olm.rst 9.47 KB
 Mark Haines committed Aug 04, 2015 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Olm: A Crytographic Ratchet =========================== An implementation of the cryptographic ratchet described by https://github.com/trevp/axolotl/wiki. The Olm Algorithm ----------------- Initial setup ~~~~~~~~~~~~~ The setup takes four Curve25519 inputs: Identity keys for Alice and Bob, :math:I_A and :math:I_B, and emphemeral keys for Alice and Bob, :math:E_A and :math:E_B. A shared secret, :math:S, is generated using Triple Diffie-Hellman. The initial 256 bit root key, :math:R_0, and 256 bit chain key, :math:C_{0,0}, are derived from the shared secret using an  Mark Haines committed Aug 05, 2015 19 HMAC-based Key Derivation Function (HKDF) with default salt.  Mark Haines committed Aug 04, 2015 20 21 22 23 24  .. math:: \begin{align} S&=ECDH\left(I_A,\,E_B\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\; \parallel\;ECDH\left(E_A,\,E_B\right)\\  Mark Haines committed Aug 05, 2015 25  R_0\;\parallel\;C_{0,0}&=HKDF\left(S,\,\text{"OLM\_ROOT"}\right)  Mark Haines committed Aug 04, 2015 26 27 28 29 30 31  \end{align} Advancing the root key ~~~~~~~~~~~~~~~~~~~~~~ Advancing a root key takes the previous root key, :math:R_{i-1}, and two  Mark Haines committed Aug 05, 2015 32 33 34 35 Curve25519 inputs: the previous ratchet key, :math:T_{i-1}, and the current ratchet key :math: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, :math:R_i, and  Mark Haines committed Aug 11, 2015 36 37 chain key, :math:C_{i,0}, are derived from the shared secret using an HKDF using :math:R_{i-1} as the salt.  Mark Haines committed Aug 04, 2015 38   Mark Haines committed Aug 05, 2015 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 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 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 .. math:: \begin{align} R_i\;\parallel\;C_{i,0}&=HKDF\left( ECDH\left(T_{i-1},\,T_i\right),\, R_{i-1},\, \text{"OLM\_RATCHET"} \right) \end{align} Advancing the chain key ~~~~~~~~~~~~~~~~~~~~~~~ Advancing a root key takes the previous chain key, :math:C_{i,j-i}. The next chain key, :math:C_{i,j}, is the HMAC of "\x02" using the previous chain key as the key. .. math:: \begin{align} C_{i,j}&=HMAC\left(C_{i,j-1},\,\text{"\textbackslash x02"}\right) \end{align} Creating a message key ~~~~~~~~~~~~~~~~~~~~~~ Creating a message key takes the current chain key, :math:C_{i,j}. The message key, :math:M_{i,j}, is the HMAC of "\x01" using the current chain key as the key. The message keys where :math:i is even are used by Alice to encrypt messages. The message keys where :math:i is odd are used by Bob to encrypt messages. .. math:: \begin{align} M_{i,j}&=HMAC\left(C_{i,j},\,\text{"\textbackslash x01"}\right) \end{align} The Olm Protocol ---------------- Creating an outbound session ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Bob publishes his identity key, :math:I_B, and some single-use one-time keys :math:E_B. Alice downloads Bob's identity key, :math:I_B, and a one-time key, :math:E_B. Alice takes her identity key, :math:I_A, and generates a new single-use key, :math:E_A. Alice computes a root key, :math:R_0, and a chain key :math:C_{0,0}. Alice generates a new ratchet key :math:T_0. Sending the first pre-key messages ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Alice computes a message key, :math:M_{0,j}, using the current chain key, :math:C_{0,j}. Alice replaces the current chain key with :math:C_{0,j+1}. Alice encrypts her plain-text with the message key, :math:M_{0,j}, using an authenticated encryption scheme to get a cipher-text, :math:X_{0,j}. Alice sends her identity key, :math:I_A, her single-use key, :math:E_A, Bob's single-use key, :math:E_B, the current chain index, :math:j, her ratchet key, :math:T_0, and the cipher-text, :math:X_{0,j}, to Bob. 