According to the paper “GQ and Schnorr Identification Schemes: Proofs of Security against Impersonation under Active and Concurrent Attacks” by Mihir Bellare and Adriana Palacio, the Schnorr identification scheme is secure under an active adversary who changes messages. I have been told that Schnorr is actually not secure against such an adversary but I am not able to find any new literature on it. Any ideas?
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It is important to consider the model in which security is proved. In this case, the attack proceeds in two phases: first a phase where the adversary as a verifier interacts with the honest prover, then a phase where the adversary as a prover interacts with an honest verifier. The adversary wins if the honest prover accepts. The paper proves, under reasonable assumptions, that the adversary cannot win in this model.
However (see the comment at the end of Section 2), this model is very restricted and not so useful. In more useful models where the adversary interacts with the honest prover and the honest verifier at the same time, the Schnorr identification protocol is absolutely hopeless, which isn't surprising since it wasn't designed with those models in mind.