Abstract:

The classic ECDSA scheme uses one inversion operation in the process of signature and verification, and the complex and time-consuming inversion operation restricts the efficiency of digital signature. In view of the limitations of ECDSA, many improvement schemes have been put forward in the industry. However, some improvement schemes only start from the improvement of ECDSA computing efficiency, but they fail to take into account such issues as forgery signature attack. Based on the analysis of the classical ECDSA scheme, taking into account the security and calculation efficiency of the elliptic curve digital signature, an improved new scheme of the elliptic curve digital signature is proposed and the security and efficiency of the new scheme are proved through theoretical analysis and simulation experiments. The results show that the improved scheme can not only improve the efficiency of digital signature calculation, but also prevent the forgery attack of digital signature by introducing two parameters and avoiding the inverse operation in the signature and verification phase.

Key words: elliptic curve digital signature, forgery attack, security, modular inverse operation

摘要：

经典的椭圆曲线数字签名（ECDSA）在签名和验证过程各使用了1次求逆运算，复杂费时的求逆运算制约着数字签名效率的提升。针对目前ECDSA的局限性，业界提出了很多改进方案，然而一些改进方案仅仅从ECDSA 计算效率的提高入手，但却未能将诸如伪造签名攻击的问题考虑在内。在对经典ECDSA方案分析的基础上，兼顾椭圆曲线数字签名的安全性和计算效率，提出了一种改进的椭圆曲线数字签名新方案，并通过理论分析和仿真实验证明了新方案的安全性和高效性。研究结果表明，改进的方案通过引入双参数以及在签名和验证阶段回避求[Zp*]逆运算，既提高了数字签名的计算效率又能防止数字签名伪造攻击。

关键词: 椭圆曲线数字签名, 伪造攻击, 安全性, 模逆运算