219 lines
8.9 KiB
ReStructuredText
219 lines
8.9 KiB
ReStructuredText
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Megolm group ratchet
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====================
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An AES-based cryptographic ratchet intended for group communications.
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The Megolm algorithm
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--------------------
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Initial setup
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~~~~~~~~~~~~~
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Each participant in a conversation generates their own Megolm session. A
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session consists of three parts: a 32 bit counter, :math:`i`; an `Ed25519`_
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keypair, :math:`K`; and a ratchet, :math:`R_i`. The ratchet consists of four
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256-bit values, :math:`R_{i,j}` for :math:`j \in {0,1,2,3}`.
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The counter :math:`i` is initialised to :math:`0`. A new Ed25519 keypair is
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generated for :math:`K`. The ratchet is simply initialised with 1024 bits of
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cryptographically-secure random data.
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A single participant may use multiple sessions over the lifetime of a
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conversation. The public part of :math:`K` is used as an identifier to
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discriminate between sessions.
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Sharing session data
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~~~~~~~~~~~~~~~~~~~~
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To allow other participants in the conversation to decrypt messages, the
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session data is formatted as described in `Session-sharing format`_. It is then
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shared with other participants in the conversation via a secure peer-to-peer
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channel (such as that provided by `Olm`_).
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When the session data is received from other participants, the recipient first
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checks that the signature matches the public key. They then store their own
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copy of the counter, ratchet, and public key.
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Message encryption
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~~~~~~~~~~~~~~~~~~
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Megolm uses AES-256_ in CBC_ mode with `PCKS#7`_ padding for and HMAC-SHA-256_
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(truncated to 64 bits). The 256 bit AES key, 256 bit HMAC key, and 128 bit AES
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IV are derived from the megolm ratchet :math:`R_i`:
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.. math::
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\begin{align}
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AES\_KEY_{i}\;\parallel\;HMAC\_KEY_{i}\;\parallel\;AES\_IV_{i}
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&= HKDF\left(0,\,R_{i},\text{"MEGOLM\_KEYS"},\,80\right) \\
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\end{align}
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where :math:`\parallel` represents string splitting, and
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:math:`HKDF\left(salt,\,IKM,\,info,\,L\right)` refers to the `HMAC-based key
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derivation function`_ using using `SHA-256`_ as the hash function
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(`HKDF-SHA-256`_) with a salt value of :math:`salt`, input key material of
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:math:`IKM`, context string :math:`info`, and output keying material length of
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:math:`L` bytes.
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The plain-text is encrypted with AES-256, using the key :math:`AES\_KEY_{i}`
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and the IV :math:`AES\_IV_{i}` to give the cipher-text, :math:`X_{i}`.
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The ratchet index :math:`i`, and the cipher-text :math:`X_{i}`, are then packed
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into a message as described in `Message format`_. Then the entire message
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(including the version bytes and all payload bytes) are passed through
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HMAC-SHA-256. The first 8 bytes of the MAC are appended to the message.
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Finally, the authenticated message is signed using the Ed25519 keypair; the 64
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byte signature is appended to the message.
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The complete signed message, together with the public part of :math:`K` (acting
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as a session identifier), can then be sent over an insecure channel. The
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message can then be authenticated and decrypted only by recipients who have
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received the session data.
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Advancing the ratchet
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~~~~~~~~~~~~~~~~~~~~~
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After each message is encrypted, the ratchet is advanced. This is done as
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follows:
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.. math::
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\begin{align}
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R_{i,0} &=
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\begin{cases}
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HMAC\left(R_{2^24(n-1),0}, \text{"\textbackslash x00"}\right)
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&\text{if }\exists n | i = 2^24n\\
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R_{i-1,0} &\text{otherwise}
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\end{cases}\\
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R_{i,1} &=
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\begin{cases}
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HMAC\left(R_{2^24(n-1),0}, \text{"\textbackslash x01"}\right)
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&\text{if }\exists n | i = 2^24n\\
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HMAC\left(R_{2^16(m-1),1}, \text{"\textbackslash x01"}\right)
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&\text{if }\exists m | i = 2^16m\\
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R_{i-1,1} &\text{otherwise}
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\end{cases}\\
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R_{i,2} &=
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\begin{cases}
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HMAC\left(R_{2^24(n-1),0}, \text{"\textbackslash x02"}\right)
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&\text{if }\exists n | i = 2^24n\\
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HMAC\left(R_{2^16(m-1),1}, \text{"\textbackslash x02"}\right)
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&\text{if }\exists m | i = 2^16m\\
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HMAC\left(R_{2^8(p-1),2}, \text{"\textbackslash x02"}\right)
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&\text{if }\exists p | i = 2^8p\\
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R_{i-1,2} &\text{otherwise}
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\end{cases}\\
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R_{i,3} &=
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\begin{cases}
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HMAC\left(R_{2^24(n-1),0}, \text{"\textbackslash x03"}\right)
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&\text{if }\exists n | i = 2^24n\\
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HMAC\left(R_{2^16(m-1),1}, \text{"\textbackslash x03"}\right)
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&\text{if }\exists m | i = 2^16m\\
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HMAC\left(R_{2^8(p-1),2}, \text{"\textbackslash x03"}\right)
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&\text{if }\exists p | i = 2^8p\\
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HMAC\left(R_{i-1,3}, \text{"\textbackslash x03"}\right)
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&\text{otherwise}
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\end{cases}
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\end{align}
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where :math:`HMAC(K, T)` is the HMAC-SHA-256_ of ``T``, using ``K`` as the
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key. In summary: every :math:`2^8` iterations, :math:`R_{i,3}` is reseeded from
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:math:`R_{i,2}`. Every :math:`2^16` iterations, :math:`R_{i,2}` and
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:math:`R_{i,3}` are reseeded from :math:`R_{i,1}`. Every :math:`2^24`
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iterations, :math:`R_{i,1}`, :math:`R_{i,2}` and :math:`R_{i,3}` are reseeded
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from :math:`R_{i,0}`.
