| Internet-Draft | MLS | July 2022 |
| Barnes, et al. | Expires 12 January 2023 | [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 12 January 2023.¶
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.¶
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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 clients 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.¶
An object that summarizes the state of the group. The group context is signed to bind a message to a particular group, and also provided to new members to help them join a 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.¶
In general, symmetric values are referred to as "keys" or "secrets" interchangeably. Either term denotes a value that MUST be kept confidential to a Client. When labeling individual values, we typically use "secret" to refer to a value that is used derive further secret values, and "key" to refer to a value that is used with an algorithm such as HMAC or an AEAD algorithm.¶
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
if prefix == 3:
raise Exception('invalid variable length integer prefix')
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()
// Check that the encoder used the minimum bits required
if prefix >= 1 && v < (1 << (8*(1 << (prefix-1))-2)):
raise Exception('minimum encoding was not used')
return v
¶
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 interoperability 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, and so on.¶
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:¶
A key schedule that describes the chain of key derivations used to progress from epoch to epoch (mainly using the init_secret and epoch_secret), as well as the derivation of a variety of other secrets (see Table 4), for example:¶
Each member of the group maintains a partial view of these components 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 and not to members who have been removed. Commits thus maintain the property that the the epoch secret is confidential to the members in the current epoch.¶
For each Commit that adds one or more members 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 align with the views held by other members of the group in this 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.¶
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.¶
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.¶
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.¶
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. Reinitialization 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.¶
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.¶
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).¶
Every tree used in this protocol is a perfect binary tree, that is, a complete
balanced binary tree with 2^d leaves all at the same depth d. This
structure is unique for a given depth d.¶
There are multiple ways that an implementation might represent a ratchet tree in memory. A convenient property of left-balanced binary trees (including the complete trees used here) is that they can be represented as an array of nodes, with node relationships computed based on the nodes' indices in the array. A more traditional representation based on linked node objects may also be used. Appendix C and Appendix D 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.¶
Each leaf node in a ratchet tree is given an index (or leaf index), starting
at 0 from the left to 2^d - 1 at the right (for a tree with 2^d leaves). A tree
with 2^d leaves has 2^(d+1) - 1 nodes, including parent nodes.¶
Each node in a ratchet tree is either blank (containing no value) or it holds an asymmetric key pair with some associated data:¶
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 8.8.¶
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 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:¶
...
/
_
______|______
/ \
X[B] _
__|__ __|__
/ \ / \
_ _ Y _
/ \ / \ / \ / \
A B _ D E F _ H
0 1 2 3 4 5 6 7
In this tree, we can see all of the above rules in play:¶
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.¶
The filtered direct path of a leaf node L is the node's direct path, with any node removed whose child on the copath of L has an empty resolution (keeping in mind that any unmerged leaves of the copath child count toward its resolution). The removed nodes do not need their own key pairs because encrypting to the node's key pair would be equivalent to encrypting to its non-copath child.¶
For example, consider the following tree (where blank nodes are indicated with
_, but also assigned a label for reference):¶
In this tree, the direct paths, copaths, and filtered direct paths for the leaf nodes are as follows:¶
| Node | Direct path | Copath | Filtered Direct Path |
|---|---|---|---|
| A | T, U, W | B, V, Y | T, W |
| B | T, U, W | A, V, Y | T, W |
| E | X, Y, W | F, Z, U | X, Y, W |
| F | X, Y, W | E, Z, U | X, Y, W |
| G | Z, Y, W | H, X, U | Y, W |
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.¶
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 MLSContentAuthData 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).¶
Like HPKE public keys, signature public keys are represented as opaque values in a format defined by the ciphersuite's signature scheme.¶
opaque SignaturePublicKey<V>;¶
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, P-384, or P-521), the public key is the output of the uncompressed Elliptic-Curve-Point-to-Octet-String conversion according to [SECG].¶
The signatures used 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].¶
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, SignatureValue) =
Signature.Verify(VerificationKey, SignContent, SignatureValue)
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 17.1.¶
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<V>; HashReference KeyPackageRef; HashReference ProposalRef;¶
MakeKeyPackageRef(value) = RefHash("MLS 1.0 KeyPackage Reference", value)
MakeProposalRef(value) = RefHash("MLS 1.0 Proposal Reference", value)
RefHash(label, value) = Hash(RefHashInput)
Where RefHashInput is defined as:
struct {
opaque label<V> = label;
opaque value<V> = value;
} RefHashInput;
¶
For a KeyPackageRef, the value input is the encoded KeyPackage, and the
ciphersuite specified in the KeyPackage determines the KDF used. For a
ProposalRef, the value input is the MLSAuthenticatedContent carrying the
proposal. In the latter two cases, the KDF is determined by the group's
ciphersuite.¶
Each member of a group presents a credential that provides one or more identities for the member, and associates them with the member's signing key. The identities and signing key are verified by the Authentication Service in use for a group.¶
It is up to the application to decide which identifier or identifiers to use at the application level. 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.¶
// See IANA registry for registered values
uint16 CredentialType;
struct {
opaque cert_data<V>;
} Certificate;
struct {
CredentialType credential_type;
select (Credential.credential_type) {
case basic:
opaque identity<V>;
case x509:
Certificate chain<V>;
};
} Credential;
¶
A BasicCredential is a bare assertion of an identity, without any additional information. The format of the encoded identity is defined by the application.¶
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 public key encoded in the
subjectPublicKeyInfo of the end-entity certificate MUST be identical to the
signature_key in the LeafNode containing this credential.¶
The application using MLS is responsible for specifying which identifiers it finds acceptable for each member in a group. In other words, following the model that [RFC6125] describes for TLS, the application maintains a list of "reference identifiers" for the members of a group, and the credentials provide "presented identifiers". A member of a group is authenticated by first validating that the member's credential legitimately represents some presented identifiers, and then ensuring that the reference identifiers for the member are authenticated by those presented identifiers.¶
