Merge branch 'markdown' into 'master'

Convert docs from RST to Markdown

See merge request matrix-org/olm!2

6 files changed, 770 insertions, 509 deletions

diff --git a/CONTRIBUTING.rst b/CONTRIBUTING.md
index d3e59bd..82661bb 100644
--- a/CONTRIBUTING.rst
+++ b/CONTRIBUTING.md
@@ -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
 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
 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
 you agree to license it under the same terms as the project's license, we've
 adopted the same lightweight approach that the
-`Linux Kernel <https://www.kernel.org/doc/Documentation/SubmittingPatches>`_,
-`Docker <https://github.com/docker/docker/blob/master/CONTRIBUTING.md>`_,
-and many other projects use: the DCO
-(`Developer Certificate of Origin <http://developercertificate.org/>`_).
+[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),
+and many other projects use: the DCO ([Developer Certificate of Origin](http://developercertificate.org/)).
 This is a simple declaration that you wrote the contribution or otherwise have
 the right to contribute it to Matrix::
 
diff --git a/README.rst b/README.md
index b05de38..8268a98 100644
--- a/README.rst
+++ b/README.md
@@ -1,78 +1,75 @@
-Olm
-===
+# Olm
 
 An implementation of the Double Ratchet cryptographic ratchet described by
 https://whispersystems.org/docs/specifications/doubleratchet/, written in C and
 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
-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:
 
-.. code:: bash
-
-    cmake . -Bbuild
-    cmake --build build
+```bash
+cmake . -Bbuild
+cmake --build build
+```
 
 or:
 
-.. code:: bash
-
-    make
+```bash
+make
+```
 
 Using cmake is the preferred method for building the shared library; the
 Makefile may be removed in the future.
 
 To run the tests when using cmake, run:
 
-.. code:: bash
-
-    cd build/tests
-    ctest .
-
+```bash
+cd build/tests
+ctest .
+```
 To run the tests when using make, run:
 
-.. code:: bash
-
-    make test
+```bash
+make test
+```
 
 To build the JavaScript bindings, install emscripten from http://kripken.github.io/emscripten-site/ and then run:
 
-.. code:: bash
-
-    make js
+```bash
+make js
+```
 
 Note that if you run emscripten in a docker container, you need to pass through
 the EMCC_CLOSURE_ARGS environment variable.
 
 To build the android project for Android bindings, run:
 
-.. code:: bash
-
-    cd android
-    ./gradlew clean assembleRelease
+```bash
+cd android
+./gradlew clean assembleRelease
+```
 
 To build the Xcode workspace for Objective-C bindings, run:
 
-.. code:: bash
-
-    cd xcode
-    pod install
-    open OLMKit.xcworkspace
+```bash
+cd xcode
+pod install
+open OLMKit.xcworkspace
+```
 
 To build the Python bindings, first build olm as a shared library as above, and
 then run:
 
-.. code:: bash
-
-    cd python
-    make
+```bash
+cd python
+make
+```
 
 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``.
@@ -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
 either:
 
-.. code:: bash
-
-    cmake . -Bbuild -DBUILD_SHARED_LIBS=NO
-    cmake --build build
+```bash
+cmake . -Bbuild -DBUILD_SHARED_LIBS=NO
+cmake --build build
+```
 
 or
 
-.. code:: bash
-
-    make static
+```bash
+make static
+```
 
 The library can also be used as a dependency with CMake using:
 
-.. code:: cmake
-
-    find_package(Olm::Olm REQUIRED)
-    target_link_libraries(my_exe Olm::Olm)
-
+```cmake
+find_package(Olm::Olm REQUIRED)
+target_link_libraries(my_exe Olm::Olm)
+```
 
-Release process
----------------
+## Release process
 
 First: bump version numbers in ``common.mk``, ``CMakeLists.txt``,
 ``javascript/package.json``, ``python/olm/__version__.py``, ``OLMKit.podspec``,
@@ -113,34 +108,32 @@ git.
 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.
 
