mirror of https://git.matrix.org/git/olm.git
358 lines
14 KiB
ReStructuredText
358 lines
14 KiB
ReStructuredText
Olm: A Cryptographic Ratchet
|
|
============================
|
|
|
|
An implementation of the double cryptographic ratchet described by
|
|
https://github.com/trevp/double_ratchet/wiki.
|
|
|
|
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-i}`. 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 mark at matrix.org.
|
|
|
|
Acknowledgements
|
|
----------------
|
|
|
|
The ratchet that Olm implements was designed by Trevor Perrin and Moxie
|
|
Marlinspike - details at https://github.com/trevp/double_ratchet/wiki. 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
|