The parts of the system that perform these functions are collectively referred to as the Authentication Service (AS) [I-D.ietf-mls-architecture]. A member's credential is said to be validated with the AS when the AS verifies the credential's presented identifiers, and verifies that those identifiers match the reference identifiers for the member.¶
Whenever a new credential is introduced in the group, it MUST be validated with the AS. In particular, at the following events in the protocol:¶
external_senders extension is added to the group, or an existing
external_senders extension is updated.¶
In cases where a member's credential is being replaced, such as Update and Commit cases above, the AS MUST also verify that the set of presented identifiers in the new credential is valid as a successor to the set of presented identifiers in the old credential, according to the application's policy.¶
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.¶
Internally to the protocol, group members are uniquely identified by their leaf index. However, a leaf index is only valid for referring to members in a given epoch. The same leaf index may represent a different member, or no member at all, in a subsequent epoch.¶
The Credentials presented by the clients in a group authenticate application-level identifiers for the clients. However, 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.¶
If needed, applications may add application-specific identifiers to the
extensions field of a LeafNode object with the application_id extension.¶
opaque application_id<V>;¶
However, applications SHOULD NOT rely on the data in an application_id extension
as if it were authenticated by the Authentication Service, and SHOULD gracefully
handle cases where the identifier presented is not unique.¶
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.¶
In most of the protocol, messages are handled in the form of MLSAuthenticatedContent objects. These structures contain the content of the message itself as well as information to authenticate the sender (see Section 7.1). The additional protections required to transmit these messages over an untrusted channel (group membership authentication or AEAD encryption) are added by encoding the MLSAuthenticatedContent as an MLSPlaintext or MLSCiphertext message, which can then be sent as an MLSMessage. Likewise, these protections are enforced (via membership verification or AEAD decryption) when decoding an MLSPlaintext or MLSCiphertext into an MLSAuthenticatedContent object.¶
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),
external(2),
new_member_proposal(3),
new_member_commit(4),
(255)
} SenderType;
struct {
SenderType sender_type;
select (Sender.sender_type) {
case member:
uint32 leaf_index;
case external:
uint32 sender_index;
case new_member_commit:
case new_member_proposal:
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 (MLSContent.content_type) {
case application:
opaque application_data<V>;
case proposal:
Proposal proposal;
case commit:
Commit commit;
}
} MLSContent;
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;
¶
Messages from senders that aren't in the group are sent as MLSPlaintext. See Section 13.1.8 and Section 13.4.3.2 for more details.¶
The following structure is used to fully describe the data transmitted in plaintexts or ciphertexts.¶
struct {
WireFormat wire_format;
MLSContent content;
MLSContentAuthData auth;
} MLSAuthenticatedContent;
¶
The following figure illustrates how the various structures described in this section relate to each other, and the high-level operations used to produce and consume them:¶
MLSContent is authenticated using the MLSContentAuthData structure.¶
struct {
ProtocolVersion version = mls10;
WireFormat wire_format;
MLSContent content;
select (MLSContentTBS.content.sender.sender_type) {
case member:
case new_member_commit:
GroupContext context;
case external:
case new_member_proposal:
struct{};
}
} MLSContentTBS;
opaque MAC<V>;
struct {
// SignWithLabel(., "MLSContentTBS", MLSContentTBS)
opaque signature<V>;
select (MLSContent.content_type) {
case commit:
// MAC(confirmation_key,
// GroupContext.confirmed_transcript_hash)
MAC confirmation_tag;
case application:
case proposal:
struct{};
}
} MLSContentAuthData;
¶
The signature is computed using SignWithLabel with label
"MLSContentTBS" and with a content that covers the message content and
the wire format that will be used for this message. If the sender's
sender_type is member, the content also covers the GroupContext for the
current epoch so that signatures are specific to a given group and epoch.¶
The sender MUST use the private key corresponding to the following signature key
depending on the sender's sender_type:¶
member: The signature key contained in the LeafNode at the index
indicated by leaf_index in the ratchet tree.¶
external: The signature key at the index
indicated by sender_index in the external_senders group context
extension (see Section 13.1.8.1). The
content_type of the message MUST be proposal.¶
new_member_commit: The signature key in the LeafNode in
the Commit's path (see Section 13.4.3.2). The
content_type of the message MUST be commit.¶
new_member_proposal: The signature key in the LeafNode in
the KeyPackage embedded in an External Add Proposal. The
content_type of the message MUST be proposaland the
proposal_type of the Proposal MUST be add.¶
Recipients of an MLSMessage MUST verify the signature with the key depending on
the sender_type of the sender as described above.¶
The confirmation tag value confirms that the members of the group have arrived
at the same state of the group. A MLSContentAuthData is said to be valid when both
the signature and confirmation_tag fields are valid.¶
Plaintexts are encoded using the MLSPlaintext structure.¶
struct {
MLSContent content;
MLSContentAuthData auth;
select (MLSPlaintext.content.sender.sender_type) {
case member:
MAC membership_tag;
case external:
case new_member_commit:
case new_member_proposal:
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 {
MLSContentTBS content_tbs;
MLSContentAuthData auth;
} MLSContentTBM;
¶
membership_tag = MAC(membership_key, MLSContentTBM)¶
When decoding an MLSPlaintext into an MLSAuthenticatedContent,
the application MUST check membership_tag and MUST check that the
MLSContentAuthData 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;
}
MLSContentAuthData auth;
opaque padding[length_of_padding];
} MLSCiphertextContent;
¶
The padding field is set by the sender, by first encoding the content (via the
select) and the auth field, then appending the chosen number of zero bytes.
A receiver identifies the padding field in a plaintext decoded from
MLSCiphertext.ciphertext by first decoding the content and the auth field;
then the padding field comprises any remaining octets of plaintext. The
padding field MUST be filled with all zero bytes. A receiver MUST verify that
there are no non-zero bytes in the padding field, and if this check fails, the
enclosing MLSCiphertext MUST be rejected as malformed.¶
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
four-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 an MLSCiphertextContent, the application MUST check that the MLSContentAuthData is valid.¶
The "sender data" used to look up the key for 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 {
uint32 leaf_index;
uint32 generation;
opaque reuse_guard[4];
} MLSSenderData;
¶
When constructing an MLSSenderData from a Sender object, the sender MUST verify
Sender.sender_type is member and use Sender.leaf_index for
MLSSenderData.leaf_index.¶
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.
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 leaf index indicated in the leaf_index field identifies a
non-blank node.¶
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 5.1.1, 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 encryption_key;
opaque parent_hash<V>;
uint32 unmerged_leaves<V>;
} ParentNode;
¶
The encryption_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 8.9.