-.. code:: bash
+```bash
+make clean
 
-    make clean
+# build and test C library
+make test
 
-    # build and test C library
-    make test
+# build and test JS wrapper
+make js
+(cd javascript && npm run test)
+npm pack javascript
 
-    # build and test JS wrapper
-    make js
-    (cd javascript && npm run test)
-    npm pack javascript
+VERSION=x.y.z
+scp olm-$VERSION.tgz packages@ares.matrix.org:packages/npm/olm/
+git tag $VERSION -s
+git push --tags
 
-    VERSION=x.y.z
-    scp olm-$VERSION.tgz packages@ares.matrix.org:packages/npm/olm/
-    git tag $VERSION -s
-    git push --tags
+# OLMKit CocoaPod release
+# Make sure the version OLMKit.podspec is the same as the git tag
+# (this must be checked before git tagging)
+pod spec lint OLMKit.podspec --use-libraries --allow-warnings
+pod trunk push OLMKit.podspec --use-libraries --allow-warnings
+# Check the pod has been successully published with:
+pod search OLMKit
+```
 
-    # OLMKit CocoaPod release
-    # Make sure the version OLMKit.podspec is the same as the git tag
-    # (this must be checked before git tagging)
-    pod spec lint OLMKit.podspec --use-libraries --allow-warnings
-    pod trunk push OLMKit.podspec --use-libraries --allow-warnings
-    # Check the pod has been successully published with:
-    pod search OLMKit
-
-
-Design
-------
+## Design
 
 Olm is designed to be easy port to different platforms and to be easy
 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
 rewritten as the need ariases.
 
-Error Handling
-~~~~~~~~~~~~~~
+### Error Handling
 
 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.
 
-Random Numbers
-~~~~~~~~~~~~~~
+### Random Numbers
 
 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
 platforms since the caller can use whatever cryptographic random number
 generator their platform provides.
 
-Memory
-~~~~~~
+### Memory
 
 Olm avoids calling malloc or allocating memory on the heap itself.
 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 Encoding
-~~~~~~~~~~~~~~~
+### Output Encoding
 
 Binary output is encoded as base64 so that languages that prefer unicode
 strings will find it easier to handle the output.
 
-Dependencies
-~~~~~~~~~~~~
+### Dependencies
 
 Olm uses pure C implementations of the cryptographic primitives used by
 the ratchet. While this decreases the performance it makes it much easier
 to compile the library for different architectures.
 
-Contributing
-------------
-Please see `<CONTRIBUTING.rst>`_ when making contributions to the library.
+## Contributing
 
-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
 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/
 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
 
-What's an olm?
---------------
+## What's an olm?
 
