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Clarifications to the doc 

Make a few bits of the Olm spec a bit clearer
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Richard van der Hoff 2015-12-07 11:44:17 +00:00
parent 1fb2e3f267
commit b5811f3b74
1 changed files with 54 additions and 26 deletions
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docs/olm.rst
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@ -18,6 +18,11 @@ 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
-----------------
@ -36,7 +41,8 @@ HMAC-based Key Derivation Function using SHA-256_ as the hash function
\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(S,\,\text{"OLM\_ROOT"}\right)
R_0\;\parallel\;C_{0,0}&=
HKDF\left(0,\,S,\,\text{"OLM\_ROOT"},\,64\right)
\end{align}
Advancing the root key
@ -54,9 +60,10 @@ info.
.. 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"}
ECDH\left(T_{i-1},\,T_i\right),\,
\text{"OLM\_RATCHET"},\,
64
\right)
\end{align}
@ -64,7 +71,7 @@ info.
Advancing the chain key
~~~~~~~~~~~~~~~~~~~~~~~
Advancing a root key takes the previous chain key, :math:`C_{i,j-i}`. The next
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.
@ -120,25 +127,35 @@ 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
Bob receives a pre-key message with the public parts of Alice's identity key,
:math:`I_A`, Alice's single-use key, :math:`E_A`, Alice's ratchet key,
:math:`T_0`, and his own single-use key, :math:`E_B`, as well as the
current chain index, :math:`j`, and the cipher-text, :math:`X_{0,j}`.
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 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
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 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,
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
@ -149,12 +166,16 @@ 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
The user receives a message 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 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
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
@ -170,6 +191,9 @@ 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
~~~~~~~~~~~~~~~
@ -207,7 +231,8 @@ 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. The MAC protects all of the bytes preceding the MAC.
being used. (Olm version 1 uses HMAC-SHA-256, giving a MAC of 32 bytes). The
MAC protects all of the bytes preceding the MAC.
Pre-Key Messages
~~~~~~~~~~~~~~~~
@ -249,17 +274,19 @@ 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-SHA-256_ using the default salt and an info of ``"OLM_KEYS"``.
First the plain-text is encrypted to get the cipher-text, :math:`X_{i,j}`.
Then the entire message, both the headers and cipher-text, are HMAC'd and the
MAC is appended to the message.
.. math::
\begin{align}
AES\_KEY_{i,j}\;\parallel\;HMAC\_KEY_{i,j}\;\parallel\;AES\_IV_{i,j}
&= HKDF\left(M_{i,j},\,\text{"OLM\_KEYS"}\right) \\
&= 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, and the MAC is appended to the message.
IPR
---
@ -279,6 +306,7 @@ 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