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. The
entries in the unmerged_leaves vector MUST be sorted in increasing order.¶
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>;
CredentialType credentials<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 encryption_key;
SignaturePublicKey signature_key;
Credential credential;
Capabilities capabilities;
LeafNodeSource leaf_node_source;
select (LeafNode.leaf_node_source) {
case key_package:
Lifetime lifetime;
case update:
struct{};
case commit:
opaque parent_hash<V>;
}
Extension extensions<V>;
// SignWithLabel(., "LeafNodeTBS", LeafNodeTBS)
opaque signature<V>;
} LeafNode;
struct {
HPKEPublicKey encryption_key;
SignaturePublicKey signature_key;
Credential credential;
Capabilities capabilities;
LeafNodeSource leaf_node_source;
select (LeafNodeTBS.leaf_node_source) {
case key_package:
Lifetime lifetime;
case update:
struct{};
case commit:
opaque parent_hash<V>;
}
Extension extensions<V>;
select (LeafNodeTBS.leaf_node_source) {
case key_package:
struct{};
case update:
opaque group_id<V>;
case commit:
opaque group_id<V>;
}
} LeafNodeTBS;
¶
The encryption_key field contains 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 signature_key field contains the
member's public signing key. The credential field contains information
authenticating both the member's identity and the provided signing key, as
described in Section 6.3.¶
The capabilities field indicates what protocol versions, ciphersuites,
extensions, credential types, and non-default proposal types are supported by a client.
Proposal and extension types defined in this document are considered "default" and thus need
not be listed, while any credential types the application wishes to use MUST
be listed. Extensions that appear in the extensions field of a LeafNode
MUST be included in the extensions field of the capabilities field, and the
credential type used in the LeafNode MUST be included in the credentials 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 8.9).¶
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:¶
signature_key.¶
required_capabilities extension, then the required
extensions, proposals, and credential types MUST be listed in the LeafNode's
capabilities field.¶
capabilities field of each member's LeafNode, and that the
capabilities field of this LeafNode indicates support for all the credential
types currently in use by other members.¶
Verify the lifetime field:¶
lifetime field.¶
lifetime field.¶
extensions field is listed in the
capabilities.extensions field of the LeafNode.¶
Verify the leaf_node_source field:¶
leaf_node_source is
set to key_package.¶
leaf_node_source
is set to update.¶
leaf_node value of the UpdatePath in
a Commit, verify that leaf_node_source is set to commit.¶
Verify that the following fields are unique among the members of the group:¶
Whenever a member initiates an epoch change (i.e., commits; see Section 13.4), they may need to refresh the key pairs of their leaf and of the nodes on their leaf's direct path in order to maintain forward secrecy and post-compromise security.¶
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 8.6.¶
A member updates the nodes along its direct path as follows:¶
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")¶
(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:¶
If member B subsequently generates an UpdatePath based on a secret "leaf_secret", then it would generate the following sequence of path secrets:¶
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:¶
After generating fresh key material and applying it to ratchet forward their local tree state as described in the Section 8.4, the generator broadcasts 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 to the subtree rooted at the parent's non-updated child, i.e., 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.¶
A member of the group updates their direct path by computing new values for their leaf node and the nodes along their filtered direct path:¶
Compute updated path secrets and public keys for the nodes on the sender's filtered direct path.¶
node_pub[n] value derived from the corresponding path secret
path_secret[n].¶
Update the leaf node for the sender.¶
Since the new leaf node effectively updates an existing leaf node in the group,
it MUST adhere to the same restrictions as LeafNodes used in Update proposals
(aside from leaf_node_source). The application MAY specify other changes to
the leaf node, e.g., providing a new signature key, updated capabilities, or
different extensions.¶
The member then encrypts path secrets to the group. For each node in the member's filtered direct path, the member takes the following steps:¶
The recipient of an UpdatePath performs the corresponding steps. First, the recipient merges UpdatePath into the tree:¶
For all nodes on the filtered direct path of the sender's leaf,¶
Compute parent hashes for the nodes in the sender's filtered direct path,
and verify that the parent_hash field of the leaf node matches the parent
hash for the first node in its filtered direct path.¶
Second, the recipient decrypts the path secrets:¶
For example, in order to communicate the example update described in Section 8.4, the member at node B 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).¶
A recipient at node A would decrypt E(pk(A), path_secret\[0\]) to obtain
path_secret\[0\], then use it to derive path_secret[1] and the resulting
node secrets and key pairs. Thus A would have the private keys to nodes X'
and Y', in accordance with the tree invariant.¶
Similarly, a recipient at node D would decrypt E(pk(Z), path_secret[1]) to
obtain path_secret[1], then use it to derive the node secret and and key pair
for the node Y'. As required to maintain the tree invariant, node D does not
receive the private key for the node X', since X' is not an ancestor of D.¶
After processing the update, each recipient MUST delete outdated key material, specifically:¶
As described in Section 13.4, each Commit message may optionally contain an UpdatePath, with a new LeafNode and set of parent nodes for the sender's filtered direct path. For each parent node, the UpdatePath contains a new public key and encrypted path secret. The parent nodes are kept in the same order as the filtered direct path.¶
struct {
opaque kem_output<V>;
opaque ciphertext<V>;
} HPKECiphertext;
struct {
HPKEPublicKey encryption_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
exclude all new leaf nodes added as part of the current Commit. The length of
the encrypted_path_secret vector MUST be equal to the length of the resolution
of the copath node (excluding new leaf nodes), 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 provisional 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.¶
