42 lines
1.4 KiB
ReStructuredText
42 lines
1.4 KiB
ReStructuredText
Olm: A Crytographic Ratchet
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===========================
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An implementation of the cryptographic ratchet described by
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https://github.com/trevp/axolotl/wiki.
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The Olm Algorithm
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-----------------
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.. figure:: Axolotl.svg
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Initial setup
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~~~~~~~~~~~~~
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The setup takes four Curve25519 inputs: Identity keys for Alice and Bob,
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:math:`I_A` and :math:`I_B`, and emphemeral keys for Alice and Bob,
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:math:`E_A` and :math:`E_B`. A shared secret, :math:`S`, is generated using
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Triple Diffie-Hellman. The initial 256 bit root key, :math:`R_0`, and 256 bit
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chain key, :math:`C_{0,0}`, are derived from the shared secret using an
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HMAC-based Key Derivation Function (HKDF).
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.. math::
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\begin{align}
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S&=ECDH\left(I_A,\,E_B\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\;
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\parallel\;ECDH\left(E_A,\,E_B\right)\\
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R_0\;\parallel\;C_{0,0}&=HKDF(S,\,\text{"OLM\_ROOT"})
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\end{align}
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Advancing the root key
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~~~~~~~~~~~~~~~~~~~~~~
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Advancing a root key takes the previous root key, :math:`R_{i-1}`, and two
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Curve25519 inputs: The previous ratchet key, :math:`T_{i-1}`, and the current
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ratchet key :math:`T_{i}`. The even ratchet keys are generated by Alice.
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The odd ratchet keys are generated by Bob. A shared secret, `S` is generated
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using Diffie-Hellman on the ratchet keys. The next root key, :math:`R_o`, and
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chain key, :math:`C_{i,0}`, are derived from the shared secret using an
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HMAC-based Key Derivation Function (HKDF).
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