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diff --git a/docs/olm.rst b/docs/olm.rst deleted file mode 100644 index 9c13478..0000000 --- a/docs/olm.rst +++ /dev/null @@ -1,358 +0,0 @@ -Olm: A Cryptographic Ratchet -============================ - -An implementation of the double cryptographic ratchet described by -https://whispersystems.org/docs/specifications/doubleratchet/. - - -Notation --------- - -This document uses :math:`\parallel` to represent string concatenation. When -:math:`\parallel` appears on the right hand side of an :math:`=` it means that -the inputs are concatenated. When :math:`\parallel` appears on the left hand -side of an :math:`=` it means that the output is split. - -When this document uses :math:`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 :math:`A` computes :math:`ECDH\left(K_B_public,\,K_A_private\right)` -and party :math:`B` computes :math:`ECDH\left(K_A_public,\,K_B_private\right)`. - -Where this document uses :math:`HKDF\left(salt,\,IKM,\,info,\,L\right)` it -refers to the `HMAC-based key derivation function`_ 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 Olm Algorithm ------------------ - -Initial setup -~~~~~~~~~~~~~ - -The setup takes four Curve25519_ inputs: Identity keys for Alice and Bob, -:math:`I_A` and :math:`I_B`, and one-time 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 -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{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)\\ - R_0\;\parallel\;C_{0,0}&= - HKDF\left(0,\,S,\,\text{"OLM\_ROOT"},\,64\right) - \end{align} - -Advancing the root key -~~~~~~~~~~~~~~~~~~~~~~ - -Advancing a root key takes the previous root key, :math:`R_{i-1}`, and two -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 -chain key, :math:`C_{i,0}`, are derived from the shared secret using -HKDF-SHA-256_ using :math:`R_{i-1}` as the salt and ``"OLM_RATCHET"`` as the -info. - -.. math:: - \begin{align} - R_i\;\parallel\;C_{i,0}&=HKDF\left( - R_{i-1},\, - ECDH\left(T_{i-1},\,T_i\right),\, - \text{"OLM\_RATCHET"},\, - 64 - \right) - \end{align} - - -Advancing the chain key -~~~~~~~~~~~~~~~~~~~~~~~ - -Advancing a chain key takes the previous chain key, :math:`C_{i,j-1}`. The next -chain key, :math:`C_{i,j}`, is the HMAC-SHA-256_ 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-SHA-256_ 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 the public parts of 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`. She generates a new single-use key, :math:`E_A`, and computes a -root key, :math:`R_0`, and a chain key :math:`C_{0,0}`. She also generates a -new ratchet key :math:`T_0`. - -Sending the first pre-key messages -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -Alice computes a message key, :math:`M_{0,j}`, and a new chain key, -:math:`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, :math:`M_{0,j}`, using an -authenticated encryption scheme (see below) to get a cipher-text, -:math:`X_{0,j}`. - -She then sends the following to Bob: - * The public part of her identity key, :math:`I_A` - * The public part of her single-use key, :math:`E_A` - * The public part of Bob's single-use key, :math:`E_B` - * The current chain index, :math:`j` - * The public part of her ratchet key, :math:`T_0` - * The cipher-text, :math:`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, :math:`E_B`. He can now -compute the root key, :math:`R_0`, and the chain key, :math:`C_{0,0}`, from -:math:`I_A`, :math:`E_A`, :math:`I_B`, and :math:`E_B`. - -Bob then advances the chain key :math:`j` times, to compute the chain key used -by the message, :math:`C_{0,j}`. He now creates the -message key, :math:`M_{0,j}`, and attempts to decrypt the cipher-text, -:math:`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, :math:`E_B`. - -Bob stores Alice's initial ratchet key, :math:`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, -:math:`C_{i,j}`. Alice uses 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 new root key :math:`R_i` and chain key -:math:`C_{i,0}` are 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 (see below) to get a cipher-text, :math:`X_{i,j}`. - -The user then sends the following to the recipient: - * The current chain index, :math:`j` - * The public part of the current ratchet key, :math:`T_i` - * The cipher-text, :math:`X_{i,j}` - -Receiving messages -~~~~~~~~~~~~~~~~~~ - -The user receives a message as above with the sender's current chain index, :math:`j`, -the sender's ratchet key, :math:`T_i`, and the cipher-text, :math:`X_{i,j}`. - -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 root key, :math:`R_i`, and a new receiver chain, with -chain key :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}`. - -If the decryption succeeds the receiver 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. - -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. - -.. 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, :math:`T_{i}`, - of the message -Chain-Index 0x10 Integer The chain index, :math:`j`, of the message -Cipher-Text 0x22 String The cipher-text, :math:`X_{i,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. - -.. code:: - - +--------------+------------------------------------+ - | 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, - :math:`E_b`. -Base-Key 0x12 String The public part of Alice's single-use key, - :math:`E_a`. -Identity-Key 0x1A String The public part of Alice's identity key, - :math:`I_a`. -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{align} - AES\_KEY_{i,j}\;\parallel\;HMAC\_KEY_{i,j}\;\parallel\;AES\_IV_{i,j} - &= HKDF\left(0,\,M_{i,j},\text{"OLM\_KEYS"},\,80\right) \\ - \end{align} - -The plain-text is encrypted with AES-256, using the key :math:`AES\_KEY_{i,j}` -and the IV :math:`AES\_IV_{i,j}` to give the cipher-text, :math:`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. - -.. admonition:: Example attacks - - 1. Alice publishes her public Curve25519 identity key, :math:`I_A`. Eve - publishes the same identity key, claiming it as her own. Bob downloads - Eve's keys, and associates :math:`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, :math:`I_B`. Eve - publishes the same identity key, claiming it as her own. Alice downloads - Eve's keys, and associates :math:`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 |