Security of Okamoto Identification Scheme

We consider the situation, where an adversary may learn the ephemeral values used by the prover within an identification protocol, aiming to get the secret keys of the user, or just to impersonate the prover subsequently. Unfortunately, most classical cryptographic identification protocols are exposed to such attacks, which might be quite realistic in case of software implementations. According to a recent proposal from SECIT-2017, we regard a scheme to be secure, if a malicious verifier, allowed to set the prover's ephemerals in the query stage, cannot impersonate the prover later on. We focus on the Okamoto Identification Scheme (IS), and show how to make it immune to the threats described above. Via reduction to the GDH Problem, we provide security guarantees in case of insufficient control over the unit executing Okamoto identification protocol (the standard Okamoto protocol is insecure in this situation).