Zero-knowledge identification scheme with companion matrices of primitive polynomials

Abstract

This paper proposes the matrix power problem, that is, to find x given CxDx, where C and D are the companion matrices of primitive polynomials over finite field. And a new zero-knowledge identification scheme based on matrix power problem is proposed. It is perfect zero-knowledge for honest verifiers. Due to its simplicity, and low-memory and low-computation costs, the proposed scheme is suitable for using in computationally limited devices for identification such as smart cards.