基于有限单群的Schnorr数字签名算法及实现  

A Schnorr Digital Signature Algorithm Based on Finite Single Group and Its Implementation

作　　者：江宝安 JIANG Bao’an(Chongqing College of Mobile Communication,Chongqing 401520,China;Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]重庆移通学院,重庆401520 [2]重庆邮电大学,重庆400065

出　　处：《通信技术》2024年第4期394-399,共6页Communications Technology

基　　金：重庆市教委科学技术研究项目:疫情防控下基于AI的校园行为识别预警系统研究(KJQN202102403)。

摘　　要：数字签名是信息安全三大基础设施之一,其中Schnorr数字签名是基于离散对数体制最简单的一种数字签名算法,天然具有线性可扩展性。提出一种新的Schnorr数字签名算法,该算法建立在有限域F2p的乘法单群F2p~*上,而不是原Schnorr数字签名数域循环群的子群上,签名和验证算法类似Schnorr数字签名方案;在新的Schnorr数字签名的基础上,改进了多重Schnorr数字签名方案。算法本身基于模2运算,便于软硬件快速实现,理论分析和MATLAB算法仿真均证明其有效性,性能优于经典的Schnorr签名算法,具有广泛的理论和实际应用价值。Digital signature is one of the three major infrastructures of information security,among which Schnorr digital signature is the simplest digital signature algorithm based on discrete logarithm system,and it naturally has linear scalability.In this paper,a new Schnorr digital signature algorithm is proposed,which is built on a multiplicative single group F2p of a finite field F2p*rather than a subgroup of the original Schnorr digital signature field Zp cyclic group Zp*cyclic group of the original number field.,and the signature and verification algorithms are similar to the Schnorr digital signature scheme.Based on the new Schnorr digital signature,the multiple Schnorr digital signature scheme is improved.The algorithm itself is based on module 2 operation,which is convenient for software and hardware to implement quickly.Theoretical analysis and MATLAB simulation have proved its effectiveness,and its performance is better than the classic Schnorr signature algorithm and has a wide range of theoretical and practical application value.

关 键 词：Schnorr 数字签名 多重数字签名 有限单群 梅森素数 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]