GQ and schnorr identification schemes: Proofs of security against impersonation under active and concurrent attacks

Abstract

The Guillou-Quisquater (GQ) and Schnorr identification schemes are amongst the most efficient and best-known Fiat-Shamir follow-ons, but the question of whether they can be proven secure against impersonation under active attack has remained open. This paper provides such a proof for GQ based on the assumed security of RSA under one more inversion, an extension of the usual one-wayness assumption that was introduced in [5]. It also provides such a proof for the Schnorr scheme based on a corresponding discrete-log related assumption. These are the first security proofs for these schemes under assumptions related to the underlying one-way functions. Both results extend to establish security against impersonation under concurrent attack.