megolm.rst 10.9 KB
Newer Older
1
2
3
4
5
Megolm group ratchet
====================

An AES-based cryptographic ratchet intended for group communications.

6
7
.. contents::

8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
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 session, which consists of a
23
ratchet and an `Ed25519`_ keypair.
24

25
26
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.
27

28
Authenticity is provided via Ed25519 signatures.
29
30
31
32
33
34
35

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.

36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
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}
74

75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
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 mesage.  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
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
~~~~~~~~~~~~~

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
~~~~~~~~~~~~~~~~~~

128
129
130
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`:
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165

.. 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
166
described in `The Megolm ratchet algorithm`_, using the following definitions:
167
168
169

.. math::
    \begin{align}
170
171
172
173
        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"}) \\
174
175
    \end{align}

176
177
where :math:`HMAC(A, T)` is the HMAC-SHA-256_ of ``T``, using ``A`` as the
key.
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235

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.

236
237
Megolm 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
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
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.

256
257
258
259
260
261
262
263
264
265
IPR
---

The Megolm specification (this document) is hereby placed in the public domain.

Feedback
--------

Can be sent to richard at matrix.org.

266
267
268
269
270
271
272
273
274
275

.. _`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