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This scheme allows the ratchet to be advanced an arbitrary amount forwards
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while needing at most 1023 hash computations. A recipient can decrypt
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conversation history onwards from the earliest value of the ratchet it is aware
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of, but cannot decrypt history from before that point without reversing the
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hash function.
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For outbound sessions, the updated ratchet and counter are stored in the
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session.
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In order to maintain the ability to decrypt conversation history, inbound
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sessions should store a copy of their earliet known ratchet value (unless they
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explicitly want to drop the ability to decrypt that history). They may also
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choose to cache calculated ratchet values, but the decision of which ratchet
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states to cache is left to the application.
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Data exchange formats
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---------------------
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Session-sharing format
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~~~~~~~~~~~~~~~~~~~~~~
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The Megolm key-sharing format is as follows:
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.. code::
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+---+----+--------+--------+--------+--------+------+-----------+
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| V | i | R(i,0) | R(i,1) | R(i,2) | R(i,3) | Kpub | Signature |
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+---+----+--------+--------+--------+--------+------+-----------+
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0 1 5 37 69 101 133 165 229
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The version byte, ``V``, is ``"\x02"``.
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This is followed by the ratchet index, :math:`i`, which is encoded as a
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big-endian 32-bit integer; the ratchet values :math:`R_{i,j}`; and the public
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part of the Ed25519 keypair :math:`K`.
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The data is then signed using the Ed25519 keypair, and the 64-byte signature is
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appended.
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Message format
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~~~~~~~~~~~~~~
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Megolm messages consist of a one byte version, followed by a variable length
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payload, a fixed length message authentication code, and a fixed length
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signature.
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.. code::
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+---+------------------------------------+-----------+------------------+
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| V | Payload Bytes | MAC Bytes | Signature Bytes |
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+---+------------------------------------+-----------+------------------+
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0 1 N N+8 N+72
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The version byte, ``V``, is ``"\x03"``.
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The payload consists of key-value pairs where the keys are integers and the
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values are integers and strings. The keys are encoded as a variable length
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integer tag where the 3 lowest bits indicates the type of the value:
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0 for integers, 2 for strings. If the value is an integer then the tag is
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followed by the value encoded as a variable length integer. If the value is
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a string then the tag is followed by the length of the string encoded as
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a variable length integer followed by the string itself.
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Olm uses a variable length encoding for integers. Each integer is encoded as a
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sequence of bytes with the high bit set followed by a byte with the high bit
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clear. The seven low bits of each byte store the bits of the integer. The least
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significant bits are stored in the first byte.
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============= ===== ======== ================================================
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Name Tag Type Meaning
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============= ===== ======== ================================================
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Message-Index 0x08 Integer The index of the ratchet, :math:`i`
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Cipher-Text 0x12 String The cipher-text, :math:`X_{i}`, of the message
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============= ===== ======== ================================================
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The length of the MAC is determined by the authenticated encryption algorithm
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being used (8 bytes in this version of the protocol). The MAC protects all of
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the bytes preceding the MAC.
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The length of the signature is determined by the signing algorithm being used
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(64 bytes in this version of the protocol). The signature covers all of the
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bytes preceding the signaure.
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.. _`Ed25519`: http://ed25519.cr.yp.to/
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.. _`HMAC-based key derivation function`: https://tools.ietf.org/html/rfc5869
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.. _`HKDF-SHA-256`: https://tools.ietf.org/html/rfc5869
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.. _`HMAC-SHA-256`: https://tools.ietf.org/html/rfc2104
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.. _`SHA-256`: https://tools.ietf.org/html/rfc6234
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.. _`AES-256`: http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf
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.. _`CBC`: http://csrc.nist.gov/publications/nistpubs/800-38a/sp800-38a.pdf
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.. _`PCKS#7`: https://tools.ietf.org/html/rfc2315
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.. _`Olm`: ./olm.html
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