megolm.rst 11.5 KB
 Richard van der Hoff committed Sep 22, 2016 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 .. 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.  Richard van der Hoff committed Sep 22, 2016 16 17 18 19 20 Megolm group ratchet ==================== An AES-based cryptographic ratchet intended for group communications.  Richard van der Hoff committed Sep 22, 2016 21 22 .. contents::  Richard van der Hoff committed Sep 22, 2016 23 24 25 26 27 28 29 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_.  Matthew Hodgson committed Sep 28, 2016 30 It also allows a recipient to decrypt received messages multiple times. For  Richard van der Hoff committed Sep 22, 2016 31 32 33 34 35 36 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 --------  Richard van der Hoff committed Sep 22, 2016 37 38 Each participant in a conversation uses their own outbound session for encrypting messages. A session consists of a ratchet and an Ed25519_ keypair.  Richard van der Hoff committed Sep 22, 2016 39   Richard van der Hoff committed Sep 22, 2016 40 41 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.  Richard van der Hoff committed Sep 22, 2016 42   Richard van der Hoff committed Sep 22, 2016 43 Authenticity is provided via Ed25519 signatures.  Richard van der Hoff committed Sep 22, 2016 44 45 46 47 48 49 50  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.  Richard van der Hoff committed Sep 22, 2016 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 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}  Richard van der Hoff committed Sep 22, 2016 89   Richard van der Hoff committed Sep 22, 2016 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  Richard van der Hoff committed Sep 22, 2016 98 to encrypt each message. This scheme allows the ratchet to be advanced an  Richard van der Hoff committed Sep 22, 2016 99 100 101 102 103 104 105 106 107 108 109 110 111 112 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  Richard van der Hoff committed Sep 22, 2016 113 114 115 ~~~~~~~~~~~~~ Each participant in a conversation generates their own Megolm session. A  Richard van der Hoff committed Sep 22, 2016 116 117 118 119 120 121 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}.  Richard van der Hoff committed Sep 22, 2016 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145  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 ~~~~~~~~~~~~~~~~~~  Richard van der Hoff committed Sep 22, 2016 146 147 148 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:  Richard van der Hoff committed Sep 22, 2016 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183  .. 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  Richard van der Hoff committed Sep 22, 2016 184 described in The Megolm ratchet algorithm_, using the following definitions:  Richard van der Hoff committed Sep 22, 2016 185 186 187  .. math:: \begin{align}  Richard van der Hoff committed Sep 22, 2016 188 189 190 191  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"}) \\  Richard van der Hoff committed Sep 22, 2016 192 193  \end{align}  Richard van der Hoff committed Sep 22, 2016 194 195 where :math:HMAC(A, T) is the HMAC-SHA-256_ of T, using A as the key.  Richard van der Hoff committed Sep 22, 2016 196 197 198 199 200  For outbound sessions, the updated ratchet and counter are stored in the session. In order to maintain the ability to decrypt conversation history, inbound  Richard van der Hoff committed Sep 22, 2016 201 sessions should store a copy of their earliest known ratchet value (unless they  Richard van der Hoff committed Sep 22, 2016 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 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 | +---+----+--------+--------+--------+--------+------+-----------+  Richard van der Hoff committed Sep 22, 2016 219  0 1 5 37 69 101 133 165 229 bytes  Richard van der Hoff committed Sep 22, 2016 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241  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 | +---+------------------------------------+-----------+------------------+  Richard van der Hoff committed Sep 22, 2016 242  0 1 N N+8 N+72 bytes  Richard van der Hoff committed Sep 22, 2016 243 244 245  The version byte, V, is "\x03".  Richard van der Hoff committed Sep 23, 2016 246 247 The payload uses a format based on the Protocol Buffers encoding_. It consists of the following key-value pairs:  Richard van der Hoff committed Sep 22, 2016 248 249 250 251 252 253 254 255  ============= ===== ======== ================================================ 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 ============= ===== ======== ================================================  Richard van der Hoff committed Sep 22, 2016 256 257 258 259 260 261 262 263 264 265 266 267 268 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.  Richard van der Hoff committed Sep 22, 2016 269 270 271 272 273  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.  Richard van der Hoff committed Sep 22, 2016 274 275 License -------  Richard van der Hoff committed Sep 22, 2016 276   Richard van der Hoff committed Sep 22, 2016 277 278 The Megolm specification (this document) is licensed under the Apache License, Version 2.0 _.  Richard van der Hoff committed Sep 22, 2016 279   Richard van der Hoff committed Sep 22, 2016 280 281 282 283 284 285 286 287 288 289  .. _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  Richard van der Hoff committed Sep 23, 2016 290 .. _Protocol Buffers encoding: https://developers.google.com/protocol-buffers/docs/encoding