基于环Z_n上的圆锥曲线数字签名和多重数字签名

Digital Signature and Multiple Digital Signatures Based on the Conic Curve over Z_n

提出了一个基于环Zn上的圆锥曲线公钥密码体系的数字签名方案.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的困难性,从而增强了该数字签名方案的安全性.在此基础上,通过将多个圆锥曲线数字签名联合起来生成对消息的签名,设计实现了多人对同一文件的多重数字签名,最后给出了多重数字签名方案的数值模拟.由于整个签名运算在环Zn上的圆锥曲线上,使得明文嵌入方便,求逆元速度快,元素阶的计算及曲线上点的运算都比较容易,因此更易于实现.在引进标准二进制计算群元素的情况下,还能节约1/4计算量.

A digital signature scheme was designed on the public-key cryptography of conic curve over Zn. The scheme made comprehensively use of the difficulties in factorizing large integer and computing discrete logarithm, thereby increasing the performance of security. Furthermore the multiple digital signatures were designed by combining several digital signatures in conic curve o vet Zn, which can be used to realize that several people sign on a same file. Finally, the numeric simulation for the multiple digital signatures was done. The whole signature was operated in con ic curve over Zn, so the scheme is easier to accomplish for convenient plaintext embedding, speed up the inverse operation, and easy for computing element order and points in curves. Moreover, when the standard binary notation system was adopted to compute the integral multiple of an ele ment of a group, the time can be saved approximately by 1/4.