一个改进的环上广义圆锥曲线上的数字签名方案

An Improved Digital Signature on Generalized Conic Curve over Z_n

针对环Zn上圆锥曲线上的Xiao数字签名方案中公布参数Nn,导致模数n被分解的缺陷,提出一个改进方案,主要通过修改签名算法实现参数Nn的保密,并改进了验证算法,同时,将其推广到环Zn上广义圆锥曲线上,以获得更多的密码曲线选择。分析表明,新方案除了保留明文嵌入、求逆元、阶的计算快速等优点外,增加了密码曲线的选择空间,其安全性真正实现同时基于离散对数问题和整数分解问题。

In order to overcome the flaw in the Xiao scheme on conic curve over Zn,of which the published parameter Nn could make the modulus n be factorized,an improved scheme was proposed.In the present scheme,the parameter Nn was kept secretly,and the verifying algorithm was presented.Moreover,generalized conic curve was chosen to replace conic curve.The security analysis showed that the improved scheme is easy to accomplish the convenient embedding plaintext,computing element order and points in the generalized co...