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+# Megolm group ratchet
+
+An AES-based cryptographic ratchet intended for group communications.
+
+## 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 $`R_i`$ consists of four parts, $`R_{i,j}`$ for
+$`j \in {0,1,2,3}`$. 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{aligned}
+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{aligned}
+```
+
+where $`H_0`$, $`H_1`$, $`H_2`$, and $`H_3`$ are different hash
+functions. In summary: every $`2^8`$ iterations, $`R_{i,3}`$ is
+reseeded from $`R_{i,2}`$. Every $`2^16`$ iterations, $`R_{i,2}`$
+and $`R_{i,3}`$ are reseeded from $`R_{i,1}`$. Every $`2^24`$
+iterations, $`R_{i,1}`$, $`R_{i,2}`$ and $`R_{i,3}`$ are reseeded
+from $`R_{i,0}`$.
+
+The complete ratchet value, $`R_{i}`$, 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 1020 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, $`i`$.
+* an [Ed25519][] keypair, $`K`$.
+* a ratchet, $`R_i`$, which consists of four 256-bit values,
+  $`R_{i,j}`$ for $`j \in {0,1,2,3}`$.
+
+The counter $`i`$ is initialised to $`0`$. A new Ed25519 keypair is
+generated for $`K`$. 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 $`K`$ 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](#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 $`R_i`$:
+
+```math
+\begin{aligned}
+AES\_KEY_{i}\;\parallel\;HMAC\_KEY_{i}\;\parallel\;AES\_IV_{i}
+    &= HKDF\left(0,\,R_{i},\text{"MEGOLM\_KEYS"},\,80\right) \\
+\end{aligned}
+```
+
+where $`\parallel`$ represents string splitting, and
+$`HKDF\left(salt,\,IKM,\,info,\,L\right)`$ refers to the [HMAC-based key
+derivation function][] using using [SHA-256][] as the hash function
+([HKDF-SHA-256][]) with a salt value of $`salt`$, input key material of
+$`IKM`$, context string $`info`$, and output keying material length of
+$`L`$ bytes.
+
+The plain-text is encrypted with AES-256, using the key $`AES\_KEY_{i}`$
+and the IV $`AES\_IV_{i}`$ to give the cipher-text, $`X_{i}`$.
+
+The ratchet index $`i`$, and the cipher-text $`X_{i}`$, are then packed
+into a message as described in [Message format](#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 $`K`$ (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](#the-megolm-ratchet-algorithm), using the following definitions:
+
+```math
+\begin{aligned}
+    H_0(A) &\equiv HMAC(A,\text{"\x00"}) \\
+    H_1(A) &\equiv HMAC(A,\text{"\x01"}) \\
+    H_2(A) &\equiv HMAC(A,\text{"\x02"}) \\
+    H_3(A) &\equiv HMAC(A,\text{"\x03"}) \\
+\end{aligned}
+```
+
+where $`HMAC(A, T)`$ 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](#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:
+
+```
++---+----+--------+--------+--------+--------+------+-----------+
+| 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, $`i`$, which is encoded as a
+big-endian 32-bit integer; the ratchet values $`R_{i,j}`$; and the public
+part of the Ed25519 keypair $`K`$.
+
+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.
+
+```
++---+------------------------------------+-----------+------------------+
+| 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, i
+Cipher-Text|0x12|String|The cipher-text, Xi, 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]: https://gitlab.matrix.org/matrix-org/olm/blob/master/docs/olm.md
+[Protocol Buffers encoding]: https://developers.google.com/protocol-buffers/docs/encoding