Public-key Cryptosystem Based on the Conic Curves over Z_n
Biao Wang, Zhu Wen-yu · Journal of Sichuan University · 2005
In order to get more efficient cryptosystem over curves , this paper discussed some basic properties of conic C_n(a,b) over the residue class ring Z_n , where n is the product of two primes . We proved that the rational points of C_n(a,b) form an abelian group, whose operation may be given in two ways: one by reduction map and another by a formula with respect to the coordinates. And we also provided a simple method to find a base point. As applications, we gave analogues of RSA and ElGamal cryptosystem over C_n(a,b). The two analogues are easy to implement and their securities are based on the difficulty of integer factorization and the discrete logarithm over C_n(a,b) respectively.