First stab at a megolm spec

1 files changed, 218 insertions, 0 deletions

diff --git a/docs/megolm.rst b/docs/megolm.rst
new file mode 100644
index 0000000..24bceed
--- /dev/null
+++ b/docs/megolm.rst
@@ -0,0 +1,218 @@
+Megolm group ratchet
+====================
+
+An AES-based cryptographic ratchet intended for group communications.
+
+The Megolm algorithm
+--------------------
+
+Initial 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`; and a ratchet, :math:`R_i`. The ratchet 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
+~~~~~~~~~~~~~~~~~~
+
+Megolm uses AES-256_ in CBC_ mode with `PCKS#7`_ padding for 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
+follows:
+
+.. math::
+    \begin{align}
+    R_{i,0} &=
+      \begin{cases}
+        HMAC\left(R_{2^24(n-1),0}, \text{"\textbackslash x00"}\right)
+          &\text{if }\exists n | i = 2^24n\\
+        R_{i-1,0} &\text{otherwise}
+      \end{cases}\\
+    R_{i,1} &=
+      \begin{cases}
+        HMAC\left(R_{2^24(n-1),0}, \text{"\textbackslash x01"}\right)
+          &\text{if }\exists n | i = 2^24n\\
+        HMAC\left(R_{2^16(m-1),1}, \text{"\textbackslash x01"}\right)
+          &\text{if }\exists m | i = 2^16m\\
+        R_{i-1,1} &\text{otherwise}
+      \end{cases}\\
+    R_{i,2} &=
+      \begin{cases}
+        HMAC\left(R_{2^24(n-1),0}, \text{"\textbackslash x02"}\right)
+          &\text{if }\exists n | i = 2^24n\\
+        HMAC\left(R_{2^16(m-1),1}, \text{"\textbackslash x02"}\right)
+          &\text{if }\exists m | i = 2^16m\\
+        HMAC\left(R_{2^8(p-1),2}, \text{"\textbackslash x02"}\right)
+          &\text{if }\exists p | i = 2^8p\\
+        R_{i-1,2} &\text{otherwise}
+      \end{cases}\\
+    R_{i,3} &=
+      \begin{cases}
+        HMAC\left(R_{2^24(n-1),0}, \text{"\textbackslash x03"}\right)
+          &\text{if }\exists n | i = 2^24n\\
+        HMAC\left(R_{2^16(m-1),1}, \text{"\textbackslash x03"}\right)
+          &\text{if }\exists m | i = 2^16m\\
+        HMAC\left(R_{2^8(p-1),2}, \text{"\textbackslash x03"}\right)
+          &\text{if }\exists p | i = 2^8p\\
+        HMAC\left(R_{i-1,3}, \text{"\textbackslash x03"}\right)
+          &\text{otherwise}
+      \end{cases}
+    \end{align}
+
+where :math:`HMAC(K, T)` is the HMAC-SHA-256_ of ``T``, using ``K`` as the
+key. 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}`.
+
+This scheme allows the ratchet to be advanced an arbitrary amount forwards
+while needing at most 1023 hash computations. A recipient can decrypt
+conversation 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.
+
+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 earliet 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
+
+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
+
+The version byte, ``V``, is ``"\x03"``.
+
+The payload consists of key-value pairs where the keys are integers and the
+values are integers and strings. The keys are encoded as a variable length
+integer tag where the 3 lowest bits indicates the type of the value:
+0 for integers, 2 for strings. If the value is an integer then the tag is
+followed by the value encoded as a variable length integer. If the value is
+a string then the tag is followed by the length of the string encoded as
+a variable length integer followed by the string itself.
+
+Olm uses a variable length encoding for integers. 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.
+
+============= ===== ======== ================================================
+    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
+============= ===== ======== ================================================
+
+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.
+
+
+.. _`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