358 lines
14 KiB
ReStructuredText
358 lines
14 KiB
ReStructuredText
Olm: A Cryptographic Ratchet
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============================
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An implementation of the double cryptographic ratchet described by
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https://whispersystems.org/docs/specifications/doubleratchet/.
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Notation
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--------
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This document uses :math:`\parallel` to represent string concatenation. When
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:math:`\parallel` appears on the right hand side of an :math:`=` it means that
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the inputs are concatenated. When :math:`\parallel` appears on the left hand
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side of an :math:`=` it means that the output is split.
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When this document uses :math:`ECDH\left(K_A,\,K_B\right)` it means that each
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party computes a Diffie-Hellman agreement using their private key and the
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remote party's public key.
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So party :math:`A` computes :math:`ECDH\left(K_B_public,\,K_A_private\right)`
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and party :math:`B` computes :math:`ECDH\left(K_A_public,\,K_B_private\right)`.
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Where this document uses :math:`HKDF\left(salt,\,IKM,\,info,\,L\right)` it
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refers to the `HMAC-based key derivation function`_ with a salt value of
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:math:`salt`, input key material of :math:`IKM`, context string :math:`info`,
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and output keying material length of :math:`L` bytes.
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The Olm Algorithm
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-----------------
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Initial setup
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~~~~~~~~~~~~~
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The setup takes four Curve25519_ inputs: Identity keys for Alice and Bob,
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:math:`I_A` and :math:`I_B`, and one-time keys for Alice and Bob,
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:math:`E_A` and :math:`E_B`. A shared secret, :math:`S`, is generated using
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`Triple Diffie-Hellman`_. The initial 256 bit root key, :math:`R_0`, and 256
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bit chain key, :math:`C_{0,0}`, are derived from the shared secret using an
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HMAC-based Key Derivation Function using SHA-256_ as the hash function
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(HKDF-SHA-256_) with default salt and ``"OLM_ROOT"`` as the info.
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.. math::
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\begin{align}
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S&=ECDH\left(I_A,\,E_B\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\;
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\parallel\;ECDH\left(E_A,\,E_B\right)\\
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R_0\;\parallel\;C_{0,0}&=
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HKDF\left(0,\,S,\,\text{"OLM\_ROOT"},\,64\right)
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\end{align}
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Advancing the root key
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~~~~~~~~~~~~~~~~~~~~~~
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Advancing a root key takes the previous root key, :math:`R_{i-1}`, and two
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Curve25519 inputs: the previous ratchet key, :math:`T_{i-1}`, and the current
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ratchet key :math:`T_i`. The even ratchet keys are generated by Alice.
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The odd ratchet keys are generated by Bob. A shared secret is generated
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using Diffie-Hellman on the ratchet keys. The next root key, :math:`R_i`, and
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chain key, :math:`C_{i,0}`, are derived from the shared secret using
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HKDF-SHA-256_ using :math:`R_{i-1}` as the salt and ``"OLM_RATCHET"`` as the
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info.
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.. math::
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\begin{align}
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R_i\;\parallel\;C_{i,0}&=HKDF\left(
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R_{i-1},\,
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ECDH\left(T_{i-1},\,T_i\right),\,
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\text{"OLM\_RATCHET"},\,
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64
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\right)
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\end{align}
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Advancing the chain key
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~~~~~~~~~~~~~~~~~~~~~~~
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Advancing a chain key takes the previous chain key, :math:`C_{i,j-1}`. The next
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chain key, :math:`C_{i,j}`, is the HMAC-SHA-256_ of ``"\x02"`` using the
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previous chain key as the key.
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.. math::
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\begin{align}
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C_{i,j}&=HMAC\left(C_{i,j-1},\,\text{"\textbackslash x02"}\right)
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\end{align}
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Creating a message key
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~~~~~~~~~~~~~~~~~~~~~~
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Creating a message key takes the current chain key, :math:`C_{i,j}`. The
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message key, :math:`M_{i,j}`, is the HMAC-SHA-256_ of ``"\x01"`` using the
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current chain key as the key. The message keys where :math:`i` is even are used
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by Alice to encrypt messages. The message keys where :math:`i` is odd are used
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by Bob to encrypt messages.
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.. math::
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\begin{align}
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M_{i,j}&=HMAC\left(C_{i,j},\,\text{"\textbackslash x01"}\right)
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\end{align}
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The Olm Protocol
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----------------
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Creating an outbound session
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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Bob publishes the public parts of his identity key, :math:`I_B`, and some
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single-use one-time keys :math:`E_B`.
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Alice downloads Bob's identity key, :math:`I_B`, and a one-time key,
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:math:`E_B`. She generates a new single-use key, :math:`E_A`, and computes a
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root key, :math:`R_0`, and a chain key :math:`C_{0,0}`. She also generates a
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new ratchet key :math:`T_0`.
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Sending the first pre-key messages
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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Alice computes a message key, :math:`M_{0,j}`, and a new chain key,
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:math:`C_{0,j+1}`, using the current chain key. She replaces the current chain
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key with the new one.