 It's a really cool species of European troglodytic salamander.
 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
 and by downloading the software the user certifies that he/she/it is
diff --git a/docs/megolm.md b/docs/megolm.md
new file mode 100644
index 0000000..b9eedec
--- /dev/null
+++ b/docs/megolm.md
@@ -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 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, $`i`$.
+* 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
diff --git a/docs/olm.md b/docs/olm.md
new file mode 100644
index 0000000..e9bb4ae
--- /dev/null
+++ b/docs/olm.md
@@ -0,0 +1,328 @@
+# 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
diff --git a/docs/olm.rst b/docs/olm.rst
deleted file mode 100644
index 9c13478..0000000
--- a/docs/olm.rst
+++ /dev/null
@@ -1,358 +0,0 @@
-Olm: A Cryptographic Ratchet
-============================
-
-An implementation of the double cryptographic ratchet described by
-https://whispersystems.org/docs/specifications/doubleratchet/.
-
-
-Notation
---------
-
-This document uses :math:`\parallel` to represent string concatenation. When
-:math:`\parallel` appears on the right hand side of an :math:`=` it means that
-the inputs are concatenated. When :math:`\parallel` appears on the left hand
-side of an :math:`=` it means that the output is split.
-
-When this document uses :math:`ECDH\left(K_A,\,K_B\right)` it means that each
-party computes a Diffie-Hellman agreement using their private key and the
-remote party's public key.
-So party :math:`A` computes :math:`ECDH\left(K_B_public,\,K_A_private\right)`
-and party :math:`B` computes :math:`ECDH\left(K_A_public,\,K_B_private\right)`.
-
-Where this document uses :math:`HKDF\left(salt,\,IKM,\,info,\,L\right)` it
-refers to the `HMAC-based key derivation function`_ with a salt value of
-:math:`salt`, input key material of :math:`IKM`, context string :math:`info`,
-and output keying material length of :math:`L` bytes.
-
-The Olm Algorithm
------------------
-
-Initial setup
-~~~~~~~~~~~~~
-
-The setup takes four Curve25519_ inputs: Identity keys for Alice and Bob,
-:math:`I_A` and :math:`I_B`, and one-time keys for Alice and Bob,
-:math:`E_A` and :math:`E_B`. A shared secret, :math:`S`, is generated using
-`Triple Diffie-Hellman`_. The initial 256 bit root key, :math:`R_0`, and 256
-bit chain key, :math:`C_{0,0}`, are derived from the shared secret using an
-HMAC-based Key Derivation Function using SHA-256_ as the hash function
-(HKDF-SHA-256_) with default salt and ``"OLM_ROOT"`` as the info.
-
-.. math::
-    \begin{align}
-        S&=ECDH\left(I_A,\,E_B\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\;
-            \parallel\;ECDH\left(E_A,\,E_B\right)\\
-        R_0\;\parallel\;C_{0,0}&=
-             HKDF\left(0,\,S,\,\text{"OLM\_ROOT"},\,64\right)
-    \end{align}
-
-Advancing the root key
-~~~~~~~~~~~~~~~~~~~~~~
-
-Advancing a root key takes the previous root key, :math:`R_{i-1}`, and two
-Curve25519 inputs: the previous ratchet key, :math:`T_{i-1}`, and the current
-ratchet key :math:`T_i`. The even ratchet keys are generated by Alice.
-The odd ratchet keys are generated by Bob. A shared secret is generated
-using Diffie-Hellman on the ratchet keys. The next root key, :math:`R_i`, and
-chain key, :math:`C_{i,0}`, are derived from the shared secret using
-HKDF-SHA-256_ using :math:`R_{i-1}` as the salt and ``"OLM_RATCHET"`` as the
-info.
-
-.. math::
-    \begin{align}
-        R_i\;\parallel\;C_{i,0}&=HKDF\left(
-            R_{i-1},\,
-            ECDH\left(T_{i-1},\,T_i\right),\,
-            \text{"OLM\_RATCHET"},\,
-            64
-        \right)
-    \end{align}
-
-
-Advancing the chain key
-~~~~~~~~~~~~~~~~~~~~~~~
-
-Advancing a chain key takes the previous chain key, :math:`C_{i,j-1}`. The next
-chain key, :math:`C_{i,j}`, is the HMAC-SHA-256_ of ``"\x02"`` using the
-previous chain key as the key.
-
-.. math::
-     \begin{align}
-        C_{i,j}&=HMAC\left(C_{i,j-1},\,\text{"\textbackslash x02"}\right)
-    \end{align}
-
-Creating a message key
-~~~~~~~~~~~~~~~~~~~~~~
-
-Creating a message key takes the current chain key, :math:`C_{i,j}`. The
-message key, :math:`M_{i,j}`, is the HMAC-SHA-256_ of ``"\x01"`` using the
-current chain key as the key. The message keys where :math:`i` is even are used
-by Alice to encrypt messages. The message keys where :math:`i` is odd are used
-by Bob to encrypt messages.
-
-.. math::
-    \begin{align}
-        M_{i,j}&=HMAC\left(C_{i,j},\,\text{"\textbackslash x01"}\right)
-    \end{align}
-
-
-The Olm Protocol
-----------------
-
-Creating an outbound session
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-Bob publishes the public parts of his identity key, :math:`I_B`, and some
-single-use one-time keys :math:`E_B`.
-
-Alice downloads Bob's identity key, :math:`I_B`, and a one-time key,
-:math:`E_B`. She generates a new single-use key, :math:`E_A`, and computes a
-root key, :math:`R_0`, and a chain key :math:`C_{0,0}`. She also generates a
-new ratchet key :math:`T_0`.
-
-Sending the first pre-key messages
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-Alice computes a message key, :math:`M_{0,j}`, and a new chain key,
-:math:`C_{0,j+1}`, using the current chain key. She replaces the current chain
-key with the new one.
-
-Alice encrypts her plain-text with the message key, :math:`M_{0,j}`, using an
-authenticated encryption scheme (see below) to get a cipher-text,
