A Zero-Knowledge Identification Scheme Based on Matrix Power Problem

Abstract

This paper shows that in some case the matrix power function f (x) = C x D x is injective, where C and D are the the companion matrices of primitive polynomials. And a new zero-knowledge identification scheme based on the matrix power problem is proposed. It is perfect zeroknowledge for honest verifiers. Due to its simplicity, lowmemory and low-computation costs, the proposed scheme is suitable for using in computationally limited devices for identification such as smart cards.