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+.. 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
+==========================================
+
+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
+with each other, rather than a man-in-the-middle. Typically this requires an
+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
+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`,
+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.
+
+However, the use of the Curve25519 key as the "fingerprint" in this way makes
+it difficult to carry out signing operations. For instance, it may be useful to
+cross-sign identity keys for different devices, or, as discussed below, to sign
+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
+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.
+
+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
+---------------------
+
+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
+recipient from this server. The decision of whether to sign these one-time keys
+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`,
+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)
+
+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
+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
+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)
+
+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
+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
+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
+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
+-------
+
+This document is licensed under the `Apache License, Version 2.0
+<http://www.apache.org/licenses/LICENSE-2.0>`_.
+
+Feedback
+--------
+
+Questions and feedback can be sent to richard at matrix.org.
+
+.. _`Ed25519`: http://ed25519.cr.yp.to/