Method to generate elliptic curves based on CM algorithm

摘要

The cryptosystem of elliptic curve had been put forward by Miller and Koblitz solely in 1985. The cryptosystem of elliptic curve owns three special advantages in terms of recent research: 1. It has larger flexibility when it chooses groups; 2. There wouldn't be any effective sub-index arithmetic to attack it if the cryptosystem of elliptic curve is suitably chosen; 3. It has a short key. In this paper, an efficient method to generate the elliptic curves which bases on the CM algorithm is presented .It may generate many elliptic curves which are suitable for building the cryptosystem. With the characteristic of high security and easy implementation, this kind of elliptic curves provides foundation for the construction of the cryptosystem over the elliptic curves, which can resist all kinds of attacks on itself. Meanwhile, in this paper the steps of the new algorithm are presented and its correctness and feasibility are proved and analyzed in theory. The advantages that the cryptosystem of elliptic curve owns are quite suitable for the encryption of the web communication, and it has become the research hotspot of web communication security field.