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switch RST to MD, thanks to @aaronraimist. fixes spec docs in gitlab

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CONTRIBUTING.rst → CONTRIBUTING.md
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@ -1,5 +1,4 @@
Contributing code to libolm # Contributing code to libolm
===========================
To contribute code to this library, the preferred way is to clone the git To contribute code to this library, the preferred way is to clone the git
repository, create a git patch series (for example via ``git repository, create a git patch series (for example via ``git
@ -8,18 +7,16 @@ format-patch --stdout origin/master``), and send this by email to
Naturally, you must be willing to license your contributions under the same Naturally, you must be willing to license your contributions under the same
license as the project itself - in this case, Apache Software License v2 (see license as the project itself - in this case, Apache Software License v2 (see
`<LICENSE>`_). [LICENSE](LICENSE)).
Sign off ## Sign off
--------
In order to have a concrete record that your contribution is intentional and In order to have a concrete record that your contribution is intentional and
you agree to license it under the same terms as the project's license, we've you agree to license it under the same terms as the project's license, we've
adopted the same lightweight approach that the adopted the same lightweight approach that the
`Linux Kernel <https://www.kernel.org/doc/Documentation/SubmittingPatches>`_, [Linux Kernel](https://www.kernel.org/doc/html/latest/process/submitting-patches.html#sign-your-work-the-developer-s-certificate-of-origin),
`Docker <https://github.com/docker/docker/blob/master/CONTRIBUTING.md>`_, [Docker](https://github.com/docker/docker/blob/master/CONTRIBUTING.md),
and many other projects use: the DCO and many other projects use: the DCO ([Developer Certificate of Origin](http://developercertificate.org/)).
(`Developer Certificate of Origin <http://developercertificate.org/>`_).
This is a simple declaration that you wrote the contribution or otherwise have This is a simple declaration that you wrote the contribution or otherwise have
the right to contribute it to Matrix:: the right to contribute it to Matrix::

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@ -1,78 +1,75 @@
Olm # Olm
===
An implementation of the Double Ratchet cryptographic ratchet described by An implementation of the Double Ratchet cryptographic ratchet described by
https://whispersystems.org/docs/specifications/doubleratchet/, written in C and https://whispersystems.org/docs/specifications/doubleratchet/, written in C and
C++11 and exposed as a C API. C++11 and exposed as a C API.
The specification of the Olm ratchet can be found in `<docs/olm.rst>`_. The specification of the Olm ratchet can be found in [docs/olm.md](docs/olm.md).
This library also includes an implementation of the Megolm cryptographic This library also includes an implementation of the Megolm cryptographic
ratchet, as specified in `<docs/megolm.rst>`_. ratchet, as specified in [docs/megolm.md](docs/megolm.md).
Building ## Building
--------
To build olm as a shared library run either: To build olm as a shared library run either:
.. code:: bash ```bash
cmake . -Bbuild cmake . -Bbuild
cmake --build build cmake --build build
```
or: or:
.. code:: bash ```bash
make make
```
Using cmake is the preferred method for building the shared library; the Using cmake is the preferred method for building the shared library; the
Makefile may be removed in the future. Makefile may be removed in the future.
To run the tests when using cmake, run: To run the tests when using cmake, run:
.. code:: bash ```bash
cd build/tests cd build/tests
ctest . ctest .
```
To run the tests when using make, run: To run the tests when using make, run:
.. code:: bash ```bash
make test make test
```
To build the JavaScript bindings, install emscripten from http://kripken.github.io/emscripten-site/ and then run: To build the JavaScript bindings, install emscripten from http://kripken.github.io/emscripten-site/ and then run:
.. code:: bash ```bash
make js make js
```
Note that if you run emscripten in a docker container, you need to pass through Note that if you run emscripten in a docker container, you need to pass through
the EMCC_CLOSURE_ARGS environment variable. the EMCC_CLOSURE_ARGS environment variable.
To build the android project for Android bindings, run: To build the android project for Android bindings, run:
.. code:: bash ```bash
cd android cd android
./gradlew clean assembleRelease ./gradlew clean assembleRelease
```
To build the Xcode workspace for Objective-C bindings, run: To build the Xcode workspace for Objective-C bindings, run:
.. code:: bash ```bash
cd xcode cd xcode
pod install pod install
open OLMKit.xcworkspace open OLMKit.xcworkspace
```
To build the Python bindings, first build olm as a shared library as above, and To build the Python bindings, first build olm as a shared library as above, and
then run: then run:
.. code:: bash ```bash
cd python cd python
make make
```
to make both the Python 2 and Python 3 bindings. To make only one version, use to make both the Python 2 and Python 3 bindings. To make only one version, use
``make olm-python2`` or ``make olm-python3`` instead of just ``make``. ``make olm-python2`` or ``make olm-python3`` instead of just ``make``.
@ -80,27 +77,25 @@ to make both the Python 2 and Python 3 bindings. To make only one version, use
To build olm as a static library (which still needs libstdc++ dynamically) run To build olm as a static library (which still needs libstdc++ dynamically) run
either: either:
.. code:: bash ```bash
cmake . -Bbuild -DBUILD_SHARED_LIBS=NO cmake . -Bbuild -DBUILD_SHARED_LIBS=NO
cmake --build build cmake --build build
```
or or
.. code:: bash ```bash
make static make static
```
The library can also be used as a dependency with CMake using: The library can also be used as a dependency with CMake using:
.. code:: cmake ```cmake
find_package(Olm::Olm REQUIRED) find_package(Olm::Olm REQUIRED)
target_link_libraries(my_exe Olm::Olm) target_link_libraries(my_exe Olm::Olm)
```
## Release process
Release process
---------------
First: bump version numbers in ``common.mk``, ``CMakeLists.txt``, First: bump version numbers in ``common.mk``, ``CMakeLists.txt``,
``javascript/package.json``, ``python/olm/__version__.py``, ``OLMKit.podspec``, ``javascript/package.json``, ``python/olm/__version__.py``, ``OLMKit.podspec``,
@ -113,8 +108,7 @@ git.
It's probably sensible to do the above on a release branch (``release-vx.y.z`` It's probably sensible to do the above on a release branch (``release-vx.y.z``
by convention), and merge back to master once the release is complete. by convention), and merge back to master once the release is complete.