context = SetupBaseR(kem_output, node_private_key, group_context)
path_secret = context.Open("", ciphertext)
¶
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). Since the tree is always full, adding or removing leaves corresponds to increasing or decreasing the depth of the tree, resulting in the number of leaves being doubled or halved. These operations are also known as extending and truncating the tree.¶
Leaves are always added and removed at the right edge of the tree. When the size of the tree needs to be increased, a new blank root node is added, whose left subtree is the existing tree and right subtree is a new all-blank subtree. This operation is typically done when adding a member to the group.¶
_ <-- new blank root _
__|__ __|__
/ \ / \
X ===> X _ <-- new blank subtree ===> X _
/ \ / \ / \ / \ / \
A B A B _ _ A B C _
^
|
+-- new member
When the right subtree of the tree no longer has any non-blank nodes, it can be safely removed. The root of the tree and the right subtree are discarded (whether or not the root node is blank). The left child of the root becomes the new root node, and the left subtree becomes the new tree. This operation is typically done after removing a member from the group.¶
Y Y
__|__ __|__
/ \ / \
X _ ===> X _ ==> X <-- new root
/ \ / \ / \ / \ / \
A B C _ A B _ _ A B
^
|
removed member --+
Concrete algorithms for these operations on array-based and link-based trees are provided in Appendix C and Appendix D. The concrete algorithms are non-normative. An implementation MAY use any algorithm that produces the correct tree in its internal representation.¶
MLS hashes the contents of the tree in two ways to authenticate different properties of the tree. This section defines tree hashes, and parent hashes are defined in Section 8.9.¶
Each node in a ratchet tree has a tree hash that summarizes the subtree below that node. The tree hash of the root is used in the GroupContext to confirm that the group agrees on the whole tree. Tree hashes are computed recursively from the leaves up to the root.¶
The tree hash of an individual node is the hash of the node's TreeHashInput
object, which may contain either a LeafNodeHashInput or a
ParentNodeHashInput depending on the type of node. LeafNodeHashInput objects
contain the leaf_index and the LeafNode (if any). ParentNodeHashInput
objects contain the ParentNode (if any) and the tree hash of the node's left
and right children. For both parent and leaf nodes, the optional node value
MUST be absent if the node is blank and present if the node contains a value.¶
enum {
reserved(0),
leaf(1),
parent(2),
(255)
} NodeType;
struct {
NodeType node_type;
select (TreeHashInput.node_type) {
case leaf: LeafNodeHashInput leaf_node;
case parent: ParentNodeHashInput parent_node;
}
} TreeHashInput;
struct {
uint32 leaf_index;
optional<LeafNode> leaf_node;
} LeafNodeHashInput;
struct {
optional<ParentNode> parent_node;
opaque left_hash<V>;
opaque right_hash<V>;
} ParentNodeHashInput;
¶
The tree hash of an entire tree corresponds to the tree hash of the root node, which is computed recursively by starting at the leaf nodes and building up.¶
While tree hashes summarize the state of a tree at point in time, parent hashes capture information about how keys in the tree were populated.¶
When a client sends a commit to change a group, it can include an UpdatePath to assign new keys to the nodes along its filtered direct path. When a client computes an UpdatePath (as defined in Section 8.5), it computes and signs a parent hash that summarizes the state of the tree after the UpdatePath has been applied. These summaries are constructed in a chain from the root to the member's leaf so that the part of the chain closer to the root can be overwritten as nodes set in one UpdatePath are reset by a later UpdatePath.¶
As a result, the signature over the parent hash in each member's leaf effectively signs the subtree of the tree that hasn't been changed since that leaf was last changed in an UpdatePath. A new member joining the group uses these parent hashes to verify that the parent nodes in the tree were set by members of the group, not chosen by an external attacker. For an example of how this works, see Appendix B.¶
Consider a ratchet tree with a non-blank parent node P and children D and S (for "parent", "direct path", and "sibling"), with D and P in the direct path of a leaf node L (for "leaf"):¶
...
/
P
__|__
/ \
D S
/ \ / \
... ... ... ...
/
L
The parent hash of P changes whenever an UpdatePath object is applied to
the ratchet tree along a path from a leaf L traversing node D (and hence also
P). The new "Parent hash of P (with copath child S)" is obtained by hashing P's
ParentHashInput struct.¶
struct {
HPKEPublicKey encryption_key;
opaque parent_hash<V>;
opaque original_sibling_tree_hash<V>;
} ParentHashInput;
¶
The field encryption_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 the leaf L. This way, P's Parent Hash fixes
the new HPKE public key of each non-blank node 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 tree hash of S in the ratchet tree
modified as follows: For each leaf L in P.unmerged_leaves, blank L and remove
it from the unmerged_leaves sets of all parent nodes.¶
Observe that original_sibling_tree_hash does not change between updates of P.
This property is crucial for the correctness of the protocol.¶
Note that original_sibling_tree_hash is the tree hash of S, not the parent
hash. The parent_hash field in ParentHashInput captures information about the
nodes above P. the original_sibling_tree_hash captures information about the
subtree under S that is not being updated (and thus the subtree to which a path
secret for P would be encrypted according to Section 8.5).¶
For example, in the following tree:¶
W [F]
______|_____
/ \
U Y [F]
__|__ __|__
/ \ / \
T _ _ _
/ \ / \ / \ / \
A B C D E F G _
With P = W and S = Y, original_sibling_tree_hash is the tree hash of the
following tree:¶
Y
__|__
/ \
_ _
/ \ / \
E _ G _
¶
Because W.unmerged_leaves includes F, F is blanked and removed from
Y.unmerged_leaves.¶
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 a 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 leaves were blanked),
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.¶
In ParentNode objects and LeafNode objects with leaf_node_source set to
commit, the value of the parent_hash field is the parent hash of the next
non-blank parent node above the node in question (the next node in the filtered
direct path). Using the node labels in Figure 14, the
parent_hash field of D is equal to the parent hash of P with copath child S.