-:math:`X_{0,j}`.
-
-She then sends the following to Bob:
- * The public part of her identity key, :math:`I_A`
- * The public part of her single-use key, :math:`E_A`
- * The public part of Bob's single-use key, :math:`E_B`
- * The current chain index, :math:`j`
- * The public part of her ratchet key, :math:`T_0`
- * The cipher-text, :math:`X_{0,j}`
-
-Alice will continue to send pre-key messages until she receives a message from
-Bob.
-
-Creating an inbound session from a pre-key message
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-Bob receives a pre-key message as above.
-
-Bob looks up the private part of his single-use key, :math:`E_B`. He can now
-compute the root key, :math:`R_0`, and the chain key, :math:`C_{0,0}`, from
-:math:`I_A`, :math:`E_A`, :math:`I_B`, and :math:`E_B`.
-
-Bob then advances the chain key :math:`j` times, to compute the chain key used
-by the message, :math:`C_{0,j}`. He now creates the
-message key, :math:`M_{0,j}`, and attempts to decrypt the cipher-text,
-:math:`X_{0,j}`. If the cipher-text's authentication is correct then Bob can
-discard the private part of his single-use one-time key, :math:`E_B`.
-
-Bob stores Alice's initial ratchet key, :math:`T_0`, until he wants to
-send a message.
-
-Sending normal messages
-~~~~~~~~~~~~~~~~~~~~~~~
-
-Once a message has been received from the other side, a session is considered
-established, and a more compact form is used.
-
-To send a message, the user checks if they have a sender chain key,
-:math:`C_{i,j}`. Alice uses chain keys where :math:`i` is even. Bob uses chain
-keys where :math:`i` is odd. If the chain key doesn't exist then a new ratchet
-key :math:`T_i` is generated and a new root key :math:`R_i` and chain key
-:math:`C_{i,0}` are computed using :math:`R_{i-1}`, :math:`T_{i-1}` and
-:math:`T_i`.
-
-A message key,
-:math:`M_{i,j}` is computed from the current chain key, :math:`C_{i,j}`, and
-the chain key is replaced with the next chain key, :math:`C_{i,j+1}`. The
-plain-text is encrypted with :math:`M_{i,j}`, using an authenticated encryption
-scheme (see below) to get a cipher-text, :math:`X_{i,j}`.
-
-The user then sends the following to the recipient:
- * The current chain index, :math:`j`
- * The public part of the current ratchet key, :math:`T_i`
- * The cipher-text, :math:`X_{i,j}`
-
-Receiving messages
-~~~~~~~~~~~~~~~~~~
-
-The user receives a message as above with the sender's current chain index, :math:`j`,
-the sender's ratchet key, :math:`T_i`, and the cipher-text, :math:`X_{i,j}`.
-
-The user checks if they have a receiver chain with the correct
-:math:`i` by comparing the ratchet key, :math:`T_i`. If the chain doesn't exist
-then they compute a new root key, :math:`R_i`, and a new receiver chain, with
-chain key :math:`C_{i,0}`, using :math:`R_{i-1}`, :math:`T_{i-1}` and
-:math:`T_i`.
-
-If the :math:`j` of the message is less than
-the current chain index on the receiver then the message may only be decrypted
-if the receiver has stored a copy of the message key :math:`M_{i,j}`. Otherwise
-the receiver computes the chain key, :math:`C_{i,j}`. The receiver computes the
-message key, :math:`M_{i,j}`, from the chain key and attempts to decrypt the
-cipher-text, :math:`X_{i,j}`.
-
-If the decryption succeeds the receiver updates the chain key for :math:`T_i`
-with :math:`C_{i,j+1}` and stores the message keys that were skipped in the
-process so that they can decode out of order messages. If the receiver created
-a new receiver chain then they discard their current sender chain so that
-they will create a new chain when they next send a message.
-
-The Olm Message Format
-----------------------
-
-Olm uses two types of messages. The underlying transport protocol must provide
-a means for recipients to distinguish between them.
-
-Normal Messages
-~~~~~~~~~~~~~~~
-
-Olm messages start with a one byte version followed by a variable length
-payload followed by a fixed length message authentication code.
-
-.. code::
-
-   +--------------+------------------------------------+-----------+
-   | Version Byte | Payload Bytes                      | MAC Bytes |
-   +--------------+------------------------------------+-----------+
-
-The version byte is ``"\x03"``.
-
-The payload consists of key-value pairs where the keys are integers and the
-values are integers and strings. The keys are encoded as a variable length
-integer tag where the 3 lowest bits indicates the type of the value:
-0 for integers, 2 for strings. If the value is an integer then the tag is
-followed by the value encoded as a variable length integer. If the value is
-a string then the tag is followed by the length of the string encoded as
-a variable length integer followed by the string itself.
-
-Olm uses a variable length encoding for integers. Each integer is encoded as a
-sequence of bytes with the high bit set followed by a byte with the high bit
-clear. The seven low bits of each byte store the bits of the integer. The least
-significant bits are stored in the first byte.
-
-=========== ===== ======== ================================================
-    Name     Tag    Type                     Meaning
-=========== ===== ======== ================================================
-Ratchet-Key  0x0A String   The public part of the ratchet key, :math:`T_{i}`,
-                           of the message
