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diff --git a/docs/megolm.rst b/docs/megolm.rst new file mode 100644 index 0000000..7853963 --- /dev/null +++ b/docs/megolm.rst @@ -0,0 +1,290 @@ +.. Copyright 2016 OpenMarket Ltd +.. +.. Licensed under the Apache License, Version 2.0 (the "License"); +.. you may not use this file except in compliance with the License. +.. You may obtain a copy of the License at +.. +.. http://www.apache.org/licenses/LICENSE-2.0 +.. +.. Unless required by applicable law or agreed to in writing, software +.. distributed under the License is distributed on an "AS IS" BASIS, +.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +.. See the License for the specific language governing permissions and +.. limitations under the License. + + +Megolm group ratchet +==================== + +An AES-based cryptographic ratchet intended for group communications. + +.. contents:: + +Background +---------- + +The Megolm ratchet is intended for encrypted messaging applications where there +may be a large number of recipients of each message, thus precluding the use of +peer-to-peer encryption systems such as `Olm`_. + +It also allows a receipient to decrypt received messages multiple times. For +instance, in client/server applications, a copy of the ciphertext can be stored +on the (untrusted) server, while the client need only store the session keys. + +Overview +-------- + +Each participant in a conversation uses their own outbound session for +encrypting messages. A session consists of a ratchet and an `Ed25519`_ keypair. + +Secrecy is provided by the ratchet, which can be wound forwards but not +backwards, and is used to derive a distinct message key for each message. + +Authenticity is provided via Ed25519 signatures. + +The value of the ratchet, and the public part of the Ed25519 key, are shared +with other participants in the conversation via secure peer-to-peer +channels. Provided that peer-to-peer channel provides authenticity of the +messages to the participants and deniability of the messages to third parties, +the Megolm session will inherit those properties. + +The Megolm ratchet algorithm +---------------------------- + +The Megolm ratchet :math:`R_i` consists of four parts, :math:`R_{i,j}` for +:math:`j \in {0,1,2,3}`. The length of each part depends on the hash function +in use (256 bits for this version of Megolm). + +The ratchet is initialised with cryptographically-secure random data, and +advanced as follows: + +.. math:: + \begin{align} + R_{i,0} &= + \begin{cases} + H_0\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\ + R_{i-1,0} &\text{otherwise} + \end{cases}\\ + R_{i,1} &= + \begin{cases} + H_1\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\ + H_1\left(R_{2^16(m-1),1}\right) &\text{if }\exists m | i = 2^16m\\ + R_{i-1,1} &\text{otherwise} + \end{cases}\\ + R_{i,2} &= + \begin{cases} + H_2\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\ + H_2\left(R_{2^16(m-1),1}\right) &\text{if }\exists m | i = 2^16m\\ + H_2\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\ + R_{i-1,2} &\text{otherwise} + \end{cases}\\ + R_{i,3} &= + \begin{cases} + H_3\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\ + H_3\left(R_{2^16(m-1),1}\right) &\text{if }\exists m | i = 2^16m\\ + H_3\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\ + H_3\left(R_{i-1,3}\right) &\text{otherwise} + \end{cases} + \end{align} + +where :math:`H_0`, :math:`H_1`, :math:`H_2`, and :math:`H_3` are different hash +functions. In summary: every :math:`2^8` iterations, :math:`R_{i,3}` is +reseeded from :math:`R_{i,2}`. Every :math:`2^16` iterations, :math:`R_{i,2}` +and :math:`R_{i,3}` are reseeded from :math:`R_{i,1}`. Every :math:`2^24` +iterations, :math:`R_{i,1}`, :math:`R_{i,2}` and :math:`R_{i,3}` are reseeded +from :math:`R_{i,0}`. + +The complete ratchet value, :math:`R_{i}`, is hashed to generate the keys used +to encrypt each message. This scheme