双参数无模逆椭圆曲线数字签名方案的分析与改进  

Analysis and Improvement on ECDSA of Two-parameter without Modular Inverse Operation

作　　者：周克元[1] 王丽 ZHOU Ke-yuan;WANG Li(School of LiberalArts and Science,Suqian University,Suqian 223800,China)

机构地区：[1]宿迁学院文理学院,江苏宿迁223800

出　　处：《计算机技术与发展》2025年第3期99-102,共4页Computer Technology and Development

基　　金：国家自然科学基金项目(12101441)。

摘　　要：对于椭圆曲线数字签名算法的改进问题主要有两个方向,一是增加各种特殊功能,例如前向安全、消息恢复等;二是降低运算复杂度。椭圆曲线数字签名算法的运算包含点积、模乘、模逆和Hash函数运算,点积运算和Hash函数运算相对模乘和模逆运算复杂度较低,同时模逆运算时间是模乘运算时间的10倍,故算法的复杂度主要考虑模逆运算的次数,经典的椭圆曲线数字签名方案(ECDSA)中模逆运算为2次。各类对复杂度的改进方案主要为对模逆运算进行改进,陈亚茹、肖帅和巫光福对ECDSA进行了改进,给出了三种双参数运算的改进方案,分别宣称模逆运算达到1次、0次和0次。该文指出了三种方案中双参数方法的错误,双参数计算公式中的模逆运算无法做到方案中宣称的次数。以肖帅方案为例,给出了新的双参数改进方案,模逆运算达到最小值0次。最后将改进方案与已有方案进行了复杂度比较,复杂度更低,较好地解决了椭圆曲线数字签名双参数方案的改进问题。There are mainly two directions for improving the elliptic curve digital signature algorithm,one is to add various special functions,such as forward security,message recovery;the other is to reduce the computational complexity.The computational complexity of the elliptic curve digital signature algorithm includes point multiplication,modular multiplication,modular inverse,and hash function operations.The complexity of point multiplication and hash function operations is lower than that of modular multiplication and modular inverse operations.At the same time,the inverse modular operation takes 10 times longer than the modular multiplication operation,so the complexity of the algorithm mainly considers the number of modular inverse operations.The classic elliptic curve digital signature scheme has two modular inverse operations.The various complexity improvement schemes mainly involve improving the modular inverse operation.Chen Yaru,Xiao Shuai,and Wu Guangfu improved ECDSA and gave three dual-parameter optimization schemes,respectively claiming one,zero,and zero modular inverse operations.The errors in the dual-parameter methods of the three schemes is pointed out,and the dual-parameter calculation formula cannot achieve the claimed modular inverse operation times.For example,a new dual-parameter optimization scheme was given for Xiao Shuai,with the minimum modular inverse operation of zero times.Finally,the complexity of the improved scheme was compared with that of the existing schemes,and the improved scheme had lower complexity,which solved the problem of improving the dual-parameter scheme of elliptic curve digital signature effectively.

关 键 词：椭圆曲线 数字签名 模逆 双参数 改进 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]