.. code:: bash ```bash
make clean make clean
# build and test C library # build and test C library
@ -137,10 +131,9 @@ by convention), and merge back to master once the release is complete.
pod trunk push OLMKit.podspec --use-libraries --allow-warnings pod trunk push OLMKit.podspec --use-libraries --allow-warnings
# Check the pod has been successully published with: # Check the pod has been successully published with:
pod search OLMKit pod search OLMKit
```
## Design
Design
------
Olm is designed to be easy port to different platforms and to be easy Olm is designed to be easy port to different platforms and to be easy
to write bindings for. to write bindings for.
@ -150,46 +143,40 @@ API. As development has progressed, it has become clear that C++ gives little
advantage, and new functionality is being added in C, with C++ parts being advantage, and new functionality is being added in C, with C++ parts being
rewritten as the need ariases. rewritten as the need ariases.
Error Handling ### Error Handling
~~~~~~~~~~~~~~
All C functions in the API for olm return ``olm_error()`` on error. All C functions in the API for olm return ``olm_error()`` on error.
This makes it easy to check for error conditions within the language bindings. This makes it easy to check for error conditions within the language bindings.
Random Numbers ### Random Numbers
~~~~~~~~~~~~~~
Olm doesn't generate random numbers itself. Instead the caller must Olm doesn't generate random numbers itself. Instead the caller must
provide the random data. This makes it easier to port the library to different provide the random data. This makes it easier to port the library to different
platforms since the caller can use whatever cryptographic random number platforms since the caller can use whatever cryptographic random number
generator their platform provides. generator their platform provides.
Memory ### Memory
~~~~~~
Olm avoids calling malloc or allocating memory on the heap itself. Olm avoids calling malloc or allocating memory on the heap itself.
Instead the library calculates how much memory will be needed to hold the Instead the library calculates how much memory will be needed to hold the
output and the caller supplies a buffer of the appropriate size. output and the caller supplies a buffer of the appropriate size.
Output Encoding ### Output Encoding
~~~~~~~~~~~~~~~
Binary output is encoded as base64 so that languages that prefer unicode Binary output is encoded as base64 so that languages that prefer unicode
strings will find it easier to handle the output. strings will find it easier to handle the output.
Dependencies ### Dependencies
~~~~~~~~~~~~
Olm uses pure C implementations of the cryptographic primitives used by Olm uses pure C implementations of the cryptographic primitives used by
the ratchet. While this decreases the performance it makes it much easier the ratchet. While this decreases the performance it makes it much easier
to compile the library for different architectures. to compile the library for different architectures.
Contributing ## Contributing
------------
Please see `<CONTRIBUTING.rst>`_ when making contributions to the library.
Security assessment Please see [CONTRIBUTING.md](CONTRIBUTING.md) when making contributions to the library.
-------------------
## Security assessment
Olm 1.3.0 was independently assessed by NCC Group's Cryptography Services Olm 1.3.0 was independently assessed by NCC Group's Cryptography Services
Practive in September 2016 to check for security issues: you can read all Practive in September 2016 to check for security issues: you can read all
@ -197,18 +184,16 @@ about it at
https://www.nccgroup.trust/us/our-research/matrix-olm-cryptographic-review/ https://www.nccgroup.trust/us/our-research/matrix-olm-cryptographic-review/
and https://matrix.org/blog/2016/11/21/matrixs-olm-end-to-end-encryption-security-assessment-released-and-implemented-cross-platform-on-riot-at-last/ and https://matrix.org/blog/2016/11/21/matrixs-olm-end-to-end-encryption-security-assessment-released-and-implemented-cross-platform-on-riot-at-last/
Bug reports ## Bug reports
-----------
Please file bug reports at https://github.com/matrix-org/olm/issues Please file bug reports at https://github.com/matrix-org/olm/issues
What's an olm? ## What's an olm?
--------------
It's a really cool species of European troglodytic salamander. It's a really cool species of European troglodytic salamander.
http://www.postojnska-jama.eu/en/come-and-visit-us/vivarium-proteus/ http://www.postojnska-jama.eu/en/come-and-visit-us/vivarium-proteus/
Legal Notice ## Legal Notice
------------
The software may be subject to the U.S. export control laws and regulations The software may be subject to the U.S. export control laws and regulations
and by downloading the software the user certifies that he/she/it is and by downloading the software the user certifies that he/she/it is

325
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@ -0,0 +1,325 @@
# Megolm group ratchet
An AES-based cryptographic ratchet intended for group communications.
## Background
The Megolm ratchet is intended for encrypted messaging applications where there
may be a large number of recipients of each message, thus precluding the use of
peer-to-peer encryption systems such as [Olm][].
It also allows a recipient to decrypt received messages multiple times. For
instance, in client/server applications, a copy of the ciphertext can be stored
on the (untrusted) server, while the client need only store the session keys.
## Overview
Each participant in a conversation uses their own outbound session for
encrypting messages. A session consists of a ratchet and an [Ed25519][] keypair.
Secrecy is provided by the ratchet, which can be wound forwards but not
backwards, and is used to derive a distinct message key for each message.
Authenticity is provided via Ed25519 signatures.
The value of the ratchet, and the public part of the Ed25519 key, are shared
with other participants in the conversation via secure peer-to-peer
channels. Provided that peer-to-peer channel provides authenticity of the
messages to the participants and deniability of the messages to third parties,
the Megolm session will inherit those properties.
## The Megolm ratchet algorithm
The Megolm ratchet $`R_i`$ consists of four parts, $`R_{i,j}`$ for
$`j \in {0,1,2,3}`$. The length of each part depends on the hash function
in use (256 bits for this version of Megolm).
The ratchet is initialised with cryptographically-secure random data, and
advanced as follows:
```math
\begin{aligned}
R_{i,0} &=
\begin{cases}
H_0\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\
R_{i-1,0} &\text{otherwise}
\end{cases}\\
R_{i,1} &=
\begin{cases}
H_1\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\
H_1\left(R_{2^16(m-1),1}\right) &\text{if }\exists m | i = 2^16m\\
R_{i-1,1} &\text{otherwise}
\end{cases}\\
R_{i,2} &=
\begin{cases}
H_2\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\
H_2\left(R_{2^16(m-1),1}\right) &\text{if }\exists m | i = 2^16m\\
H_2\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
R_{i-1,2} &\text{otherwise}
\end{cases}\\
R_{i,3} &=
\begin{cases}
H_3\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\
H_3\left(R_{2^16(m-1),1}\right) &\text{if }\exists m | i = 2^16m\\
H_3\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
H_3\left(R_{i-1,3}\right) &\text{otherwise}
\end{cases}
\end{aligned}
```
where $`H_0`$, $`H_1`$, $`H_2`$, and $`H_3`$ are different hash
functions. In summary: every $`2^8`$ iterations, $`R_{i,3}`$ is
reseeded from $`R_{i,2}`$. Every $`2^16`$ iterations, $`R_{i,2}`$
and $`R_{i,3}`$ are reseeded from $`R_{i,1}`$. Every $`2^24`$
iterations, $`R_{i,1}`$, $`R_{i,2}`$ and $`R_{i,3}`$ are reseeded
from $`R_{i,0}`$.