This is the case even when the node D is a leaf node.¶
The parent_hash field of a LeafNode is signed by the member. 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
prevents malicious insiders from constructing artificial ratchet trees with a
node D whose HPKE secret key is known to the insider yet where the insider isn't
assigned a leaf in the subtree rooted at D. 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 D is valid with respect to a parent node P if the following criteria hold. Here C and S are the children of P (for "child" and "sibling"), with C being the child that is on the direct path of D (possibly D itself) and S the other child:¶
parent_hash field of D is equal to the parent hash of P with copath
child S.¶
unmerged_leaves
with the subtree under C is equal to the resolution of C with D removed.¶
These checks verify that D and P were updated at the same time (in the same UpdatePath), and that they were neighbors in the UpdatePath because the nodes in between them would have omitted from the filtered direct path.¶
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.¶
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)
DeriveSecret(Secret, Label) =
ExpandWithLabel(Secret, Label, "", KDF.Nh)
¶
Where KDFLabel is specified as:¶
struct {
uint16 length = Length;
opaque label<V> = "MLS 1.0 " + Label;
opaque context<V> = Context;
} KDFLabel;
¶
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:¶
A number of values are derived from the epoch secret for different purposes:¶
| Label | Secret | Purpose |
|---|---|---|
| "sender data" |
sender_data_secret
|
Deriving keys to encrypt sender data |
| "encryption" |
encryption_secret
|
Deriving message encryption keys (via the secret tree) |
| "exporter" |
exporter_secret
|
Deriving exported secrets |
| "external" |
external_secret
|
Deriving the external init key |
| "confirm" |
confirmation_key
|
Computing the confirmation MAC for an epoch |
| "membership" |
membership_key
|
Computing the membership MAC for an MLSPlaintext |
| "resumption" |
resumption_psk
|
Proving membership in this epoch (via a PSK injected later) |
| "authentication" |
epoch_authenticator
|
Confirming that two clients have the same view of the group |
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 {
ProtocolVersion version = mls10;
CipherSuite cipher_suite;
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:¶
cipher_suite is the cipher suite used by the group.¶
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 8.8.¶
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
MLSAuthenticatedContent 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 MLSAuthenticatedContent object in which they were sent.¶
The transcript hash comprises two individual hashes:¶
confirmed_transcript_hash that represents a transcript over the whole
history of Commit messages, up to and including the signature of the most
recent Commit.¶
interim_transcript_hash that covers the confirmed transcript hash plus
the confirmation_tag of the most recent Commit.¶
New members compute the interim transcript hash using the confirmation_tag
field of the GroupInfo struct, while existing members can compute it directly.¶
Each Commit message updates these hashes by way of its enclosing MLSAuthenticatedContent. The MLSAuthenticatedContent struct is split into ConfirmedTranscriptHashInput and InterimTranscriptHashInput. The former is used to update the confirmed transcript hash and the latter to update the interim transcript hash.¶
struct {
WireFormat wire_format;
MLSContent content; // with content.content_type == commit
opaque signature<V>;
} ConfirmedTranscriptHashInput;
struct {
MAC confirmation_tag;
} InterimTranscriptHashInput;
¶
interim_transcript_hash_[0] = ""; // zero-length octet string
confirmed_transcript_hash_[n] =
Hash(interim_transcript_hash_[n] ||
ConfirmedTranscriptHashInput_[n]);
interim_transcript_hash_[n+1] =
Hash(confirmed_transcript_hash_[n] ||
InterimTranscriptHashInput_[n]);
¶
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
perform 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 to derive new secrets for use outside of MLS.¶
MLS-Exporter(Label, Context, Length) =
ExpandWithLabel(DeriveSecret(exporter_secret, Label),
"exporter", Hash(Context), Length)
¶
Applications SHOULD provide a unique label to MLS-Exporter that
identifies the secret's intended purpose. This is to help prevent the same
secret from being generated and used in two different places.¶
The exported values are bound to the group epoch from which the
exporter_secret is derived, and hence reflect 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_psk 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_psk may be stored.¶
The main MLS key schedule provides a per-epoch epoch_authenticator. If one
member of the group is being impersonated by an active attacker, the
epoch_authenticator computed by their client will differ from those computed
by the other group members.¶
This property can be used to construct defenses against impersonation attacks that are effective even if members' signature keys are compromised. As a trivial example, if the users of the clients in an MLS group were to meet in person and reliably confirm that their epoch authenticator values were equal (using some suitable user interface), then each user would be assured that the others were not being impersonated in the current epoch. As soon as the epoch changed, though, they would need to re-do this confirmation. The state of the group would have changed, possibly introducing an attacker.¶
More generally, in order for the members of an MLS group to obtain concrete
authentication protections using the epoch_authenticator, they will need to
use it in some secondary protocol (such as the face-to-face protocol above).
The details of that protocol will then determine the specific authentication
protections provided to the MLS 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):¶
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:¶
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".¶
The following figure shows a secret tree for a four-member group, with the handshake and application ratchets that member D will use for sending and the first two application keys and nonces.¶
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 big endian uint32.¶
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, consider the Secret Tree shown in Figure 16. Client A, B, or C would generate the illustrated values on receiving a message from D with generation equal to 1, having not received a message with generation 0 (e.g., due to out-of-order delivery). In such a case, the following values would be consumed:¶
encryption_secret for the
epoch)¶
epoch_secret, commit_secret, psk_secret, and joiner_secret for the
current epoch¶
Other values may be retained (not consumed):¶
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 the case of last resort (see Section 16.4). 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 encryption_key and
signature_key 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
KeyPackageTBS 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, credential types, and non-default proposal/extension types are supported
by the client. (Proposal and extension 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:¶
GroupContext.¶
leaf_node of the KeyPackage is valid for a KeyPackage
according to Section 8.3.¶
leaf_node.credential.¶
leaf_node.encryption_key is different from the value of
the init_key field.¶
A group is always created with a single member, the "creator". The other members are added when the creator effectively sends itself Add proposals, commits them, and then sends the corresponding Welcome message to the new participants. These processes are described in detail in Section 13.1.1, Section 13.4, and Section 13.4.3.1.¶
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¶
Group IDs SHOULD be constructed in such a way that there's an overwhelmingly low
probability of honest group creators generating the same group ID, even without
assistance from the Delivery Service. For example, by making the group ID a
freshly generated random value of size KDF.Nh. The Delivery Service MAY
attempt to ensure that group IDs are globally unique by rejecting the creation
of new groups with a previously used ID.¶
The recipient of a Welcome message processes it as described in Section 13.4.3.1.¶
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>;
CredentialType credential_types<V>;
} RequiredCapabilities;
¶
This extension lists the extensions, proposals, and credential 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. Note that this is not true for credential types.¶
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 are updated, a GroupContextExtensions
proposal is deemed 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 creates an initial Commit setting up a new group that matches the ReInit and sends a Welcome message¶
group_id, version, cipher_suite, and extensions fields in the Welcome
message MUST be the same as the corresponding fields in the ReInit
proposal. The epoch in the Welcome message MUST be 1.¶
resumption with usage
reinit, where the group_id field matches the old group and the epoch
field indicates the epoch after the Commit covering the ReInit.¶
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 recreate the group instead. 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.¶
A member can create a subgroup by performing the following steps:¶
resumption with usage branch. To avoid key
re-use, the psk_nonce included in the PreSharedKeyID object MUST be a
randomly sampled nonce of length KDF.Nh.¶
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 by checking:¶
version and ciphersuite values in the Welcome are the same as
those used by the old group.¶
epoch in the Welcome message MUST be 1.¶
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 MLSContent 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 group_context_extensions: GroupContextExtensions;
};
} Proposal;
¶
On receiving an MLSContent containing a Proposal, a client MUST verify the
signature inside MLSContentAuthData and that the epoch field of the enclosing
MLSContent is equal to the epoch field of the current GroupContext object.