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 with Alice's identity key, :math:I_A, Alice's single-use key, :math:E_A, the public part of his single-use key, :math:E_B, the current chain index, :math:j, Alice's ratchet key, :math:T_0, and the cipher-text, :math:X_{0,j}. Bob looks up the private part of the single-use key, :math:E_B. Bob computes the root key :math:R_0, and the chain key :math:C_{0,0}. Bob then advances the chain key to compute the chain key used by the message, :math:C_{0,j}. Bob then creates the message key, :math:M_{0,j}, and attempts to decrypt the ciphertext, :math:X_{0,j}. If the cipher-text's authentication is correct then Bob can discard private part of his single-use one-time key, :math:E_B. Sending messages ~~~~~~~~~~~~~~~~ To send a message the user checks if they have a sender chain key, :math:C_{i,j}. Alice use chain keys where :math:i is even. Bob uses chain keys where :math:i is odd. If the chain key doesn't exist then a new ratchet key :math:T_i is generated and a the chain key, :math:C_{i,0}, is computed using :math:R_{i-1}, :math:T_{i-1} and :math:T_i. A message key, :math:M_{i,j} is computed from the current chain key, :math:C_{i,j}, and the chain key is replaced with the next chain key, :math:C_{i,j+1}. The plain-text is encrypted with :math:M_{i,j}, using an authenticated encryption scheme to get a cipher-text, :math:X_{i,j}. Then user sends the current chain index, :math:j, the ratchet key, :math:T_i, and the cipher-text, :math:X_{i,j}, to the other user. Receiving messages ~~~~~~~~~~~~~~~~~~ The user receives a message with the current chain index, :math:j, the ratchet key, :math:T_i, and the cipher-text, :math:X_{i,j}, from the other user. The user checks if they have a receiver chain with the correct :math:i by comparing the ratchet key, :math:T_i. If the chain doesn't exist then they compute a new receiver chain, :math:C_{i,0}, using :math:R_{i-1}, :math:T_{i-1} and :math:T_i. If the :math: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 :math:M_{i,j}. Otherwise the receiver computes the chain key, :math:C_{i,j}. The receiver computes the message key, :math:M_{i,j}, from the chain key and attempts to decrypt the cipher-text, :math:X_{i,j}.  Mark Haines committed Aug 04, 2015 147   Mark Haines committed Aug 05, 2015 148 149 150 151 152 If the decryption succeeds the reciever updates the chain key for :math:T_i with :math: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.  Mark Haines committed Aug 10, 2015 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168  The Olm Message Format ---------------------- Normal Messages ~~~~~~~~~~~~~~~ Olm messages start with a one byte version followed by a variable length payload followed by a fixed length message authentication code. .. code:: +--------------+------------------------------------+-----------+ | Version Byte | Payload Bytes | MAC Bytes | +--------------+------------------------------------+-----------+  Mark Haines committed Aug 11, 2015 169 170 The version byte is "\x01".  Mark Haines committed Aug 10, 2015 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 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 =========== ===== ======== ================================================  Mark Haines committed Aug 11, 2015 187 188 Ratchet-Key 0x0A String The ratchet key, :math:T_{i}, of the message Chain-Index 0x10 Integer The chain index, :math:j, of the message  Mark Haines committed Aug 10, 2015 189 190 191 Cipher-Text 0x22 String The cipher-text, :math:X_{i,j}, of the message =========== ===== ======== ================================================  Mark Haines committed Aug 11, 2015 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 The length of the MAC is determined by the authenticated encryption algorithm being used. The MAC protects all of the bytes preceeding the MAC. Pre-Key Messages ~~~~~~~~~~~~~~~~ Olm pre-key messages start with a one byte version followed by a variable length payload. .. code:: +--------------+------------------------------------+ | Version Byte | Payload Bytes | +--------------+------------------------------------+ The version byte is "\x01". The payload uses the same key-value format as for normal messages. ============ ===== ======== ================================================ Name Tag Type Meaning ============ ===== ======== ================================================ One-Time-Key 0x0A String Bob's single-use key, :math:E_b. Base-Key 0x12 String Alice's single-use key, :math:E_a. Identity-Key 0x1A String Alice's identity key, :math:I_a. Message 0x22 String An embedded Olm message with its own version and MAC. ============ ===== ======== ================================================ Olm Authenticated Encryption ----------------------------  Mark Haines committed Aug 10, 2015 223   Mark Haines committed Aug 11, 2015 224 225 Version 1 ~~~~~~~~~  Mark Haines committed Aug 10, 2015 226   Mark Haines committed Aug 11, 2015 227 228 229 Version 1 of Olm uses AES-256 in CBC mode for encryption and HMAC-SHA-256 for authentication. The 256 bit AES key, 256 bit HMAC key, and 128 bit AES IV are derived from the message key using HKDF.