A New Three-Pass Code-based Zero-Knowledge Identification Scheme with Cheating Probability of Exactly Half

Abstract

In 1996, Stern proposed a three-pass zero-knowledge identification (ID) scheme where the cheating probability, i.e., the success probability of cheating prover, is 2/3. Since then, variants and generalization of Stern's ID have been proposed. However, within two-bit challenge space, all of them are having the cheating probability of more than half or reaching half only in an asymptotic manner with more than three passes in one round. In this paper, we propose the first code-based zero-knowledge three-pass ID scheme with the cheating probability of exactly half even with only two-bit challenge space. Our proposed ID scheme can reduce the necessary number of rounds in order to achieve the targeted security against impersonation. Since rewinding technique cannot be used against a quantum adversary in the security proof, we prove the security using the lossy paradigm and rely on the decisional version of syndrome decoding problem so that we do not have to rewind the adversary.