If the verification is successful, 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.¶
struct {
KeyPackage key_package;
} Add;
¶
An Add proposal is invalid if the KeyPackage is invalid according to Section 11.1.¶
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.¶
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;
¶
An Update proposal is invalid if the LeafNode is invalid for an Update proposal according to Section 8.3.¶
A member of the group applies an Update message by taking the following steps:¶
A Remove proposal requests that the member with the leaf index removed be removed
from the group.¶
struct {
uint32 removed;
} Remove;
¶
A Remove proposal is invalid if the removed field does not identify a non-blank
leaf node.¶
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 13.4), since proposals such as Update can change the
LeafNode stored at a leaf. Let L be this leaf node.¶
2^d leaves, where d is
the smallest value such that 2^d > L.¶
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 ReInit proposal is invalid if the version field is less than the version
for the current group.¶
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.¶
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.¶
A GroupContextExtensions proposal is used to update the list of extensions in the GroupContext for the group.¶
struct {
Extension extensions<V>;
} GroupContextExtensions;
¶
A GroupContextExtensions proposal is invalid if it includes a
required_capabilities extension and some members of the group do not support
some of the required capabilities (including those added in the same commit,
and excluding those removed).¶
A member of the group applies a GroupContextExtensions proposal with the following steps:¶
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 in two cases. One case, indicated by an external SenderType
is useful in cases where, for example, an automated 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.¶
ReInit proposals can also be sent to the group by an external sender, for
example to enforce a changed policy regarding MLS version or ciphersuite.¶
The external SenderType requires that signers are pre-provisioned
to the clients within a group and can only be used if the
external_senders extension is present in the group's GroupContext.¶
The other case, indicated by a new_member_proposal SenderType is useful when
existing members of the group can independently authorize the addition of an
MLS client proposing it be added to the group. External proposals which are not
authorized are considered invalid.¶
An external proposal MUST be sent as an MLSPlaintext object, since the sender will not have the keys necessary to construct an MLSCiphertext object.¶
The external_senders extension is a group context extension that contains
the credentials and signature keys of senders that are permitted to send
external proposals to the group.¶
struct {
SignaturePublicKey signature_key;
Credential credential;
} ExternalSender;
ExternalSender external_senders<V>;
¶
A group member creating a commit and a group member processing a commit MUST verify that the list of committed proposals is valid using one of the following procedures, depending on whether the commit is external or not.¶
For a regular, i.e. not external, commit the list is invalid if any of the following occurs:¶
An application may extend the above procedure by additional rules, for example, requiring application-level permissions to add members, or rules concerning non-default proposal types.¶
For an external commit, the list is valid if it contains only the following proposals (not necessarily in this order):¶
path field of the external commit MUST meet the same criteria as would 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.¶
Proposal types defined in the future may make updates to the above validation logic to incorporate considerations related to proposals of the new type.¶
The sections above defining each proposal type describe how each individual proposals is applied. When creating or processing a Commit, a client applies a list of proposals to the ratchet tree and GroupContext. The client MUST apply the proposals in the list in the following order:¶
extensions field
of the GroupContext for the group with the contents of the proposal. The
new extensions MUST be used for evaluating other proposals in this list. For
example, if a GroupContextExtensions proposal adds a required_capabilities
extension, then any Add proposals need to indicate support for those
capabilities.¶
init_secret for
use later in Commit processing.¶
Proposal types defined in the future MUST specify how the above steps are to be adjusted to accommodate the application of proposals of the new type.¶
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 MLSAuthenticatedContent object 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.¶
A sender and a receiver of a Commit MUST verify that the committed list of proposals is valid as specified in Section 13.2. A list is invalid if, for example, it includes an Update and a Remove for the same member, or an Add when the sender does not have the application-level permission to add new users.¶
The sender of a Commit SHOULD include all proposals that it has received during the current epoch, that are valid according to the rules for their proposal types and according to application policy, as long as this results in a valid proposal list.¶
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 17.3.¶
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, a client updates the ratchet tree and GroupContext for the group. These values advance from an "old" state reflecting the current epoch to a "new" state reflecting the new epoch initiated by the Commit. When the Commit includes an UpdatePath, a "provisional" group context is constructed that reflects changes due to the proposals and UpdatePath, but with the old confirmed transcript hash.¶
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.¶
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:¶
commit_secret as the value path_secret[n+1] derived from the
last path secret value (path_secret[n]) derived for the UpdatePath.¶
Construct a provisional GroupContext object containing the following values:¶
path field in the Commit.¶
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).¶
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 MLSContent object containing the Commit object. Sign the MLSContent 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.¶
confirmation_tag from the MLSContentAuthData.¶
Protect the MLSAuthenticatedContent object using keys from the old epoch:¶
Construct a GroupInfo reflecting the new state:¶
joiner_secret
for the new epoch (see Section 13.4.3.1)¶
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 MLSContent is equal
to the epoch field of the current GroupContext object¶
Unprotect the Commit using the keys from the current epoch:¶
proposals vector is valid as specified in Section 13.2.¶
proposals vector are available.¶
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, validate it and apply it to the tree:¶
leaf_node_source field MUST be set to commit.¶
encryption_key value in the LeafNode is different from the
committer's current leaf node.¶
Construct a provisional GroupContext object containing the following values:¶
commit_secret as the value path_secret[n+1] derived from the
last path secret value (path_secret[n]) derived for the UpdatePath.¶
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 MLSContentAuthData 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 {
GroupContext group_context;
Extension extensions<V>;
MAC confirmation_tag;
uint32 signer;
// SignWithLabel(., "GroupInfoTBS", GroupInfoTBS)
opaque signature<V>;
} GroupInfo;
¶
New members MUST verify that group_id is unique among the groups they're
currently participating in.¶
New members also MUST verify the signature using the public key taken from the
leaf node of the ratchet tree with leaf index signer. The
signature covers the following structure, comprising all the fields in the
GroupInfo above signature:¶
struct {
GroupContext group_context;
Extension extensions<V>;
MAC confirmation_tag;
uint32 signer;
} GroupInfoTBS;
¶
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;
PreSharedKeyID psks<V>