-Chain-Index  0x10 Integer  The chain index, :math:`j`, of the message
-Cipher-Text  0x22 String   The cipher-text, :math:`X_{i,j}`, of the message
-=========== ===== ======== ================================================
-
-The length of the MAC is determined by the authenticated encryption algorithm
-being used. (Olm version 1 uses HMAC-SHA-256, truncated to 8 bytes). The
-MAC protects all of the bytes preceding the MAC.
-
-Pre-Key Messages
-~~~~~~~~~~~~~~~~
-
-Olm pre-key messages start with a one byte version followed by a variable
-length payload.
-
-.. code::
-
-   +--------------+------------------------------------+
-   | Version Byte | Payload Bytes                      |
-   +--------------+------------------------------------+
-
-The version byte is ``"\x03"``.
-
-The payload uses the same key-value format as for normal messages.
-
-============ ===== ======== ================================================
-    Name      Tag    Type                     Meaning
-============ ===== ======== ================================================
-One-Time-Key  0x0A String   The public part of Bob's single-use key,
-                            :math:`E_b`.
-Base-Key      0x12 String   The public part of Alice's single-use key,
-                            :math:`E_a`.
-Identity-Key  0x1A String   The public part of Alice's identity key,
-                            :math:`I_a`.
-Message       0x22 String   An embedded Olm message with its own version and
-                            MAC.
-============ ===== ======== ================================================
-
-Olm Authenticated Encryption
-----------------------------
-
-Version 1
-~~~~~~~~~
-
-Version 1 of Olm uses AES-256_ in CBC_ mode with `PKCS#7`_ padding for
-encryption and HMAC-SHA-256_ (truncated to 64 bits) for authentication.  The
-256 bit AES key, 256 bit HMAC key, and 128 bit AES IV are derived from the
-message key using HKDF-SHA-256_ using the default salt and an info of
-``"OLM_KEYS"``.
-
-.. math::
-
-    \begin{align}
-    AES\_KEY_{i,j}\;\parallel\;HMAC\_KEY_{i,j}\;\parallel\;AES\_IV_{i,j}
-        &= HKDF\left(0,\,M_{i,j},\text{"OLM\_KEYS"},\,80\right) \\
-    \end{align}
-
-The plain-text is encrypted with AES-256, using the key :math:`AES\_KEY_{i,j}`
-and the IV :math:`AES\_IV_{i,j}` to give the cipher-text, :math:`X_{i,j}`.
-
-Then the entire message (including the Version Byte and all Payload Bytes) are
-passed through HMAC-SHA-256. The first 8 bytes of the MAC are appended to the message.
-
-Message authentication concerns
--------------------------------
-
-To avoid unknown key-share attacks, the application must include identifying
-data for the sending and receiving user in the plain-text of (at least) the
-pre-key messages. Such data could be a user ID, a telephone number;
-alternatively it could be the public part of a keypair which the relevant user
-has proven ownership of.
-
-.. admonition:: Example attacks
-
-   1. Alice publishes her public Curve25519 identity key, :math:`I_A`. Eve
-      publishes the same identity key, claiming it as her own. Bob downloads
-      Eve's keys, and associates :math:`I_A` with Eve. Alice sends a message to
-      Bob; Eve intercepts it before forwarding it to Bob. Bob believes the
-      message came from Eve rather than Alice.
-
-      This is prevented if Alice includes her user ID in the plain-text of the
-      pre-key message, so that Bob can see that the message was sent by Alice
-      originally.
-
-   2. Bob publishes his public Curve25519 identity key, :math:`I_B`. Eve
-      publishes the same identity key, claiming it as her own. Alice downloads
-      Eve's keys, and associates :math:`I_B` with Eve. Alice sends a message to
-      Eve; Eve cannot decrypt it, but forwards it to Bob. Bob believes the
-      Alice sent the message to him, wheras Alice intended it to go to Eve.
-
-      This is prevented by Alice including the user ID of the intended recpient
-      (Eve) in the plain-text of the pre-key message. Bob can now tell that the
-      message was meant for Eve rather than him.
-
-IPR
----
-
-The Olm specification (this document) is hereby placed in the public domain.
-
-Feedback
---------
-
-Can be sent to olm at matrix.org.
-
-Acknowledgements
-----------------
-
-The ratchet that Olm implements was designed by Trevor Perrin and Moxie
-Marlinspike - details at https://whispersystems.org/docs/specifications/doubleratchet/.  Olm is
-an entirely new implementation written by the Matrix.org team.
-
-.. _`Curve25519`: http://cr.yp.to/ecdh.html
-.. _`Triple Diffie-Hellman`: https://whispersystems.org/blog/simplifying-otr-deniability/
-.. _`HMAC-based key derivation function`: https://tools.ietf.org/html/rfc5869
-.. _`HKDF-SHA-256`: https://tools.ietf.org/html/rfc5869
-.. _`HMAC-SHA-256`: https://tools.ietf.org/html/rfc2104
-.. _`SHA-256`: https://tools.ietf.org/html/rfc6234
-.. _`AES-256`: http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf
-.. _`CBC`: http://csrc.nist.gov/publications/nistpubs/800-38a/sp800-38a.pdf
-.. _`PKCS#7`: https://tools.ietf.org/html/rfc2315
diff --git a/docs/signing.rst b/docs/signing.md
index 05c55eb..fcc5342 100644
--- a/docs/signing.rst
+++ b/docs/signing.md
@@ -1,20 +1,4 @@
-.. 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.
-
-
-Signature keys and user identity in libolm
-==========================================
+# Signature keys and user identity in libolm
 