The complete ratchet value, $`R_{i}`$, is hashed to generate the keys used
to encrypt each message. This scheme allows the ratchet to be advanced an
arbitrary amount forwards while needing at most 1023 hash computations. A
client can decrypt chat history onwards from the earliest value of the ratchet
it is aware of, but cannot decrypt history from before that point without
reversing the hash function.
This allows a participant to share its ability to decrypt chat history with
another from a point in the conversation onwards by giving a copy of the
ratchet at that point in the conversation.
## The Megolm protocol
### Session setup
Each participant in a conversation generates their own Megolm session. A
session consists of three parts:
* a 32 bit counter, $`i`$.
* an [Ed25519][] keypair, $`K`$.
* a ratchet, $`R_i`$, which consists of four 256-bit values,
$`R_{i,j}`$ for $`j \in {0,1,2,3}`$.
The counter $`i`$ is initialised to $`0`$. A new Ed25519 keypair is
generated for $`K`$. The ratchet is simply initialised with 1024 bits of
cryptographically-secure random data.
A single participant may use multiple sessions over the lifetime of a
conversation. The public part of $`K`$ is used as an identifier to
discriminate between sessions.
### Sharing session data
To allow other participants in the conversation to decrypt messages, the
session data is formatted as described in [Session-sharing format](#Session-sharing-format). It is then
shared with other participants in the conversation via a secure peer-to-peer
channel (such as that provided by [Olm][]).
When the session data is received from other participants, the recipient first
checks that the signature matches the public key. They then store their own
copy of the counter, ratchet, and public key.
### Message encryption
This version of Megolm uses AES-256_ in CBC_ mode with [PKCS#7][] padding and
HMAC-SHA-256_ (truncated to 64 bits). The 256 bit AES key, 256 bit HMAC key,
and 128 bit AES IV are derived from the megolm ratchet $`R_i`$:
```math
\begin{aligned}
AES\_KEY_{i}\;\parallel\;HMAC\_KEY_{i}\;\parallel\;AES\_IV_{i}
&= HKDF\left(0,\,R_{i},\text{"MEGOLM\_KEYS"},\,80\right) \\
\end{aligned}
```
where $`\parallel`$ represents string splitting, and
$`HKDF\left(salt,\,IKM,\,info,\,L\right)`$ refers to the [HMAC-based key
derivation function][] using using [SHA-256][] as the hash function
([HKDF-SHA-256][]) with a salt value of $`salt`$, input key material of
$`IKM`$, context string $`info`$, and output keying material length of
$`L`$ bytes.
The plain-text is encrypted with AES-256, using the key $`AES\_KEY_{i}`$
and the IV $`AES\_IV_{i}`$ to give the cipher-text, $`X_{i}`$.
The ratchet index $`i`$, and the cipher-text $`X_{i}`$, are then packed
into a message as described in [Message format](#message-format). Then the entire message
(including the version bytes and all payload bytes) are passed through
HMAC-SHA-256. The first 8 bytes of the MAC are appended to the message.
Finally, the authenticated message is signed using the Ed25519 keypair; the 64
byte signature is appended to the message.
The complete signed message, together with the public part of $`K`$ (acting
as a session identifier), can then be sent over an insecure channel. The
message can then be authenticated and decrypted only by recipients who have
received the session data.
### Advancing the ratchet
After each message is encrypted, the ratchet is advanced. This is done as
described in [The Megolm ratchet algorithm](#the-megolm-ratchet-algorithm), using the following definitions:
```math
\begin{aligned}
H_0(A) &\equiv HMAC(A,\text{"\x00"}) \\
H_1(A) &\equiv HMAC(A,\text{"\x01"}) \\
H_2(A) &\equiv HMAC(A,\text{"\x02"}) \\
H_3(A) &\equiv HMAC(A,\text{"\x03"}) \\
\end{aligned}
```
where $`HMAC(A, T)`$ is the HMAC-SHA-256 of ``T``, using ``A`` as the
key.
For outbound sessions, the updated ratchet and counter are stored in the
session.
In order to maintain the ability to decrypt conversation history, inbound
sessions should store a copy of their earliest known ratchet value (unless they
explicitly want to drop the ability to decrypt that history - see [Partial
Forward Secrecy](#partial-forward-secrecy)). They may also choose to cache calculated ratchet values,
but the decision of which ratchet states to cache is left to the application.
## Data exchange formats
### Session-sharing format
The Megolm key-sharing format is as follows:
```
+---+----+--------+--------+--------+--------+------+-----------+
| V | i | R(i,0) | R(i,1) | R(i,2) | R(i,3) | Kpub | Signature |
+---+----+--------+--------+--------+--------+------+-----------+
0 1 5 37 69 101 133 165 229 bytes
```
The version byte, ``V``, is ``"\x02"``.
This is followed by the ratchet index, $`i`$, which is encoded as a
big-endian 32-bit integer; the ratchet values $`R_{i,j}`$; and the public
part of the Ed25519 keypair $`K`$.
The data is then signed using the Ed25519 keypair, and the 64-byte signature is
appended.
### Message format
Megolm messages consist of a one byte version, followed by a variable length
payload, a fixed length message authentication code, and a fixed length
signature.
```
+---+------------------------------------+-----------+------------------+
| V | Payload Bytes | MAC Bytes | Signature Bytes |
+---+------------------------------------+-----------+------------------+
0 1 N N+8 N+72 bytes
```
The version byte, ``V``, is ``"\x03"``.
The payload uses a format based on the [Protocol Buffers encoding][]. It
consists of the following key-value pairs:
**Name**|**Tag**|**Type**|**Meaning**
:-----:|:-----:|:-----:|:-----:
Message-Index|0x08|Integer|The index of the ratchet, i
Cipher-Text|0x12|String|The cipher-text, Xi, of the message
Within the payload, integers are encoded using a variable length encoding. 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.
Strings are encoded as a variable-length integer followed by the string itself.
