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diff --git a/docs/megolm.rst b/docs/megolm.rst deleted file mode 100644 index 03ee426..0000000 --- a/docs/megolm.rst +++ /dev/null @@ -1,362 +0,0 @@ -.. 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 recipient 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 `PKCS#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 - see `Partial -Forward Secrecy`_\ ). 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 signature. - -Limitations ------------ - -Message Replays ---------------- - -A message can be decrypted successfully multiple times. This means that an -attacker can re-send a copy of an old message, and the recipient will treat it -as a new message. - -To mitigate this it is recommended that applications track the ratchet indices -they have received and that they reject messages with a ratchet index that -they have already decrypted. - -Lack of Transcript Consistency -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -In a group conversation, there is no guarantee that all recipients have -received the same messages. For example, if Alice is in a conversation with Bob -and Charlie, she could send different messages to Bob and Charlie, or could -send some messages to Bob but not Charlie, or vice versa. - -Solving this is, in general, a hard problem, particularly in a protocol which -does not guarantee in-order message delivery. For now it remains the subject of -future research. - -Lack of Backward Secrecy -~~~~~~~~~~~~~~~~~~~~~~~~ - -Once the key to a Megolm session is compromised, the attacker can decrypt any -future messages sent via that session. - -In order to mitigate this, the application should ensure that Megolm sessions -are not used indefinitely. Instead it should periodically start a new session, -with new keys shared over a secure channel. - -.. TODO: Can we recommend sensible lifetimes for Megolm sessions? Probably - depends how paranoid we're feeling, but some guidelines might be useful. - -Partial Forward Secrecy -~~~~~~~~~~~~~~~~~~~~~~~ - -Each recipient maintains a record of the ratchet value which allows them to -decrypt any messages sent in the session after the corresponding point in the -conversation. If this value is compromised, an attacker can similarly decrypt -those past messages. - -To mitigate this issue, the application should offer the user the option to -discard historical conversations, by winding forward any stored ratchet values, -or discarding sessions altogether. - -Dependency on secure channel for key exchange -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -The design of the Megolm ratchet relies on the availability of a secure -peer-to-peer channel for the exchange of session keys. Any vulnerabilities in -the underlying channel are likely to be amplified when applied to Megolm -session setup. - -For example, if the peer-to-peer channel is vulnerable to an unknown key-share -attack, the entire Megolm session become similarly vulnerable. For example: -Alice starts a group chat with Eve, and shares the session keys with Eve. Eve -uses the unknown key-share attack to forward the session keys to Bob, who -believes Alice is starting the session with him. Eve then forwards messages -from the Megolm session to Bob, who again believes they are coming from -Alice. Provided the peer-to-peer channel is not vulnerable to this attack, Bob -will realise that the key-sharing message was forwarded by Eve, and can treat -the Megolm session as a forgery. - -A second example: if the peer-to-peer channel is vulnerable to a replay -attack, this can be extended to entire Megolm sessions. - -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 -.. _`PKCS#7`: https://tools.ietf.org/html/rfc2315 -.. _`Olm`: ./olm.html -.. _`Protocol Buffers encoding`: https://developers.google.com/protocol-buffers/docs/encoding |