olm.md 13 KB
 Aaron Raimist committed May 14, 2019 1 2 3 4 5 6 7 8 9 10 11 12 # Olm: A Cryptographic Ratchet An implementation of the double cryptographic ratchet described by https://whispersystems.org/docs/specifications/doubleratchet/. ## Notation This document uses $\parallel$ to represent string concatenation. When $\parallel$ appears on the right hand side of an $=$ it means that the inputs are concatenated. When $\parallel$ appears on the left hand side of an $=$ it means that the output is split.  Richard van der Hoff committed Nov 08, 2019 13 14 15 16 17 When this document uses $\operatorname{ECDH}\left(K_A,K_B\right)$ it means that each party computes a Diffie-Hellman agreement using their private key and the remote party's public key. So party $A$ computes $\operatorname{ECDH}\left(K_B^{public},K_A^{private}\right)$ and party $B$ computes $\operatorname{ECDH}\left(K_A^{public},K_B^{private}\right)$.  Aaron Raimist committed May 14, 2019 18   Richard van der Hoff committed Nov 08, 2019 19 Where this document uses $\operatorname{HKDF}\left(salt,IKM,info,L\right)$ it  Aaron Raimist committed May 14, 2019 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 refers to the [HMAC-based key derivation function][] with a salt value of $salt$, input key material of $IKM$, context string $info$, and output keying material length of $L$ bytes. ## The Olm Algorithm ### Initial setup The setup takes four [Curve25519][] inputs: Identity keys for Alice and Bob, $I_A$ and $I_B$, and one-time keys for Alice and Bob, $E_A$ and $E_B$. A shared secret, $S$, is generated using [Triple Diffie-Hellman][]. The initial 256 bit root key, $R_0$, and 256 bit chain key, $C_{0,0}$, are derived from the shared secret using an HMAC-based Key Derivation Function using [SHA-256][] as the hash function ([HKDF-SHA-256][]) with default salt and "OLM_ROOT" as the info. math \begin{aligned}  Richard van der Hoff committed Nov 08, 2019 38 39 40 41  S&=\operatorname{ECDH}\left(I_A,E_B\right)\;\parallel\; \operatorname{ECDH}\left(E_A,I_B\right)\;\parallel\; \operatorname{ECDH}\left(E_A,E_B\right)\\  Aaron Raimist committed May 14, 2019 42  R_0\;\parallel\;C_{0,0}&=  Richard van der Hoff committed Nov 08, 2019 43  \operatorname{HKDF}\left(0,S,\text{OLM\_ROOT"},64\right)  Aaron Raimist committed May 14, 2019 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \end{aligned}  ### Advancing the root key Advancing a root key takes the previous root key, $R_{i-1}$, and two Curve25519 inputs: the previous ratchet key, $T_{i-1}$, and the current ratchet key $T_i$. The even ratchet keys are generated by Alice. The odd ratchet keys are generated by Bob. A shared secret is generated using Diffie-Hellman on the ratchet keys. The next root key, $R_i$, and chain key, $C_{i,0}$, are derived from the shared secret using [HKDF-SHA-256][] using $R_{i-1}$ as the salt and "OLM_RATCHET" as the info. math \begin{aligned}  Richard van der Hoff committed Nov 08, 2019 60 61 62 63 64 65 66  R_i\;\parallel\;C_{i,0}&= \operatorname{HKDF}\left( R_{i-1}, \operatorname{ECDH}\left(T_{i-1},T_i\right), \text{OLM\_RATCHET"}, 64 \right)  Aaron Raimist committed May 14, 2019 67 68 69 70 71 72 73 74 75 76 77 \end{aligned}  ### Advancing the chain key Advancing a chain key takes the previous chain key, $C_{i,j-1}$. The next chain key, $C_{i,j}$, is the [HMAC-SHA-256][] of "\x02" using the previous chain key as the key. math \begin{aligned}  Richard van der Hoff committed Nov 08, 2019 78  C_{i,j}&=\operatorname{HMAC}\left(C_{i,j-1},\text{\char\\x02"}\right)  Aaron Raimist committed May 14, 2019 79 80 81 82 83 84 85 86 87 88 89 90 91 \end{aligned}  ### Creating a message key Creating a message key takes the current chain key, $C_{i,j}$. The message key, $M_{i,j}$, is the [HMAC-SHA-256][] of "\x01" using the current chain key as the key. The message keys where $i$ is even are used by Alice to encrypt messages. The message keys where $i$ is odd are used by Bob to encrypt messages. math \begin{aligned}  Richard van der Hoff committed Nov 08, 2019 92  M_{i,j}&=\operatorname{HMAC}\left(C_{i,j},\text{\char\\x01"}\right)  Aaron Raimist committed May 14, 2019 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 \end{aligned}  ## The Olm Protocol ### Creating an outbound session Bob publishes the public parts of his identity key, $I_B$, and some single-use one-time keys $E_B$. Alice downloads Bob's identity key, $I_B$, and a one-time key, $E_B$. She generates a new single-use key, $E_A$, and computes a root key, $R_0$, and a chain key $C_{0,0}$. She also generates a new ratchet key $T_0$. ### Sending the first pre-key messages Alice computes a message key, $M_{0,j}$, and a new chain key, $C_{0,j+1}$, using the current chain key. She replaces the current chain key with the new one. Alice encrypts her plain-text with the message key, $M_{0,j}$, using an authenticated encryption scheme (see below) to get a cipher-text, $X_{0,j}$. She then sends the following to Bob: * The public part of her identity key, $I_A$ * The public part of her single-use key, $E_A$ * The public part of Bob's single-use key, $E_B$ * The current chain index, $j$ * The public part of her ratchet key, $T_0$ * The cipher-text, $X_{0,j}$ Alice will continue to send pre-key messages until she receives a message from Bob. ### Creating an inbound session from a pre-key message Bob receives a pre-key message as above. Bob looks up the private part of his single-use key, $E_B$. He can now compute the root key, $R_0$, and the chain key, $C_{0,0}$, from $I_A$, $E_A$, $I_B$, and $E_B$. Bob then advances the chain key $j$ times, to compute the chain key used by the message, $C_{0,j}$. He now creates the message key, $M_{0,j}$, and attempts to decrypt the cipher-text, $X_{0,j}$. If the cipher-text's authentication is correct then Bob can discard the private part of his single-use one-time key, $E_B$. Bob stores Alice's initial ratchet key, $T_0$, until he wants to send a message. ### Sending normal messages Once a message has been received from the other side, a session is considered established, and a more compact form is used. To send a message, the user checks if they have a sender chain key, $C_{i,j}$. Alice uses chain keys where $i$ is even. Bob uses chain keys where $i$ is odd. If the chain key doesn't exist then a new ratchet key $T_i$ is generated and a new root key $R_i$ and chain key $C_{i,0}$ are computed using $R_{i-1}$, $T_{i-1}$ and $T_i$. A message key, $M_{i,j}$ is computed from the current chain key, $C_{i,j}$, and the chain key is replaced with the next chain key, $C_{i,j+1}$. The plain-text is encrypted with $M_{i,j}$, using an authenticated encryption scheme (see below) to get a cipher-text, $X_{i,j}$. The user then sends the following to the recipient: * The current chain index, $j$ * The public part of the current ratchet key, $T_i$ * The cipher-text, $X_{i,j}$ ### Receiving messages The user receives a message as above with the sender's current chain index, $j$, the sender's ratchet key, $T_i$, and the cipher-text, $X_{i,j}$. The user checks if they have a receiver chain with the correct $i$ by comparing the ratchet key, $T_i$. If the chain doesn't exist then they compute a new root key, $R_i$, and a new receiver chain, with chain key $C_{i,0}$, using $R_{i-1}$, $T_{i-1}$ and $T_i$. If the $j$ of the message is less than the current chain index on the receiver then the message may only be decrypted if the receiver has stored a copy of the message key $M_{i,j}$. Otherwise the receiver computes the chain key, $C_{i,j}$. The receiver computes the message key, $M_{i,j}$, from the chain key and attempts to decrypt the cipher-text, $X_{i,j}$. If the decryption succeeds the receiver updates the chain key for $T_i$ with $C_{i,j+1}$ and stores the message keys that were skipped in the process so that they can decode out of order messages. If the receiver created a new receiver chain then they discard their current sender chain so that they will create a new chain when they next send a message. ## The Olm Message Format Olm uses two types of messages. The underlying transport protocol must provide a means for recipients to distinguish between them. ### Normal Messages Olm messages start with a one byte version followed by a variable length payload followed by a fixed length message authentication code.  +--------------+------------------------------------+-----------+ | Version Byte | Payload Bytes | MAC Bytes | +--------------+------------------------------------+-----------+  The version byte 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** :-----:|:-----:|:-----:|:-----: Ratchet-Key|0x0A|String|The public part of the ratchet key, Ti, of the message Chain-Index|0x10|Integer|The chain index, j, of the message Cipher-Text|0x22|String|The cipher-text, Xi, j, of the message The length of the MAC is determined by the authenticated encryption algorithm being used. (Olm version 1 uses [HMAC-SHA-256][], truncated to 8 bytes). The MAC protects all of the bytes preceding the MAC. ### Pre-Key Messages Olm pre-key messages start with a one byte version followed by a variable length payload.  +--------------+------------------------------------+ | Version Byte | Payload Bytes | +--------------+------------------------------------+  The version byte is "\x03". The payload uses the same key-value format as for normal messages. **Name**|**Tag**|**Type**|**Meaning** :-----:|:-----:|:-----:|:-----: One-Time-Key|0x0A|String|The public part of Bob's single-use key, Eb. Base-Key|0x12|String|The public part of Alice's single-use key, Ea. Identity-Key|0x1A|String|The public part of Alice's identity key, Ia. Message|0x22|String|An embedded Olm message with its own version and MAC. ## Olm Authenticated Encryption ### Version 1 Version 1 of Olm uses [AES-256][] in [CBC][] mode with [PKCS#7][] padding for encryption and [HMAC-SHA-256][] (truncated to 64 bits) for authentication. The 256 bit AES key, 256 bit HMAC key, and 128 bit AES IV are derived from the message key using [HKDF-SHA-256][] using the default salt and an info of "OLM_KEYS". math \begin{aligned} AES\_KEY_{i,j}\;\parallel\;HMAC\_KEY_{i,j}\;\parallel\;AES\_IV_{i,j}  Richard van der Hoff committed Nov 08, 2019 269  &= \operatorname{HKDF}\left(0,M_{i,j},\text{OLM\_KEYS"},80\right)  Aaron Raimist committed May 14, 2019 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 \end{aligned}  The plain-text is encrypted with AES-256, using the key $AES\_KEY_{i,j}$ and the IV $AES\_IV_{i,j}$ to give the cipher-text, $X_{i,j}$. Then the entire message (including the Version Byte and all Payload Bytes) are passed through [HMAC-SHA-256][]. The first 8 bytes of the MAC are appended to the message. ## Message authentication concerns To avoid unknown key-share attacks, the application must include identifying data for the sending and receiving user in the plain-text of (at least) the pre-key messages. Such data could be a user ID, a telephone number; alternatively it could be the public part of a keypair which the relevant user has proven ownership of. ### Example attacks 1. Alice publishes her public [Curve25519][] identity key, $I_A$. Eve publishes the same identity key, claiming it as her own. Bob downloads Eve's keys, and associates $I_A$ with Eve. Alice sends a message to Bob; Eve intercepts it before forwarding it to Bob. Bob believes the message came from Eve rather than Alice. This is prevented if Alice includes her user ID in the plain-text of the pre-key message, so that Bob can see that the message was sent by Alice originally. 2. Bob publishes his public [Curve25519][] identity key, $I_B$. Eve publishes the same identity key, claiming it as her own. Alice downloads Eve's keys, and associates $I_B$ with Eve. Alice sends a message to Eve; Eve cannot decrypt it, but forwards it to Bob. Bob believes the Alice sent the message to him, wheras Alice intended it to go to Eve. This is prevented by Alice including the user ID of the intended recpient (Eve) in the plain-text of the pre-key message. Bob can now tell that the message was meant for Eve rather than him. ## IPR The Olm specification (this document) is hereby placed in the public domain. ## Feedback Can be sent to olm at matrix.org. ## Acknowledgements The ratchet that Olm implements was designed by Trevor Perrin and Moxie Marlinspike - details at https://whispersystems.org/docs/specifications/doubleratchet/. Olm is an entirely new implementation written by the Matrix.org team. [Curve25519]: http://cr.yp.to/ecdh.html [Triple Diffie-Hellman]: https://whispersystems.org/blog/simplifying-otr-deniability/ [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