allows the ratchet to be advanced an +arbitrary amount forwards while needing at most 1023 hash computations. A +client can decrypt chat history onwards from the earliest value of the ratchet +it is aware of, but cannot decrypt history from before that point without +reversing the hash function. + +This allows a participant to share its ability to decrypt chat history with +another from a point in the conversation onwards by giving a copy of the +ratchet at that point in the conversation. + + +The Megolm protocol +------------------- + +Session setup +~~~~~~~~~~~~~ + +Each participant in a conversation generates their own Megolm session. A +session consists of three parts: + +* a 32 bit counter, :math:`i`. +* an `Ed25519`_ keypair, :math:`K`. +* a ratchet, :math:`R_i`, which consists of four 256-bit values, + :math:`R_{i,j}` for :math:`j \in {0,1,2,3}`. + +The counter :math:`i` is initialised to :math:`0`. A new Ed25519 keypair is +generated for :math:`K`. The ratchet is simply initialised with 1024 bits of +cryptographically-secure random data. + +A single participant may use multiple sessions over the lifetime of a +conversation. The public part of :math:`K` is used as an identifier to +discriminate between sessions. + +Sharing session data +~~~~~~~~~~~~~~~~~~~~ + +To allow other participants in the conversation to decrypt messages, the +session data is formatted as described in `Session-sharing format`_. It is then +shared with other participants in the conversation via a secure peer-to-peer +channel (such as that provided by `Olm`_). + +When the session data is received from other participants, the recipient first +checks that the signature matches the public key. They then store their own +copy of the counter, ratchet, and public key. + +Message encryption +~~~~~~~~~~~~~~~~~~ + +This version of Megolm uses AES-256_ in CBC_ mode with `PCKS#7`_ padding and +HMAC-SHA-256_ (truncated to 64 bits). The 256 bit AES key, 256 bit HMAC key, +and 128 bit AES IV are derived from the megolm ratchet :math:`R_i`: + +.. math:: + + \begin{align} + AES\_KEY_{i}\;\parallel\;HMAC\_KEY_{i}\;\parallel\;AES\_IV_{i} + &= HKDF\left(0,\,R_{i},\text{"MEGOLM\_KEYS"},\,80\right) \\ + \end{align} + +where :math:`\parallel` represents string splitting, and +:math:`HKDF\left(salt,\,IKM,\,info,\,L\right)` refers to the `HMAC-based key +derivation function`_ using using `SHA-256`_ as the hash function +(`HKDF-SHA-256`_) with a salt value of :math:`salt`, input key material of +:math:`IKM`, context string :math:`info`, and output keying material length of +:math:`L` bytes. + +The plain-text is encrypted with AES-256, using the key :math:`AES\_KEY_{i}` +and the IV :math:`AES\_IV_{i}` to give the cipher-text, :math:`X_{i}`. + +The ratchet index :math:`i`, and the cipher-text :math:`X_{i}`, are then packed +into a message as described in `Message format`_. Then the entire message +(including the version bytes and all payload bytes) are passed through +HMAC-SHA-256. The first 8 bytes of the MAC are appended to the message. + +Finally, the authenticated message is signed using the Ed25519 keypair; the 64 +byte signature is appended to the message. + +The complete signed message, together with the public part of :math:`K` (acting +as a session identifier), can then be sent over an insecure channel. The +message can then be authenticated and decrypted only by recipients who have +received the session data. + +Advancing the ratchet +~~~~~~~~~~~~~~~~~~~~~ + +After each message is encrypted, the ratchet is advanced. This is done as +described in `The Megolm ratchet algorithm`_, using the following definitions: + +.. math:: + \begin{align} + H_0(A) &\equiv HMAC(A,\text{"\textbackslash x00"}) \\ + H_1(A) &\equiv HMAC(A,\text{"\textbackslash x01"}) \\ + H_2(A) &\equiv HMAC(A,\text{"\textbackslash x02"}) \\ + H_3(A) &\equiv HMAC(A,\text{"\textbackslash x03"}) \\ + \end{align} + +where :math:`HMAC(A, T)` is the HMAC-SHA-256_ of ``T``, using ``A`` as the +key. + +For outbound sessions, the updated ratchet and counter are stored in the +session. + +In order to maintain the ability to decrypt conversation history, inbound +sessions should store a copy of their earliest known ratchet value (unless they +explicitly want to drop the ability to decrypt that history). They may also +choose to cache calculated ratchet values, but the decision of which ratchet +states to cache is left to the application. + +Data exchange formats +--------------------- + +Session-sharing format +~~~~~~~~~~~~~~~~~~~~~~ + +The Megolm key-sharing format is as follows: + +.. code:: + + +---+----+--------+--------+--------+--------+------+-----------+ + | V | i | R(i,0) | R(i,1) | R(i,2) | R(i,3) | Kpub | Signature | + +---+----+--------+--------+--------+--------+------+-----------+ + 0 1 5 37 69 101 133 165 229 bytes + +The version byte, ``V``, is ``"\x02"``. + +This is followed by the ratchet index, :math:`i`, which is encoded as a +big-endian 32-bit integer; the ratchet values :math:`R_{i,j}`; and the public +part of the Ed25519 keypair :math:`K`. + +The data is then signed using the Ed25519 keypair, and the 64-byte signature is +appended. + +Message format +~~~~~~~~~~~~~~ + +Megolm messages consist of a one byte version, followed by a variable length +payload, a fixed length message authentication code, and a fixed length +signature. + +.. code:: + + +---+------------------------------------+-----------+------------------+ + | V | Payload Bytes | MAC Bytes | Signature Bytes | + +---+------------------------------------+-----------+------------------+ + 0 1 N N+8 N+72 bytes + +The version byte, ``V``, is ``"\x03"``. + +The payload uses a format based on the `Protocol Buffers encoding`_. It +consists of the following key-value pairs: + +============= ===== ======== ================================================ + Name Tag Type Meaning +============= ===== ======== ================================================ +Message-Index 0x08 Integer The index of the ratchet, :math:`i` +Cipher-Text 0x12 String The cipher-text, :math:`X_{i}`, of the message +============= ===== ======== ================================================ + +Within the payload, integers are encoded using a variable length encoding. Each +integer is encoded as a sequence of bytes with the high bit set followed by a +byte with the high bit clear. The seven low bits of each byte store the bits of +the integer. The least significant bits are stored in the first byte. + +Strings are encoded as a variable-length integer followed by the string itself. + +Each key-value pair is encoded as a variable-length integer giving the tag, +followed by a string or variable-length integer giving the value. + +The payload is followed by the MAC. The length of the MAC is determined by the +authenticated encryption algorithm being used (8 bytes in this version of the +protocol). The MAC protects all of the bytes preceding the MAC. + +The length of the signature is determined by the signing algorithm being used +(64 bytes in this version of the protocol). The signature covers all of the +bytes preceding the signaure. + +License +------- + +The Megolm specification (this document) is licensed under the `Apache License, +Version 2.0 <http://www.apache.org/licenses/LICENSE-2.0>`_. + + +.. _`Ed25519`: http://ed25519.cr.yp.to/ +.. _`HMAC-based key derivation function`: https://tools.ietf.org/html/rfc5869 +.. _`HKDF-SHA-256`: https://tools.ietf.org/html/rfc5869 +.. _`HMAC-SHA-256`: https://tools.ietf.org/html/rfc2104 +.. _`SHA-256`: https://tools.ietf.org/html/rfc6234 +.. _`AES-256`: http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf +.. _`CBC`: http://csrc.nist.gov/publications/nistpubs/800-38a/sp800-38a.pdf +.. _`PCKS#7`: https://tools.ietf.org/html/rfc2315 +.. _`Olm`: ./olm.html +.. _`Protocol Buffers encoding`: https://developers.google.com/protocol-buffers/docs/encoding |