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Alice encrypts her plain-text with the message key, :math:`M_{0,j}`, using an
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authenticated encryption scheme (see below) to get a cipher-text,
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:math:`X_{0,j}`.
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She then sends the following to Bob:
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* The public part of her identity key, :math:`I_A`
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* The public part of her single-use key, :math:`E_A`
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* The public part of Bob's single-use key, :math:`E_B`
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* The current chain index, :math:`j`
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* The public part of her ratchet key, :math:`T_0`
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* The cipher-text, :math:`X_{0,j}`
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Alice will continue to send pre-key messages until she receives a message from
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Bob.
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Creating an inbound session from a pre-key message
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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Bob receives a pre-key message as above.
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Bob looks up the private part of his single-use key, :math:`E_B`. He can now
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compute the root key, :math:`R_0`, and the chain key, :math:`C_{0,0}`, from
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:math:`I_A`, :math:`E_A`, :math:`I_B`, and :math:`E_B`.
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Bob then advances the chain key :math:`j` times, to compute the chain key used
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by the message, :math:`C_{0,j}`. He now creates the
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message key, :math:`M_{0,j}`, and attempts to decrypt the cipher-text,
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:math:`X_{0,j}`. If the cipher-text's authentication is correct then Bob can
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discard the private part of his single-use one-time key, :math:`E_B`.
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Bob stores Alice's initial ratchet key, :math:`T_0`, until he wants to
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send a message.
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Sending normal messages
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~~~~~~~~~~~~~~~~~~~~~~~
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Once a message has been received from the other side, a session is considered
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established, and a more compact form is used.
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To send a message, the user checks if they have a sender chain key,
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:math:`C_{i,j}`. Alice uses chain keys where :math:`i` is even. Bob uses chain
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keys where :math:`i` is odd. If the chain key doesn't exist then a new ratchet
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key :math:`T_i` is generated and a new root key :math:`R_i` and chain key
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:math:`C_{i,0}` are computed using :math:`R_{i-1}`, :math:`T_{i-1}` and
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:math:`T_i`.
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A message key,
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:math:`M_{i,j}` is computed from the current chain key, :math:`C_{i,j}`, and
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the chain key is replaced with the next chain key, :math:`C_{i,j+1}`. The
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plain-text is encrypted with :math:`M_{i,j}`, using an authenticated encryption
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scheme (see below) to get a cipher-text, :math:`X_{i,j}`.
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The user then sends the following to the recipient:
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* The current chain index, :math:`j`
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* The public part of the current ratchet key, :math:`T_i`
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* The cipher-text, :math:`X_{i,j}`
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Receiving messages
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~~~~~~~~~~~~~~~~~~
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The user receives a message as above with the sender's current chain index, :math:`j`,
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the sender's ratchet key, :math:`T_i`, and the cipher-text, :math:`X_{i,j}`.
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The user checks if they have a receiver chain with the correct
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:math:`i` by comparing the ratchet key, :math:`T_i`. If the chain doesn't exist
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then they compute a new root key, :math:`R_i`, and a new receiver chain, with
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chain key :math:`C_{i,0}`, using :math:`R_{i-1}`, :math:`T_{i-1}` and
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:math:`T_i`.
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If the :math:`j` of the message is less than
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the current chain index on the receiver then the message may only be decrypted
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if the receiver has stored a copy of the message key :math:`M_{i,j}`. Otherwise
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the receiver computes the chain key, :math:`C_{i,j}`. The receiver computes the
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message key, :math:`M_{i,j}`, from the chain key and attempts to decrypt the
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cipher-text, :math:`X_{i,j}`.
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If the decryption succeeds the receiver updates the chain key for :math:`T_i`
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with :math:`C_{i,j+1}` and stores the message keys that were skipped in the
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process so that they can decode out of order messages. If the receiver created
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a new receiver chain then they discard their current sender chain so that
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they will create a new chain when they next send a message.
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The Olm Message Format
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----------------------
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Olm uses two types of messages. The underlying transport protocol must provide
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a means for recipients to distinguish between them.
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Normal Messages
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~~~~~~~~~~~~~~~
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Olm messages start with a one byte version followed by a variable length
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payload followed by a fixed length message authentication code.
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.. code::
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+--------------+------------------------------------+-----------+
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| Version Byte | Payload Bytes | MAC Bytes |
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+--------------+------------------------------------+-----------+
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The version byte is ``"\x03"``.
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The payload consists of key-value pairs where the keys are integers and the
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values are integers and strings. The keys are encoded as a variable length
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integer tag where the 3 lowest bits indicates the type of the value:
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0 for integers, 2 for strings. If the value is an integer then the tag is
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followed by the value encoded as a variable length integer. If the value is
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a string then the tag is followed by the length of the string encoded as
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a variable length integer followed by the string itself.
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Olm uses a variable length encoding for integers. Each integer is encoded as a
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sequence of bytes with the high bit set followed by a byte with the high bit
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clear. The seven low bits of each byte store the bits of the integer. The least
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significant bits are stored in the first byte.