} 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 value with the algorithms indicated
by the ciphersuite and the private key corresponding to init_key in the
referenced KeyPackage.¶
PreSharedKeyID is part of the GroupSecrets and the client is not in
possession of the corresponding PSK, return an error. Additionally, if a
PreSharedKeyID has type resumption with usage reinit or branch, verify
that it is the only such PSK.¶
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 the node is blank or if
signature verification fails, return an error.¶
group_id is unique among the groups that the client is
currently participating in.¶
cipher_suite in the GroupInfo matches the cipher_suite in
the KeyPackage.¶
Verify the integrity of the ratchet tree.¶
tree_hash field
in GroupInfo.¶
unmerged_leaves represents a non-blank leaf node that is a descendant of
the parent node.¶
my_leaf represent this leaf in the tree.¶
Construct a new group state using the information in the GroupInfo object.¶
group_context field 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 leaf index 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.¶
If a PreSharedKeyID was used that has type resumption with usage reinit
or branch, verify that the epoch field in the GroupInfo is equal to 1.¶
reinit, verify that the last Commit to the referenced group
contains a ReInit proposal and that the group_id, version,
cipher_suite, and group_context.extensions fields of the GroupInfo match
the ReInit proposal. Additionally, verify that all the members of the old
group are also members of the new group, according to the application.¶
branch, verify that the version and cipher_suite of the new
group match those of the old group, and that the members of the new group
compose a subset of the members of the old group, according to the
application.¶
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 its extensions field.¶
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 13.4.3.3.¶
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.¶
leaf_node of the path field.¶
new_member_commit.¶
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.¶
By default, a GroupInfo message only provides the joiner with a hash of 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:¶
struct {
NodeType node_type;
select (Node.node_type) {
case leaf: LeafNode leaf_node;
case parent: ParentNode parent_node;
};
} Node;
optional<Node> ratchet_tree<V>;
¶
Each entry in the ratchet_tree vector provides the value for a node in the
tree, or the null optional for a blank node.¶
The nodes are listed in the order specified by a left-to-right in-order traversal of the ratchet 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 C.)¶
If the tree has 2^d leaves, then it has 2^(d+1) - 1 nodes. The
ratchet_tree vector logically has this number of entries, but the sender
SHOULD NOT include blank nodes after the last non-blank node. If a receiver
encounters a vector whose length L is not of the form 2^(d+1) - 1, then the
receiver MUST extend it to the right with blank values until it has such a
length, adding the minimum number of blank values possible. (Obviously, this
may be done "virtually", by synthesizing blank nodes when required, as opposed
to actually changing the structure in memory.)¶
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^d - 1 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
d = 0
while (2**(d+1)) < len(nodes):
d += 1
R = 2**d - 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 C. The algorithms in that section may be used to simplify decoding this extension into other representations.)¶
For example, the following tree with six non-blank leaves would be represented
as an array of eleven elements, [A, W, B, X, C, _, D, Y, E, Z, F]. The above
decoding procedure would identify the subtree roots as follows (using R to
represent a subtree root):¶
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.
# Extensibility¶
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 17.1 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 proposals is extensible. As discussed in Section 13.4, 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.¶
In order to ensure that MLS provides meaningful authentication it is important that each member is able to authenticate some identity information for each other member. Identity information is encoded in Credentials, so this property is provided by ensuring that members use compatible credential types.¶
The types of credential that may be used in a group is restricted to what all
members of the group support, as specified by the capabilities field of each
LeafNode in the ratchet tree. An application can introduce new credential types
by choosing an unallocated identifier from the registry in
Section 17.4 and indicating support for the credential type in
published LeafNodes, whether in Update proposals to existing groups or
KeyPackages that are added to new groups. Once all members in a group indicate
support for the credential type, members can start using LeafNodes with the new
credential. Application may enforce that certain credential types always remain
supported by adding a required_capabilities extension to the group's
GroupContext, which would prevent any member from being added to the group that
doesn't support them.¶
In future extensions to MLS, it may be useful to allow a member to present more than one credential. For example, such credentials might present different attributes attested by different authorities. To be consistent with the general principle stated at the beginning of this section, such an extension would need to ensure that each member can authenticate some identity for each other member. For each pair of members (Alice, Bob), Alice would need to present at least one credential of a type that Bob supports.¶
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
extensions field in the group_context field of the GroupInfo object. The
extensions field in a GroupInfo object (outside of the group_context field)
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 the 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.¶
The parameters of a group may be changed by sending a GroupContextExtensions proposal to enable additional extensions, or by reinitializing the group as described in Section 12.2.¶
Each Commit message is premised on a given starting state,
indicated by the epoch field of the enclosing MLSContent.
If the changes implied by a Commit message 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.¶
Applications MUST have an established way to resolve conflicting Commit messages for the same epoch. They can do this either by preventing conflicting messages from occurring in the first place, or by developing rules for deciding which Commit out of several sent in an epoch will be canonical. The approach chosen MUST minimize the amount of time that forked or previous group states are kept in memory, and promptly delete them once they're no longer necessary to ensure forward secrecy.¶
The generation of Commit messages MUST NOT modify a client's state, since the client doesn't know at that time whether the changes implied by the Commit message will conflict with another Commit or not. Similarly, the Welcome message corresponding to a Commit MUST NOT be delivered to a new joiner until it's clear that the Commit has been accepted.¶
Regardless of how messages are kept in sequence, there is a risk that in a sufficiently busy group, a given member may never be able to send a Commit message because they always lose to other members. The degree to which this is a practical problem will depend on the dynamics of the application.¶
The primary purpose of handshake messages are to provide an authenticated group
key exchange to clients. In order to protect application messages sent among the
members of a group, the encryption_secret provided by the key schedule is used
to derive a sequence of nonces and keys for message encryption. Every epoch
moves the key schedule forward which triggers the creation of a new secret
tree, as described in Section 10, along with a new set of symmetric
ratchets of nonces and keys for each member.¶
Each client maintains their own local copy of the 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.¶
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.
