Zero-Knowledge Identification Scheme Based on Symmetry Ergodic Matrices Exponentiation Problem

Abstract

Symmetry ergodic matrices exponentiation (SEME) problem is to find x, given CxMDx, where C and D are the companion matrices of primitive polynomials and M is an invertible matrix over finite field. This paper proposes a new zero-knowledge identification scheme based on SEME problem. It is perfect zero-knowledge for honest verifiers. The scheme could provide a candidate cryptographic primitive in post quantum cryptography. Due to its simplicity and naturalness, low-memory, low-computation costs, the proposed scheme is suitable for using in computationally limited devices for identification such as smart cards.