Title: Zero-knowledge identification scheme with companion matrices of primitive polynomials

Authors: Huawei Huang; Lunzhi Deng; Yunyun Qu; Chunhua Li

Addresses: School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, China ' School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, China ' School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, China ' School of Science, East China Jiaotong University, Nanchang, 330013, China

Abstract: This paper proposes the matrix power problem, that is, to find x given C^xD^x, 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.

Keywords: finite field; primitive polynomials; companion matrix; discrete logarithm problem; identification scheme.

DOI: 10.1504/IJES.2020.105931

International Journal of Embedded Systems, 2020 Vol.12 No.2, pp.216 - 225

Received: 09 Feb 2016
Accepted: 15 Jun 2016
Published online: 19 Mar 2020 *

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