Each key-value pair is encoded as a variable-length integer giving the tag,
followed by a string or variable-length integer giving the value.
The payload is followed by the MAC. The length of the MAC is determined by the
authenticated encryption algorithm being used (8 bytes in this version of the
protocol). The MAC protects all of the bytes preceding the MAC.
The length of the signature is determined by the signing algorithm being used
(64 bytes in this version of the protocol). The signature covers all of the
bytes preceding the signature.
## Limitations
### Message Replays
A message can be decrypted successfully multiple times. This means that an
attacker can re-send a copy of an old message, and the recipient will treat it
as a new message.
To mitigate this it is recommended that applications track the ratchet indices
they have received and that they reject messages with a ratchet index that
they have already decrypted.
### Lack of Transcript Consistency
In a group conversation, there is no guarantee that all recipients have
received the same messages. For example, if Alice is in a conversation with Bob
and Charlie, she could send different messages to Bob and Charlie, or could
send some messages to Bob but not Charlie, or vice versa.
Solving this is, in general, a hard problem, particularly in a protocol which
does not guarantee in-order message delivery. For now it remains the subject of
future research.
### Lack of Backward Secrecy
Once the key to a Megolm session is compromised, the attacker can decrypt any
future messages sent via that session.
In order to mitigate this, the application should ensure that Megolm sessions
are not used indefinitely. Instead it should periodically start a new session,
with new keys shared over a secure channel.
<!-- TODO: Can we recommend sensible lifetimes for Megolm sessions? Probably
depends how paranoid we're feeling, but some guidelines might be useful. -->
### Partial Forward Secrecy
Each recipient maintains a record of the ratchet value which allows them to
decrypt any messages sent in the session after the corresponding point in the
conversation. If this value is compromised, an attacker can similarly decrypt
those past messages.
To mitigate this issue, the application should offer the user the option to
discard historical conversations, by winding forward any stored ratchet values,
or discarding sessions altogether.
### Dependency on secure channel for key exchange
The design of the Megolm ratchet relies on the availability of a secure
peer-to-peer channel for the exchange of session keys. Any vulnerabilities in
the underlying channel are likely to be amplified when applied to Megolm
session setup.
For example, if the peer-to-peer channel is vulnerable to an unknown key-share
attack, the entire Megolm session become similarly vulnerable. For example:
Alice starts a group chat with Eve, and shares the session keys with Eve. Eve
uses the unknown key-share attack to forward the session keys to Bob, who
believes Alice is starting the session with him. Eve then forwards messages
from the Megolm session to Bob, who again believes they are coming from
Alice. Provided the peer-to-peer channel is not vulnerable to this attack, Bob
will realise that the key-sharing message was forwarded by Eve, and can treat
the Megolm session as a forgery.
A second example: if the peer-to-peer channel is vulnerable to a replay
attack, this can be extended to entire Megolm sessions.
## License
The Megolm specification (this document) is licensed under the Apache License,
Version 2.0 http://www.apache.org/licenses/LICENSE-2.0.
[Ed25519]: http://ed25519.cr.yp.to/
[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
[Olm]: https://gitlab.matrix.org/matrix-org/olm/blob/master/docs/olm.md
[Protocol Buffers encoding]: https://developers.google.com/protocol-buffers/docs/encoding

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@ -1,362 +0,0 @@
.. Copyright 2016 OpenMarket Ltd
..
.. Licensed under the Apache License, Version 2.0 (the "License");
.. you may not use this file except in compliance with the License.
.. You may obtain a copy of the License at
..
.. http://www.apache.org/licenses/LICENSE-2.0
..
.. Unless required by applicable law or agreed to in writing, software
.. distributed under the License is distributed on an "AS IS" BASIS,
.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
.. See the License for the specific language governing permissions and
.. limitations under the License.
Megolm group ratchet
====================
An AES-based cryptographic ratchet intended for group communications.
.. contents::
Background
----------
The Megolm ratchet is intended for encrypted messaging applications where there
may be a large number of recipients of each message, thus precluding the use of
peer-to-peer encryption systems such as `Olm`_.
It also allows a recipient to decrypt received messages multiple times. For
instance, in client/server applications, a copy of the ciphertext can be stored
on the (untrusted) server, while the client need only store the session keys.
Overview
--------
Each participant in a conversation uses their own outbound session for
encrypting messages. A session consists of a ratchet and an `Ed25519`_ keypair.
Secrecy is provided by the ratchet, which can be wound forwards but not
backwards, and is used to derive a distinct message key for each message.
Authenticity is provided via Ed25519 signatures.
The value of the ratchet, and the public part of the Ed25519 key, are shared
with other participants in the conversation via secure peer-to-peer
channels. Provided that peer-to-peer channel provides authenticity of the
messages to the participants and deniability of the messages to third parties,
the Megolm session will inherit those properties.
The Megolm ratchet algorithm
----------------------------
The Megolm ratchet :math:`R_i` consists of four parts, :math:`R_{i,j}` for
:math:`j \in {0,1,2,3}`. The length of each part depends on the hash function
in use (256 bits for this version of Megolm).
The ratchet is initialised with cryptographically-secure random data, and
advanced as follows:
.. math::
\begin{align}
R_{i,0} &=
\begin{cases}
H_0\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\
R_{i-1,0} &\text{otherwise}
\end{cases}\\
R_{i,1} &=
\begin{cases}
H_1\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\
H_1\left(R_{2^16(m-1),1}\right) &\text{if }\exists m | i = 2^16m\\
R_{i-1,1} &\text{otherwise}
\end{cases}\\
R_{i,2} &=
\begin{cases}
H_2\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\
H_2\left(R_{2^16(m-1),1}\right) &\text{if }\exists m | i = 2^16m\\
H_2\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
R_{i-1,2} &\text{otherwise}
\end{cases}\\
R_{i,3} &=
\begin{cases}
H_3\left(R_{2^24(n-1),0}\right) &\text{if }\exists n | i = 2^24n\\
H_3\left(R_{2^16(m-1),1}\right) &\text{if }\exists m | i = 2^16m\\
H_3\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
H_3\left(R_{i-1,3}\right) &\text{otherwise}
\end{cases}
\end{align}
where :math:`H_0`, :math:`H_1`, :math:`H_2`, and :math:`H_3` are different hash
functions. In summary: every :math:`2^8` iterations, :math:`R_{i,3}` is
reseeded from :math:`R_{i,2}`. Every :math:`2^16` iterations, :math:`R_{i,2}`
and :math:`R_{i,3}` are reseeded from :math:`R_{i,1}`. Every :math:`2^24`
iterations, :math:`R_{i,1}`, :math:`R_{i,2}` and :math:`R_{i,3}` are reseeded
from :math:`R_{i,0}`.
