Commit c07444d3 authored by Richard van der Hoff's avatar Richard van der Hoff
Browse files

First stab at a megolm spec

parent 047927d8
......@@ -44,6 +44,7 @@ JS_POST := javascript/olm_outbound_group_session.js \
javascript/olm_inbound_group_session.js \
DOCS := tracing/README.html \
docs/megolm.html \
docs/olm.html \
README.html \
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::
&= HKDF\left(0,\,R_{i},\text{"MEGOLM\_KEYS"},\,80\right) \\
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
.. math::
R_{i,0} &=
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}
R_{i,1} &=
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}
R_{i,2} &=
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}
R_{i,3} &=
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)
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
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
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
.. 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`:
.. _`HMAC-based key derivation function`:
.. _`HKDF-SHA-256`:
.. _`HMAC-SHA-256`:
.. _`SHA-256`:
.. _`AES-256`:
.. _`CBC`:
.. _`PCKS#7`:
.. _`Olm`: ./olm.html
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