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=========== ===== ======== ================================================
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Name Tag Type Meaning
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=========== ===== ======== ================================================
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Ratchet-Key 0x0A String The public part of the ratchet key, :math:`T_{i}`,
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of the message
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Chain-Index 0x10 Integer The chain index, :math:`j`, of the message
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Cipher-Text 0x22 String The cipher-text, :math:`X_{i,j}`, of the message
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=========== ===== ======== ================================================
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The length of the MAC is determined by the authenticated encryption algorithm
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being used. (Olm version 1 uses HMAC-SHA-256, truncated to 8 bytes). The
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MAC protects all of the bytes preceding the MAC.
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Pre-Key Messages
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~~~~~~~~~~~~~~~~
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Olm pre-key messages start with a one byte version followed by a variable
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length payload.
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.. code::
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+--------------+------------------------------------+
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| Version Byte | Payload Bytes |
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+--------------+------------------------------------+
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The version byte is ``"\x03"``.
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The payload uses the same key-value format as for normal messages.
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============ ===== ======== ================================================
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Name Tag Type Meaning
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============ ===== ======== ================================================
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One-Time-Key 0x0A String The public part of Bob's single-use key,
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:math:`E_b`.
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Base-Key 0x12 String The public part of Alice's single-use key,
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:math:`E_a`.
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Identity-Key 0x1A String The public part of Alice's identity key,
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:math:`I_a`.
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Message 0x22 String An embedded Olm message with its own version and
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MAC.
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============ ===== ======== ================================================
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Olm Authenticated Encryption
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----------------------------
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Version 1
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~~~~~~~~~
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Version 1 of Olm uses AES-256_ in CBC_ mode with `PKCS#7`_ padding for
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encryption and HMAC-SHA-256_ (truncated to 64 bits) for authentication. The
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256 bit AES key, 256 bit HMAC key, and 128 bit AES IV are derived from the
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message key using HKDF-SHA-256_ using the default salt and an info of
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``"OLM_KEYS"``.
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.. math::
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\begin{align}
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AES\_KEY_{i,j}\;\parallel\;HMAC\_KEY_{i,j}\;\parallel\;AES\_IV_{i,j}
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&= HKDF\left(0,\,M_{i,j},\text{"OLM\_KEYS"},\,80\right) \\
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\end{align}
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The plain-text is encrypted with AES-256, using the key :math:`AES\_KEY_{i,j}`
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and the IV :math:`AES\_IV_{i,j}` to give the cipher-text, :math:`X_{i,j}`.
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Then the entire message (including the Version Byte and all Payload Bytes) are
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passed through HMAC-SHA-256. The first 8 bytes of the MAC are appended to the message.
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Message authentication concerns
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-------------------------------
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To avoid unknown key-share attacks, the application must include identifying
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data for the sending and receiving user in the plain-text of (at least) the
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pre-key messages. Such data could be a user ID, a telephone number;
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alternatively it could be the public part of a keypair which the relevant user
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has proven ownership of.
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.. admonition:: Example attacks
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1. Alice publishes her public Curve25519 identity key, :math:`I_A`. Eve
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publishes the same identity key, claiming it as her own. Bob downloads
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Eve's keys, and associates :math:`I_A` with Eve. Alice sends a message to
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Bob; Eve intercepts it before forwarding it to Bob. Bob believes the
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message came from Eve rather than Alice.
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This is prevented if Alice includes her user ID in the plain-text of the
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pre-key message, so that Bob can see that the message was sent by Alice
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originally.
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2. Bob publishes his public Curve25519 identity key, :math:`I_B`. Eve
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publishes the same identity key, claiming it as her own. Alice downloads
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Eve's keys, and associates :math:`I_B` with Eve. Alice sends a message to
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Eve; Eve cannot decrypt it, but forwards it to Bob. Bob believes the
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Alice sent the message to him, wheras Alice intended it to go to Eve.
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This is prevented by Alice including the user ID of the intended recpient
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(Eve) in the plain-text of the pre-key message. Bob can now tell that the
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message was meant for Eve rather than him.
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IPR
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---
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The Olm specification (this document) is hereby placed in the public domain.
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Feedback
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--------
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Can be sent to olm at matrix.org.
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Acknowledgements
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----------------
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The ratchet that Olm implements was designed by Trevor Perrin and Moxie
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Marlinspike - details at https://whispersystems.org/docs/specifications/doubleratchet/. Olm is
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an entirely new implementation written by the Matrix.org team.
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.. _`Curve25519`: http://cr.yp.to/ecdh.html
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.. _`Triple Diffie-Hellman`: https://whispersystems.org/blog/simplifying-otr-deniability/
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.. _`HMAC-based key derivation function`: https://tools.ietf.org/html/rfc5869
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.. _`HKDF-SHA-256`: https://tools.ietf.org/html/rfc5869
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.. _`HMAC-SHA-256`: https://tools.ietf.org/html/rfc2104
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.. _`SHA-256`: https://tools.ietf.org/html/rfc6234
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.. _`AES-256`: http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf
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.. _`CBC`: http://csrc.nist.gov/publications/nistpubs/800-38a/sp800-38a.pdf
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.. _`PKCS#7`: https://tools.ietf.org/html/rfc2315
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