The complete ratchet value, :math:`R_{i}`, is hashed to generate the keys used
to encrypt each message. This scheme allows the ratchet to be advanced an
arbitrary amount forwards while needing at most 1020 hash computations. A
client can decrypt chat history onwards from the earliest value of the ratchet
it is aware of, but cannot decrypt history from before that point without
reversing the hash function.
This allows a participant to share its ability to decrypt chat history with
another from a point in the conversation onwards by giving a copy of the
ratchet at that point in the conversation.
The Megolm protocol
-------------------
Session setup
~~~~~~~~~~~~~
Each participant in a conversation generates their own Megolm session. A
session consists of three parts:
* a 32 bit counter, :math:`i`.
* an `Ed25519`_ keypair, :math:`K`.
* a ratchet, :math:`R_i`, which consists of four 256-bit values,
:math:`R_{i,j}` for :math:`j \in {0,1,2,3}`.
The counter :math:`i` is initialised to :math:`0`. A new Ed25519 keypair is
generated for :math:`K`. The ratchet is simply initialised with 1024 bits of
cryptographically-secure random data.
A single participant may use multiple sessions over the lifetime of a
conversation. The public part of :math:`K` is used as an identifier to
discriminate between sessions.
Sharing session data
~~~~~~~~~~~~~~~~~~~~
To allow other participants in the conversation to decrypt messages, the
session data is formatted as described in `Session-sharing format`_. It is then
shared with other participants in the conversation via a secure peer-to-peer
channel (such as that provided by `Olm`_).
When the session data is received from other participants, the recipient first
checks that the signature matches the public key. They then store their own
copy of the counter, ratchet, and public key.
Message encryption
~~~~~~~~~~~~~~~~~~
This version of Megolm uses AES-256_ in CBC_ mode with `PKCS#7`_ padding and
HMAC-SHA-256_ (truncated to 64 bits). The 256 bit AES key, 256 bit HMAC key,
and 128 bit AES IV are derived from the megolm ratchet :math:`R_i`:
.. math::
\begin{align}
AES\_KEY_{i}\;\parallel\;HMAC\_KEY_{i}\;\parallel\;AES\_IV_{i}
&= HKDF\left(0,\,R_{i},\text{"MEGOLM\_KEYS"},\,80\right) \\
\end{align}
where :math:`\parallel` represents string splitting, and
:math:`HKDF\left(salt,\,IKM,\,info,\,L\right)` refers to the `HMAC-based key
derivation function`_ using using `SHA-256`_ as the hash function
(`HKDF-SHA-256`_) 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 plain-text is encrypted with AES-256, using the key :math:`AES\_KEY_{i}`
and the IV :math:`AES\_IV_{i}` to give the cipher-text, :math:`X_{i}`.
The ratchet index :math:`i`, and the cipher-text :math:`X_{i}`, are then packed
into a message as described in `Message format`_. Then the entire message
(including the version bytes and all payload bytes) are passed through
HMAC-SHA-256. The first 8 bytes of the MAC are appended to the message.
Finally, the authenticated message is signed using the Ed25519 keypair; the 64
byte signature is appended to the message.
The complete signed message, together with the public part of :math:`K` (acting
as a session identifier), can then be sent over an insecure channel. The
message can then be authenticated and decrypted only by recipients who have
received the session data.
Advancing the ratchet
~~~~~~~~~~~~~~~~~~~~~
After each message is encrypted, the ratchet is advanced. This is done as
described in `The Megolm ratchet algorithm`_, using the following definitions:
.. math::
\begin{align}
H_0(A) &\equiv HMAC(A,\text{"\textbackslash x00"}) \\
H_1(A) &\equiv HMAC(A,\text{"\textbackslash x01"}) \\
H_2(A) &\equiv HMAC(A,\text{"\textbackslash x02"}) \\
H_3(A) &\equiv HMAC(A,\text{"\textbackslash x03"}) \\
\end{align}
where :math:`HMAC(A, T)` is the HMAC-SHA-256_ of ``T``, using ``A`` as the
key.
For outbound sessions, the updated ratchet and counter are stored in the
session.
In order to maintain the ability to decrypt conversation history, inbound
sessions should store a copy of their earliest known ratchet value (unless they
explicitly want to drop the ability to decrypt that history - see `Partial
Forward Secrecy`_\ ). They may also choose to cache calculated ratchet values,
but the decision of which ratchet states to cache is left to the application.
Data exchange formats
---------------------
Session-sharing format
~~~~~~~~~~~~~~~~~~~~~~
The Megolm key-sharing format is as follows:
.. code::
+---+----+--------+--------+--------+--------+------+-----------+
| V | i | R(i,0) | R(i,1) | R(i,2) | R(i,3) | Kpub | Signature |
+---+----+--------+--------+--------+--------+------+-----------+
0 1 5 37 69 101 133 165 229 bytes
The version byte, ``V``, is ``"\x02"``.
This is followed by the ratchet index, :math:`i`, which is encoded as a
big-endian 32-bit integer; the ratchet values :math:`R_{i,j}`; and the public
part of the Ed25519 keypair :math:`K`.
The data is then signed using the Ed25519 keypair, and the 64-byte signature is
appended.
Message format
~~~~~~~~~~~~~~
Megolm messages consist of a one byte version, followed by a variable length
payload, a fixed length message authentication code, and a fixed length
signature.
.. code::
+---+------------------------------------+-----------+------------------+
| V | Payload Bytes | MAC Bytes | Signature Bytes |
+---+------------------------------------+-----------+------------------+
0 1 N N+8 N+72 bytes
The version byte, ``V``, is ``"\x03"``.
The payload uses a format based on the `Protocol Buffers encoding`_. It
consists of the following key-value pairs:
============= ===== ======== ================================================
Name Tag Type Meaning
============= ===== ======== ================================================
Message-Index 0x08 Integer The index of the ratchet, :math:`i`
Cipher-Text 0x12 String The cipher-text, :math:`X_{i}`, of the message
============= ===== ======== ================================================
Within the payload, integers are encoded using a variable length encoding. 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.
Strings are encoded as a variable-length integer followed by the string itself.
Each key-value pair is encoded as a variable-length integer giving the tag,
followed by a string or variable-length integer giving the value.