The sender identifier and content type is used to identify which
symmetric ratchet to use from the secret tree. The
generation counter determines how far into the ratchet to iterate in
order to produce the required nonce and key for encryption or decryption.¶
Application messages MAY 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?", then the answer "Wednesday" could be leaked to an adversary solely by the ciphertext length.¶
The length of the padding field in MLSCiphertextContent can be
chosen at the time of message encryption by the sender. Senders may use padding
to reduce the ability of attackers outside the group to infer the size of the
encrypted content.¶
During each epoch, senders MUST NOT encrypt more data than permitted by the security bounds of the AEAD scheme used [I-D.irtf-cfrg-aead-limits].¶
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 generation counter, a client can receive messages out of order. When messages are received out of order, the client moves the sender ratchet forward to match the received generation counter. Any unused nonce and key pairs from the ratchet are potentially stored so that they can be used to decrypt the messages which were delayed or reordered.¶
Applications SHOULD define a policy on how long to keep unused nonce and key
pairs for a sender, and the maximum number to keep. This is in addition to
ensuring that these nonce and key pairs are promptly deleted when the epoch
ends. Applications SHOULD also define a policy limiting the maximum number of
steps that clients will move the ratchet forward in response to a new message.
Messages received with a generation counter that's too much higher than the last
message received would then be rejected. This avoids causing a denial-of-service
attack by requiring the recipient to perform an excessive number of key
derivations. For example, a malicious group member could send a message with
generation = 0xffffffff at the beginning of a new epoch, forcing recipients to
perform billions of key derivations.¶
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 versions 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 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 reinitialize the group 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. These members will either need to add themselves back with an external Commit, or reinitialize the group from scratch.¶
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 17.5 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 17.¶
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 | application_id | LN | Y | RFC XXXX |
| 0x0002 | ratchet_tree | GI | Y | RFC XXXX |
| 0x0003 | required_capabilities | GC | Y | RFC XXXX |
| 0x0004 | external_pub | GI | Y | RFC XXXX |
| 0x0005 | external_senders | GC | 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:¶
path field populated (see Section 13.4).¶
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 | 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 (e.g., HTTP [RFC7540]) to convey MLS messages.¶
message¶
mls¶
none¶
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.¶
MLS messages are represented using the TLS presentation language [RFC8446]. Therefore MLS messages need to be treated as binary data.¶
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 10:¶
To construct the tree in Figure 9:¶
D removes B and C, with the following effects:¶
To better understand how parent hashes are maintained, let's look in detail at how they evolve in a small group. Consider the following sequence of operations:¶
Then the parent hashes associated to the nodes will be updated as follows (where
we use the shorthand ph for parent hash, th for tree hash, and osth for
original sibling tree hash):¶
A adds B: set X¶
A.parent_hash = ph(X) = H(X, ph="", osth=th(B))¶
B adds C, D: set B', X', Y¶
C sends empty Commit: set C', Z', Y'¶
When a new member joins, they will receive a tree that has the following parent hash values, and compute the indicated parent-hash validity relationships:¶
| Node | Parent hash value | Valid? |
|---|---|---|
| A | H(X, ph="", osth=th(B)) | No, B changed |
| B' | H(X', ph=X'.parent_hash, osth=th(A)) | Yes |
| C' | H(Z', ph=Z'.parent_hash, osth=th(D)) | Yes |
| D | (none, never sent an UpdatePath) | N/A |
| X' | H(Y, ph="", osth=th(Z)) | No, Y and Z changed |
| Z' | H(Y', ph="", osth=th(X')) | Yes |
In other words, the joiner will find the following path-hash links in the tree:¶
Since these chains collectively cover all non-blank parent nodes in the tree, the tree is parent-hash valid.¶
Note that this tree, though valid, contains invalid parent-hash links. If a client were checking parent hashes top-down from Y', for example, they would find that X' has an invalid parent hash relative to Y', but that Z' has valid parent hash. Likewise, if the client were checking bottom-up, they would find that the chain from B' ends in an invalid link from X' to Y'. These invalid links are the natural result of multiple clients having committed.¶
Note also the way the tree hash and the parent hash interact. The parent hash of node C' includes the tree hash of node D. The parent hash of node Z' includes the tree hash of X', which covers nodes A and B' (including the parent hash of B'). Although the tree hash and the parent hash depend on each other, the dependency relationships are structured so that there's never a circular dependency.¶
In the particular case where a new member first receives the tree for a group (e.g., in a ratchet tree GroupInfo extension Section 13.4.3.3), the parent hashes will be expressed in the tree representation, but the tree hash need not be. Instead, the new member will recompute the tree hashes for all the nodes in the tree, verifying that this matches the tree hash in the GroupInfo object. Then, if the tree is valid, then the subtree hashes computed in this way will align with the inputs needed for parent hash validation (except where recomputation is needed to account for unmerged leaves).¶
One benefit of using complete 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, the tree with 8 leaves has
the following structure:¶
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. If there are N nodes in
the array:¶
N + 1 blank values to the end of the array.¶
(N-1) / 2 entries.¶
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.
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.
def right(x):
k = level(x)
if k == 0:
raise Exception('leaf node has no children')
return x ^ (0x03 << (k - 1))
# The parent of a node.
def parent(x, n):
if x == root(n):
raise Exception('root node has no parent')
k = level(x)
b = (x >> (k + 1)) & 0x01
return (x | (1 << k)) ^ (b << (k + 1))
# The other child of the node's parent.
def sibling(x, n):
p = parent(x, n)
if x < p:
return right(p)
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 balanced structure of the tree as the tree is extended to add new members, or truncated when members are removed.¶
The following code snippet shows how these algorithms could be implemented in Python.¶
class Node:
def __init__(self, value, left=None, right=None):
self.value = value # Value of the node
self.left = left # Left child node
self.right = right # Right child node
@staticmethod
def blank_subtree(depth):
if depth == 1:
return Node(None)
L = Node.blank_subtree(depth-1)
R = Node.blank_subtree(depth-1)
return Node(None, left=L, right=R)
def empty(self):
L_empty = (self.left == None) or self.left.empty()
R_empty = (self.left == None) or self.left.empty()
return (self.value == None) and L_empty and R_empty
class Tree:
def __init__(self):
self.depth = 0 # Depth of the tree
self.root = None # Root node of the tree, initially empty
# Add a blank subtree to the right
def extend(self):
if self.depth == 0:
self.depth = 1
self.root = Node(None)
L = self.root
R = Node.blank_subtree(self.depth)
self.root = Node(None, left=self.root, right=R)
self.depth += 1
# Truncate the right subtree
def truncate(self):
if self.root == None or self.root.right == None:
raise Exception("Cannot truncate a tree with 0 or 1 nodes")
if not self.root.right.empty():
raise Exception("Cannot truncate non-blank subtree")
self.depth -= 1
self.root = self.root.left
¶