Provably Secure Identity-Based Identification and Signature Schemes with Parallel-PVR

Abstract

Identity-based identification and signature (IBI/IBS) schemes are two of the most fundamental cryptographic primitives with greatly simplified public key management. Meanwhile, code-based cryptography is one of few alternatives supposed to be secure in a post-quantum world, so several code-based IBI/IBS schemes have been proposed. However, with increasingly profound researches on coding theory, the security reduction and efficiency of such schemes have been invalidated and challenged. In this paper, we construct provably secure IBI/IBS schemes from code assumptions against impersonation under active and concurrent attacks through PVR signature and Or-proof technique. We also present the parallel-PVR technique to decrease parameter values while maintaining the standard security level. Compared to other code-based IBI/IBS schemes, our schemes achieve not only preferable public parameter size, private key size, communication cost and signature length due to better parameter choices, but also provably secure.