The payload is followed by the MAC. The length of the MAC is determined by the
authenticated encryption algorithm being used (8 bytes in this version of the
protocol). The MAC protects all of the bytes preceding the MAC.
The length of the signature is determined by the signing algorithm being used
(64 bytes in this version of the protocol). The signature covers all of the
bytes preceding the signature.
Limitations
-----------
Message Replays
---------------
A message can be decrypted successfully multiple times. This means that an
attacker can re-send a copy of an old message, and the recipient will treat it
as a new message.
To mitigate this it is recommended that applications track the ratchet indices
they have received and that they reject messages with a ratchet index that
they have already decrypted.
Lack of Transcript Consistency
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In a group conversation, there is no guarantee that all recipients have
received the same messages. For example, if Alice is in a conversation with Bob
and Charlie, she could send different messages to Bob and Charlie, or could
send some messages to Bob but not Charlie, or vice versa.
Solving this is, in general, a hard problem, particularly in a protocol which
does not guarantee in-order message delivery. For now it remains the subject of
future research.
Lack of Backward Secrecy
~~~~~~~~~~~~~~~~~~~~~~~~
Once the key to a Megolm session is compromised, the attacker can decrypt any
future messages sent via that session.
In order to mitigate this, the application should ensure that Megolm sessions
are not used indefinitely. Instead it should periodically start a new session,
with new keys shared over a secure channel.
.. TODO: Can we recommend sensible lifetimes for Megolm sessions? Probably
depends how paranoid we're feeling, but some guidelines might be useful.
Partial Forward Secrecy
~~~~~~~~~~~~~~~~~~~~~~~
Each recipient maintains a record of the ratchet value which allows them to
decrypt any messages sent in the session after the corresponding point in the
conversation. If this value is compromised, an attacker can similarly decrypt
those past messages.
To mitigate this issue, the application should offer the user the option to
discard historical conversations, by winding forward any stored ratchet values,
or discarding sessions altogether.
Dependency on secure channel for key exchange
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The design of the Megolm ratchet relies on the availability of a secure
peer-to-peer channel for the exchange of session keys. Any vulnerabilities in
the underlying channel are likely to be amplified when applied to Megolm
session setup.
For example, if the peer-to-peer channel is vulnerable to an unknown key-share
attack, the entire Megolm session become similarly vulnerable. For example:
Alice starts a group chat with Eve, and shares the session keys with Eve. Eve
uses the unknown key-share attack to forward the session keys to Bob, who
believes Alice is starting the session with him. Eve then forwards messages
from the Megolm session to Bob, who again believes they are coming from
Alice. Provided the peer-to-peer channel is not vulnerable to this attack, Bob
will realise that the key-sharing message was forwarded by Eve, and can treat
the Megolm session as a forgery.
A second example: if the peer-to-peer channel is vulnerable to a replay
attack, this can be extended to entire Megolm sessions.
License
-------
The Megolm specification (this document) is licensed under the `Apache License,
Version 2.0 <http://www.apache.org/licenses/LICENSE-2.0>`_.
.. _`Ed25519`: http://ed25519.cr.yp.to/
.. _`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
.. _`Olm`: ./olm.html
.. _`Protocol Buffers encoding`: https://developers.google.com/protocol-buffers/docs/encoding

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# Olm: A Cryptographic Ratchet
An implementation of the double cryptographic ratchet described by
https://whispersystems.org/docs/specifications/doubleratchet/.
## Notation
This document uses $`\parallel`$ to represent string concatenation. When
$`\parallel`$ appears on the right hand side of an $`=`$ it means that
the inputs are concatenated. When $`\parallel`$ appears on the left hand
side of an $`=`$ it means that the output is split.
When this document uses $`ECDH\left(K_A,\,K_B\right)`$ it means that each
party computes a Diffie-Hellman agreement using their private key and the
remote party's public key.
So party $`A`$ computes $`ECDH\left(K_B^{public},\,K_A^{private}\right)`$
and party $`B`$ computes $`ECDH\left(K_A^{public},\,K_B^{private}\right)`$.
Where this document uses $`HKDF\left(salt,\,IKM,\,info,\,L\right)`$ it
refers to the [HMAC-based key derivation function][] with a salt value of
$`salt`$, input key material of $`IKM`$, context string $`info`$,
and output keying material length of $`L`$ bytes.
## The Olm Algorithm
### Initial setup
The setup takes four [Curve25519][] inputs: Identity keys for Alice and Bob,
$`I_A`$ and $`I_B`$, and one-time keys for Alice and Bob,
$`E_A`$ and $`E_B`$. A shared secret, $`S`$, is generated using
[Triple Diffie-Hellman][]. The initial 256 bit root key, $`R_0`$, and 256
bit chain key, $`C_{0,0}`$, 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{aligned}
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{aligned}
```
### Advancing the root key
Advancing a root key takes the previous root key, $`R_{i-1}`$, and two
Curve25519 inputs: the previous ratchet key, $`T_{i-1}`$, and the current
ratchet key $`T_i`$. 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, $`R_i`$, and
chain key, $`C_{i,0}`$, are derived from the shared secret using
[HKDF-SHA-256][] using $`R_{i-1}`$ as the salt and ``"OLM_RATCHET"`` as the
info.
```math
\begin{aligned}
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{aligned}
```
### Advancing the chain key
Advancing a chain key takes the previous chain key, $`C_{i,j-1}`$. The next
chain key, $`C_{i,j}`$, is the [HMAC-SHA-256][] of ``"\x02"`` using the
previous chain key as the key.
```math
\begin{aligned}
C_{i,j}&=HMAC\left(C_{i,j-1},\,\text{"\x02"}\right)
\end{aligned}
```
### Creating a message key
Creating a message key takes the current chain key, $`C_{i,j}`$. The
message key, $`M_{i,j}`$, is the [HMAC-SHA-256][] of ``"\x01"`` using the
current chain key as the key. The message keys where $`i`$ is even are used
by Alice to encrypt messages. The message keys where $`i`$ is odd are used
by Bob to encrypt messages.
```math
\begin{aligned}
M_{i,j}&=HMAC\left(C_{i,j},\,\text{"\x01"}\right)
\end{aligned}
```
## The Olm Protocol
### Creating an outbound session
Bob publishes the public parts of his identity key, $`I_B`$, and some
single-use one-time keys $`E_B`$.
Alice downloads Bob's identity key, $`I_B`$, and a one-time key,
$`E_B`$. She generates a new single-use key, $`E_A`$, and computes a
root key, $`R_0`$, and a chain key $`C_{0,0}`$. She also generates a
new ratchet key $`T_0`$.
