基于环Z_n上圆锥曲线的ElGamal数字签名方案

ElGamal Digital Signature Based on the Conic Curves over Z_n

首先介绍了剩余类环Zn上圆锥曲线Cn(a,b)的基本性质,给出了基于环Zn上圆锥曲线的ElGamal数字签名方案及其数值模拟。该方案综合利用了大数分解的困难性和有限群上计算离散对数问题的困难性,从而增强了该数字签名方案的安全性。由于在Cn(a,b)上明文的嵌入,阶的运算以及点的运算都比较容易,且通过引进标准二进制计算群元素的整数倍的算法,使该方案具有运算速度快,更易于实现等优点。

Some basic properties of conic Cn （a,b）over the residue class ring Z. are presented. The EIGamal digital signature scheme on conic C. （a,b） over the residue class ring Z. is designed and its numeric simulation is done. Comprehensively using the difficulties in factorizing large integer and computing discrete logarithm, the security of this digital signature scheme is increased. For the facility of plaintext embedding and the computing of rank and point on conic C. （a,b）, this scheme has the advantages of speedy operation and easy realization,especially by using the NAF.