Quickly Generate Secure Elliptic Curve

It is generally believed that the discrete logarithm problem in a non-supersingular elliptic curve E/K is much more difficult than the discrete logarithm problem in a finite field of the same size as K. So the elliptic curve cryptosystems can provide equivalent security as the existing public key schemes, using much shorter secret keys. So ECC has the advantage of low resource requirement (such as smart card) and it is very fast.Fast generation of secure elliptic curves is precondition in the ECC's research and application. There are a number of ways to generate elliptic curve parameters. Select an appropriate finite field. Then select an elliptic curve over the field at random, count the number of points on the curve using Schoof's algorithm , check whether the number of points is nearly prime, and repeat until appropriate parameters are found. However existing implementations of Schoof's algorithm are less efficient.Select an appropriate field, then select an appropriate curve order, and generate a curve over the field with this number of points using techniques based on 'complex multiplication'. If the curve order is prime, the leakage of information is prevented. In the paper, a scheme of constructing elliptic curves over the prime field is analyzed. A method to implement the scheme is designed. A new paralleled scheme based on MPICH is implemented to improve the efficiency of the computation.