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通过对一个剩余类环Zn上圆锥曲线Cn(a,b)数字签名方案(X iao 06方案)的安全性分析,发现该方案的公开参数选取和算法设计存在问题,导致利用韦达定理可以分解模数n,说明X iao06方案的安全性不是基于整数分解难题的.针对此缺陷,采取保密部分参数和修改验证算法的方法,提出了一个改进的环Zn上圆锥曲线的数字签名方案,并且给出了改进方案的数值模拟.分析表明,改进的方案是一个同时基于离散对数和整数分解双难题的环Zn上圆锥曲线的数字签名方案,不仅保留了原X iao 06方案的优点(明文嵌入方便,求逆元速度快,元素阶的计算及曲线上点的运算容易),还具有很强的抗破解能力.
By analyzing the security of Cn (a, b) digital signature scheme (X iao 06 scheme) for a conicoid of the remaining ring-like loops Zn, it is found that there is a problem with the selection of the public parameters and the algorithm design of this scheme, which leads to the use of the Veda theorem to decompose Modulo n, which shows that the security of X iao06 scheme is not based on the integer decomposition problem.Aiming at this defect, we adopt a method of secret partial parameters and modify the verification algorithm to propose an improved digital signature scheme of conic on ring Zn, The numerical simulation results show that the improved scheme is a digital signature scheme for ring Zn conic at the same time based on the double logarithms of discrete logarithms and integer decomposition, which not only retains the advantages of the original Xao06 scheme Convenient, fast seeking inverse element, the calculation of elemental levels and points on the curve easy to operate), but also has a strong anti-crack capability.