 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
@@ -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
 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
 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
 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
-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
 new messages with valid MACs. Obviously, for protection to be complete, Bob
 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.
 
 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
 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.
@@ -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
 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
 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.
 
 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
-replaces them with ones she controls, :math:`E_E`. Alice downloads one of the
-compromised keys, and sends a pre-key message using a shared secret :math:`S`,
+an Olm session with Bob. Bob uploads his one-time keys, $`E_B`$, but Eve
+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 $`S`$,
 where:
 
-.. math::
-    S = ECDH\left(I_A,\,E_E\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\;
-         \parallel\;ECDH\left(E_A,\,E_E\right)
+```math
+S = ECDH\left(I_A,\,E_E\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\;
+        \parallel\;ECDH\left(E_A,\,E_E\right)
+```
 
 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
-:math:`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
+either $`E_A`$ nor $`I_B`$, so cannot calculate
+$`ECDH\left(E_A,\,I_B\right)`$. However, suppose she later compromises
+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
 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
@@ -81,38 +65,38 @@ is avoided.
 On the other hand, signing the one-time keys leads to a reduction in
 deniability. Recall that the shared secret is calculated as follows:
 
-.. math::
-        S = ECDH\left(I_A,\,E_B\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\;
-            \parallel\;ECDH\left(E_A,\,E_B\right)
+```math
+S = ECDH\left(I_A,\,E_B\right)\;\parallel\;ECDH\left(E_A,\,I_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
-:math:`E_B`, and construct a transcript of a conversation which looks like it
+If keys are unsigned, a forger can make up values of $`E_A`$ and
+$`E_B`$, and construct a transcript of a conversation which looks like it
 was between Alice and Bob. Alice and Bob can therefore plausibly deny their
 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
 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
 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
-knowledge of the private parts of either :math:`I_A` (proving Alice's
-involvement) or :math:`E_B` (proving Bob's involvement, via the
+because the ability to calculate $`ECDH\left(I_A,\,E_B\right)`$ requires
+knowledge of the private parts of either $`I_A`$ (proving Alice's
+involvement) or $`E_B`$ (proving Bob's involvement, via the
 signature). Note that it remains impossible to show that *both* Alice and Bob
 were involved.
 
 In conclusion, applications should consider whether to sign one-time keys based
 on the trade-off between forward secrecy and deniability.
 
-License
--------
+## License
 
-This document is licensed under the `Apache License, Version 2.0
-<http://www.apache.org/licenses/LICENSE-2.0>`_.
+This document is licensed under the Apache License, Version 2.0
+http://www.apache.org/licenses/LICENSE-2.0.
 
-Feedback
---------
+## Feedback
 
 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