### Sending the first pre-key messages
Alice computes a message key, $`M_{0,j}`$, and a new chain key,
$`C_{0,j+1}`$, using the current chain key. She replaces the current chain
key with the new one.
Alice encrypts her plain-text with the message key, $`M_{0,j}`$, using an
authenticated encryption scheme (see below) to get a cipher-text,
$`X_{0,j}`$.
She then sends the following to Bob:
* The public part of her identity key, $`I_A`$
* The public part of her single-use key, $`E_A`$
* The public part of Bob's single-use key, $`E_B`$
* The current chain index, $`j`$
* The public part of her ratchet key, $`T_0`$
* The cipher-text, $`X_{0,j}`$
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, $`E_B`$. He can now
compute the root key, $`R_0`$, and the chain key, $`C_{0,0}`$, from
$`I_A`$, $`E_A`$, $`I_B`$, and $`E_B`$.
Bob then advances the chain key $`j`$ times, to compute the chain key used
by the message, $`C_{0,j}`$. He now creates the
message key, $`M_{0,j}`$, and attempts to decrypt the cipher-text,
$`X_{0,j}`$. If the cipher-text's authentication is correct then Bob can
discard the private part of his single-use one-time key, $`E_B`$.
Bob stores Alice's initial ratchet key, $`T_0`$, 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,
$`C_{i,j}`$. Alice uses chain keys where $`i`$ is even. Bob uses chain
keys where $`i`$ is odd. If the chain key doesn't exist then a new ratchet
key $`T_i`$ is generated and a new root key $`R_i`$ and chain key
$`C_{i,0}`$ are computed using $`R_{i-1}`$, $`T_{i-1}`$ and
$`T_i`$.
A message key,
$`M_{i,j}`$ is computed from the current chain key, $`C_{i,j}`$, and
the chain key is replaced with the next chain key, $`C_{i,j+1}`$. The
plain-text is encrypted with $`M_{i,j}`$, using an authenticated encryption
scheme (see below) to get a cipher-text, $`X_{i,j}`$.
The user then sends the following to the recipient:
* The current chain index, $`j`$
* The public part of the current ratchet key, $`T_i`$
* The cipher-text, $`X_{i,j}`$
### Receiving messages
The user receives a message as above with the sender's current chain index, $`j`$,
the sender's ratchet key, $`T_i`$, and the cipher-text, $`X_{i,j}`$.
The user checks if they have a receiver chain with the correct
$`i`$ by comparing the ratchet key, $`T_i`$. If the chain doesn't exist
then they compute a new root key, $`R_i`$, and a new receiver chain, with
chain key $`C_{i,0}`$, using $`R_{i-1}`$, $`T_{i-1}`$ and
$`T_i`$.
If the $`j`$ 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 $`M_{i,j}`$. Otherwise
the receiver computes the chain key, $`C_{i,j}`$. The receiver computes the
message key, $`M_{i,j}`$, from the chain key and attempts to decrypt the
cipher-text, $`X_{i,j}`$.
If the decryption succeeds the receiver updates the chain key for $`T_i`$
with $`C_{i,j+1}`$ 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.
```
+--------------+------------------------------------+-----------+
| 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, Ti, of the message
Chain-Index|0x10|Integer|The chain index, j, of the message
Cipher-Text|0x22|String|The cipher-text, Xi, 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.
```
+--------------+------------------------------------+
| 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, Eb.
Base-Key|0x12|String|The public part of Alice's single-use key, Ea.
Identity-Key|0x1A|String|The public part of Alice's identity key, Ia.
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{aligned}
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{aligned}
```
The plain-text is encrypted with AES-256, using the key $`AES\_KEY_{i,j}`$
and the IV $`AES\_IV_{i,j}`$ to give the cipher-text, $`X_{i,j}`$.
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.
### Example attacks
1. Alice publishes her public [Curve25519][] identity key, $`I_A`$. Eve
publishes the same identity key, claiming it as her own. Bob downloads
Eve's keys, and associates $`I_A`$ 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, $`I_B`$. Eve
publishes the same identity key, claiming it as her own. Alice downloads
Eve's keys, and associates $`I_B`$ 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

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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

70
docs/signing.rst → docs/signing.md
View file

@ -1,20 +1,4 @@
.. Copyright 2016 OpenMarket Ltd # Signature keys and user identity in libolm
..
.. Licensed under the Apache License, Version 2.0 (the "License");
.. you may not use this file except in compliance with the License.
.. You may obtain a copy of the License at
..
.. http://www.apache.org/licenses/LICENSE-2.0
..
.. Unless required by applicable law or agreed to in writing, software
.. distributed under the License is distributed on an "AS IS" BASIS,
.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
.. See the License for the specific language governing permissions and
.. limitations under the License.
Signature keys and user identity in libolm
==========================================
The use of any public-key based cryptography system such as Olm presents the The use of any public-key based cryptography system such as Olm presents the
need for our users Alice and Bob to verify that they are in fact communicating need for our users Alice and Bob to verify that they are in fact communicating
@ -23,13 +7,13 @@ out-of-band process in which Alice and Bob verify that they have the correct
public keys for each other. For example, this might be done via physical public keys for each other. For example, this might be done via physical
presence or via a voice call. presence or via a voice call.
In the basic `Olm <olm.html>`_ protocol, it is sufficient to compare the public In the basic [Olm][] protocol, it is sufficient to compare the public
Curve25519 identity keys. As a naive example, Alice would meet Bob and ensure Curve25519 identity keys. As a naive example, Alice would meet Bob and ensure
that the identity key she downloaded from the key server matched that shown by that the identity key she downloaded from the key server matched that shown by
his device. This prevents the eavesdropper Eve from decrypting any messages his device. This prevents the eavesdropper Eve from decrypting any messages
sent from Alice to Bob, or from masquerading as Bob to send messages to Alice: sent from Alice to Bob, or from masquerading as Bob to send messages to Alice:
she has neither Alice's nor Bob's private identity key, so cannot successfully she has neither Alice's nor Bob's private identity key, so cannot successfully
complete the triple-DH calculation to compute the shared secret, :math:`S`, complete the triple-DH calculation to compute the shared secret, $`S`$,
which in turn prevents her decrypting intercepted messages, or from creating which in turn prevents her decrypting intercepted messages, or from creating
new messages with valid MACs. Obviously, for protection to be complete, Bob new messages with valid MACs. Obviously, for protection to be complete, Bob
must similarly verify Alice's key. must similarly verify Alice's key.
