GroupContext extensions via the
group_context_extensions field in the GroupInfo 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:¶
capabilities
field MUST indicate support for each extension in the GroupContext.¶
capabilities of the corresponding KeyPackage), then the client MUST
reject the Welcome message and not join the group.¶
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 MLSMessageContent.
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.¶
The content and length of the padding field in MLSCiphertextContent can be
chosen at the time of message encryption by the sender. It is recommended that
padding data is comprised of zero-valued bytes and follows an established
deterministic padding scheme.¶
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 LeafNodes and 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 KeyPackages 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.¶
KeyPackages are intended to be used only once. That is, once a KeyPackage has been used to introduce the corresponding client to a group, it SHOULD be deleted from the KeyPackage publication system. Reuse of KeyPackages can lead to replay attacks.¶
An application MAY allow for reuse of a "last resort" KeyPackage in order to prevent denial of service attacks. Since a KeyPackage 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 KeyPackages. To prevent such a denial of service attack, the KeyPackage publication system SHOULD rate limit KeyPackage requests, especially if not authenticated.¶
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 8.4, 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 18.5 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 |
|---|---|
| LVL | The security level |
| KEM | The KEM algorithm used for HPKE in ratchet tree 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 | R | Ref |
|---|---|---|---|
| 0x0000 | RESERVED | - | RFC XXXX |
| 0x0001 | MLS_128_DHKEMX25519_AES128GCM_SHA256_Ed25519 | Y | RFC XXXX |
| 0x0002 | MLS_128_DHKEMP256_AES128GCM_SHA256_P256 | Y | RFC XXXX |
| 0x0003 | MLS_128_DHKEMX25519_CHACHA20POLY1305_SHA256_Ed25519 | Y | RFC XXXX |
| 0x0004 | MLS_256_DHKEMX448_AES256GCM_SHA512_Ed448 | Y | RFC XXXX |
| 0x0005 | MLS_256_DHKEMP521_AES256GCM_SHA512_P521 | Y | RFC XXXX |
| 0x0006 | MLS_256_DHKEMX448_CHACHA20POLY1305_SHA512_Ed448 | Y | RFC XXXX |
| 0x0007 | MLS_256_DHKEMP384_AES256GCM_SHA384_P384. | Y | RFC XXXX |
| 0xff00 - 0xffff | Reserved for Private Use | - | 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 [RFC9180] [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 |
| 0x0007 | 0x0011 | 0x0002 | 0x0002 | SHA384 | ecdsa_secp384r1_sha384 |
The hash used for the MLS transcript hash is the one referenced in the ciphersuite name. In the ciphersuites defined above, "SHA256", "SHA384", and "SHA512" refer to the SHA-256, SHA-384, 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 include 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
MLS_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 18.¶
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 | external_key_id | KP | Y | RFC XXXX |
| 0x0002 | ratchet_tree | GI | Y | RFC XXXX |
| 0x0003 | required_capabilities | GC | Y | RFC XXXX |
| 0x0004 | external_pub | 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 | Path Required | Reference |
|---|---|---|---|---|
| 0x0000 | RESERVED | N/A | N/A | RFC XXXX |
| 0x0001 | add | Y | N | RFC XXXX |
| 0x0002 | update | Y | Y | RFC XXXX |
| 0x0003 | remove | Y | Y | RFC XXXX |
| 0x0004 | psk | Y | N | RFC XXXX |
| 0x0005 | reinit | Y | N | RFC XXXX |
| 0x0006 | external_init | Y | Y | RFC XXXX |
| 0x0007 | app_ack | Y | N | RFC XXXX |
| 0x0008 | group_context_extensions | Y | Y | RFC XXXX |
| 0xff00 - 0xffff | Reserved for Private Use | N/A | 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.¶
This document registers the "message/mls" MIME media type in order to allow other protocols (ex: HTTP [RFC7540]) to convey MLS messages.¶
Media type name: message
Media subtype name: mls
Required parameters: none
Optional parameters: version
version: The MLS protocol version expressed as a string
<major>.<minor>. If omitted the version is "1.0", which
corresponds to MLS ProtocolVersion mls10. If for some reason
the version number in the MIME type parameter differs from the
ProtocolVersion embedded in the protocol, the protocol takes
precedence.
Encoding scheme: MLS messages are represented using the TLS
presentation language [RFC8446]. Therefore MLS messages need to be
treated as binary data.
Security considerations: MLS is an encrypted messaging layer designed
to be transmitted over arbitrary lower layer protocols. The
security considerations in this document (RFC XXXX) also apply.
¶
Protocol operations in MLS give rise to specific forms of ratchet tree, typically affecting a whole direct path at once. In this section, we describe the protocol operations that could have given rise to the various example trees in this document.¶
To construct the tree in Figure 9:¶
To construct the tree in Figure 10:¶
To construct the tree in Figure 11:¶
B adds a new member at C with a full Commit¶
To construct the tree in Figure 12:¶
A adds new memebers at D and H in a partial commit¶
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, tree with 11 leaves 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
Node: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Leaf: 0 1 2 3 4 5 6 7 8 9 10
¶
This allows us to compute relationships between tree nodes simply by
manipulating indices, rather than having to maintain complicated structures in
memory. The basic rule is that the high-order bits of parent and child nodes
indices have the following relation (where x is an arbitrary bit string):¶
parent=01x => left=00x, right=10x¶
Since node relationships are implicit, the algorithms for adding and removing nodes at the right edge of the tree are quite simple:¶
The following python code demonstrates the tree computations necessary to use an array-based tree for MLS.¶
# 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
¶
An implementation may choose to store ratchet trees in a "link-based" representation, where each node stores references to its parents and/or children. (As opposed to the array-based representation suggested above, where these relationships are computed from relationships between nodes' indices in the array.) Such an implementation needs to update these links to maintain the left-balanced structure of the tree as the tree is extended to add new members, or truncated when memebers are removed.¶
The following code snippet shows how these algorithms could be implemented in Python.¶
class Node:
def __init__(self, value, parent=None, left=None, right=None):
self.value = value # Value of the node
self.parent = parent # Parent node
self.left = left # Left child node
self.right = right # Right child node
def leaf(self):
return self.left == None and self.right == None
def span(self):
if self.leaf():
return 1
return self.left.span() + self.right.span()
def full(self):
span = self.span()
while span % 2 == 0:
span >>= 1
return span == 1
def rightmost_leaf(self):
X = self
while X.right != None:
X = X.right
return X
class Tree:
def __init__(self):
self.root = None # Root node of the tree, initially empty
def extend(self, N):
if self.root == None:
self.root = N
return
# Identify the proper point to insert the new parent node
X = self.root.rightmost_leaf()
while X.full() and X != self.root:
X = X.parent
# If X is not full, insert the new parent under X
P = Node("_", right=N)
N.parent = P
if not X.full():
P.parent = X
P.left = X.right
X.right.parent = P
X.right = P
return
# If X is full, then X is the root, so P replaces the root
P.left = self.root
self.root.parent = P
self.root = P
return
def truncate(self):
X = self.root.rightmost_leaf()
if X == self.root:
self.root = None
return
# If X's parent is the root, then shift the root to the left
if X.parent == self.root:
self.root = self.root.left
self.root.parent = None
return
# Otherwise, reassign the right child of the parent's parent
Q = X.parent.parent
Q.right = X.parent.left
Q.right.parent = Q
return
¶