# 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 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, 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, 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:

S = \operatorname{ECDH}\left(I_A,E_E\right)\;\parallel\; \operatorname{ECDH}\left(E_A,I_B\right)\;\parallel\; \operatorname{ECDH}\left(E_A,E_E\right)

Eve cannot decrypt the message because she does not have the private parts of 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 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:

S = \operatorname{ECDH}\left(I_A,E_B\right)\;\parallel\; \operatorname{ECDH}\left(E_A,I_B\right)\;\parallel\; \operatorname{ECDH}\left(E_A,E_B\right)

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 participation 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 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 \operatorname{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

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 olm at matrix.org.