环Z_n上广义圆锥曲线和公钥密码体系  

The generalized conic curves over Z_n and Public-Key cryptosystem

作　　者：孙琦[1] 朱文余[1] 王标[1] 

机构地区：[1]四川大学数学学院

出　　处：《四川大学学报（自然科学版）》2007年第2期213-220,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：现代通信国家重点实验室基金(51436010505SC010)

摘　　要：引入了环Zn上广义圆锥曲线Rn(a,b,c),并在Rn(a,b,c)上定义了加法运算,这里n=pq,p、q是不同的奇素数,证明了Zn上的广义圆锥曲线在加法运算下构成一个有限交换群.然后定义了环Zn上Ⅰ类Rn(a,b,c)和Ⅱ类Rn(a,b,c),指出环Zn上Ⅰ类Rn(a,b,c)等价于环Zn上的圆锥曲线Cn(a,b),可用于构造公钥密码体系,而Ⅱ类Rn(a,b,c)则不宜用来构造公钥密码体系.作为一个实例,给出了KMOV签名方案在Ⅰ类Rn(a,b,c)上的数字模拟.In this paper, the authors introduce a class of generalized conic curve（GCC） over the residue class ring Zn with an addition operation on the points of GCCs, where n is a product of two large distinct primes. They show that GCC under the defined addition forms a finite Abelian group（GCCG）. They define that the Type Ⅰ and Type Ⅱ of GCCs over the residue class ring Zn, and point out that Type Ⅰ is equivalent to （2. （a, b ） based on the conic curves over the ring Z., which can be used to construct various cryptosystems, but Type Ⅱ can not be in public key cryptosystem. As an example,GCCG analogues of KMOV digital signature scheme is proposed.

关 键 词：环Zn 广义圆锥曲线 公钥密码体系 数字签名方案 

分 类 号：O156.1[理学—数学]