@ -41,7 +25,7 @@ one-time keys. Curve25519 keys are intended for use in DH calculations, and
their use to calculate signatures is non-trivial. their use to calculate signatures is non-trivial.
The solution adopted in this library is to generate a signing key for each The solution adopted in this library is to generate a signing key for each
user. This is an `Ed25519`_ keypair, which is used to calculate a signature on user. This is an [Ed25519][] keypair, which is used to calculate a signature on
an object including both the public Ed25519 signing key and the public an object including both the public Ed25519 signing key and the public
Curve25519 identity key. It is then the **public Ed25519 signing key** which is Curve25519 identity key. It is then the **public Ed25519 signing key** which is
used as the device fingerprint which Alice and Bob verify with each other. used as the device fingerprint which Alice and Bob verify with each other.
@ -50,8 +34,7 @@ By verifying the signatures on the key object, Alice and Bob then get the same
level of assurance about the ownership of the Curve25519 identity keys as if level of assurance about the ownership of the Curve25519 identity keys as if
they had compared those directly. they had compared those directly.
Signing one-time keys ## Signing one-time keys
---------------------
The Olm protocol requires users to publish a set of one-time keys to a key The Olm protocol requires users to publish a set of one-time keys to a key
server. To establish an Olm session, the originator downloads a key for the server. To establish an Olm session, the originator downloads a key for the
@ -60,19 +43,20 @@ is left to the application. There are both advantages and disadvantages to
doing so. doing so.
Consider the scenario where one-time keys are unsigned. Alice wants to initiate Consider the scenario where one-time keys are unsigned. Alice wants to initiate
an Olm session with Bob. Bob uploads his one-time keys, :math:`E_B`, but Eve an Olm session with Bob. Bob uploads his one-time keys, $`E_B`$, but Eve
replaces them with ones she controls, :math:`E_E`. Alice downloads one of the replaces them with ones she controls, $`E_E`$. Alice downloads one of the
compromised keys, and sends a pre-key message using a shared secret :math:`S`, compromised keys, and sends a pre-key message using a shared secret $`S`$,
where: where:
.. math:: ```math
S = ECDH\left(I_A,\,E_E\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\; S = ECDH\left(I_A,\,E_E\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\;
\parallel\;ECDH\left(E_A,\,E_E\right) \parallel\;ECDH\left(E_A,\,E_E\right)
```
Eve cannot decrypt the message because she does not have the private parts of Eve cannot decrypt the message because she does not have the private parts of
either :math:`E_A` nor :math:`I_B`, so cannot calculate either $`E_A`$ nor $`I_B`$, so cannot calculate
:math:`ECDH\left(E_A,\,I_B\right)`. However, suppose she later compromises $`ECDH\left(E_A,\,I_B\right)`$. However, suppose she later compromises
Bob's identity key :math:`I_B`. This would give her the ability to decrypt any Bob's identity key $`I_B`$. This would give her the ability to decrypt any
pre-key messages sent to Bob using the compromised one-time keys, and is thus a pre-key messages sent to Bob using the compromised one-time keys, and is thus a
problematic loss of forward secrecy. If Bob signs his keys with his Ed25519 problematic loss of forward secrecy. If Bob signs his keys with his Ed25519
signing key (and Alice verifies the signature before using them), this problem signing key (and Alice verifies the signature before using them), this problem
@ -81,38 +65,38 @@ is avoided.
On the other hand, signing the one-time keys leads to a reduction in On the other hand, signing the one-time keys leads to a reduction in
deniability. Recall that the shared secret is calculated as follows: deniability. Recall that the shared secret is calculated as follows:
.. math:: ```math
S = ECDH\left(I_A,\,E_B\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\; S = ECDH\left(I_A,\,E_B\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\;
\parallel\;ECDH\left(E_A,\,E_B\right) \parallel\;ECDH\left(E_A,\,E_B\right)
```
If keys are unsigned, a forger can make up values of :math:`E_A` and If keys are unsigned, a forger can make up values of $`E_A`$ and
:math:`E_B`, and construct a transcript of a conversation which looks like it $`E_B`$, and construct a transcript of a conversation which looks like it
was between Alice and Bob. Alice and Bob can therefore plausibly deny their was between Alice and Bob. Alice and Bob can therefore plausibly deny their
partition in any conversation even if they are both forced to divulge their partition in any conversation even if they are both forced to divulge their
private identity keys, since it is impossible to prove that the transcript was private identity keys, since it is impossible to prove that the transcript was
a conversation between the two of them, rather than constructed by a forger. a conversation between the two of them, rather than constructed by a forger.
If :math:`E_B` is signed, it is no longer possible to construct arbitrary If $`E_B`$ is signed, it is no longer possible to construct arbitrary
transcripts. Given a transcript and Alice and Bob's identity keys, we can now transcripts. Given a transcript and Alice and Bob's identity keys, we can now
show that at least one of Alice or Bob was involved in the conversation, show that at least one of Alice or Bob was involved in the conversation,
because the ability to calculate :math:`ECDH\left(I_A,\,E_B\right)` requires because the ability to calculate $`ECDH\left(I_A,\,E_B\right)`$ requires
knowledge of the private parts of either :math:`I_A` (proving Alice's knowledge of the private parts of either $`I_A`$ (proving Alice's
involvement) or :math:`E_B` (proving Bob's involvement, via the involvement) or $`E_B`$ (proving Bob's involvement, via the
signature). Note that it remains impossible to show that *both* Alice and Bob signature). Note that it remains impossible to show that *both* Alice and Bob
were involved. were involved.
In conclusion, applications should consider whether to sign one-time keys based In conclusion, applications should consider whether to sign one-time keys based
on the trade-off between forward secrecy and deniability. on the trade-off between forward secrecy and deniability.
License ## License
-------
This document is licensed under the `Apache License, Version 2.0 This document is licensed under the Apache License, Version 2.0
<http://www.apache.org/licenses/LICENSE-2.0>`_. http://www.apache.org/licenses/LICENSE-2.0.
Feedback ## Feedback
--------
Questions and feedback can be sent to olm at matrix.org. Questions and feedback can be sent to olm at matrix.org.
.. _`Ed25519`: http://ed25519.cr.yp.to/ [Ed25519]: http://ed25519.cr.yp.to/
[Olm]: https://gitlab.matrix.org/matrix-org/olm/blob/master/docs/olm.md