基于椭圆曲线的无证书SM2数字签名方案  

Certificate free SM2 digital signature scheme based on elliptic curve

作　　者：陈楠 Chen Nan(School of Mathematics and Statistics,Xianyang Normal University,Xianyang 712000,China)

机构地区：[1]咸阳师范学院数学与统计学院,咸阳712000

出　　处：《现代计算机》2023年第23期53-57,63,共6页Modern Computer

基　　金：陕西省教育厅科研计划项目(21JK0969)。

摘　　要：为有效解决椭圆曲线数字签名在签名与验证时需反复求逆,运算繁杂且速度较慢,系统性能无法最优化的问题,基于椭圆曲线的无证书SM2数字签名方案由此诞生。通过解析数字签名与椭圆曲线离散对数问题,进一步研究了椭圆曲线无证书SM2数字签名方案相关算法以及正确性、安全性、效率。研究结果表明,基于椭圆曲线的无证书SM2数字签名方案正确,且基于随机语言模型下是可证安全性的,适应性消息选择性攻击时具备不可伪造性,同时相比其他既有数字签名方案计算效率更高。In order to effectively solve the problem of repeated inversion,complex and slow operation,and inability to opti-mize system performance during signature and verification of elliptic curve digital signatures,a certificateless SM2 digital signature scheme based on elliptic curve was born.This article further studies the algorithms,correctness,security,and efficiency of the el-liptic curve certificateless SM2 digital signature scheme by analyzing digital signatures and the elliptic curve discrete logarithm problem.The research results indicate that the certificateless SM2 digital signature scheme based on elliptic curves is correct,and it is provably secure under random language models.It has unforgeability under adaptive message selective attacks,and has higher computational efficiency compared to other existing digital signature schemes.

关 键 词：椭圆曲线 无证书 SM2 数字签名 正确性 安全性 

分 类 号：TN918.4[电子电信—通信与信息系统]