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

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.