An improved complex multiplication algorithm

An efficient algorithm of generate elliptic curves for public key cryptosystems based on discrete logarithm is presented to resist possible attacks such as MOV reduction.The algorithm differs from the(existing) methods of building an elliptic curve with nearly prime order.An elliptic curve constructed by this method contains two large prime factors and satisfies conditions of security.This kind of elliptic curve can be used for various situations where composite order groups are needed.In the cryptosystems based on such elliptic curves,the leakage of information is prevented,and then the cryptosystems are also robust against attacks.Algorithm analysis has been done.Results show that it is much faster to generate a suitable(elliptic) curve with new-scheme than with original scheme.