关键词: 环Zn上圆锥曲线, 群签名, 电子现金, 标准二进制

Abstract: A group signature scheme was designed on conic curve Cn(a,b) over Zn. It can be applied in system of E-cash issuance. The scheme security is based on difficulties in factorizing large integer and computing discrete logarithm on Abel group (Cn(a,b),). By fetching NAF in calculating the multiples of an element in a group, 1/4 amount of computation was reduced. Compared with classical group signature, the conic analog over Zn has strongly improved the security of computing discrete logarithm. Compared with its counterparts based on elliptic curves over Zn, the conic analog is easier to accomplish, for they not only maintain the existing advantages but also advance with more advantages such as convenient plaintext embedding and speedy operation.

Key words: conic curve over Zn, group signature, E-cash, NAF