We consider the generation of prime order elliptic curves (ECs) over a prime field Fp using the Complex Multiplication (CM) method. A crucial step of this method is to compute the ...
Let g be an element of prime order p in an abelian group and Zp. We show that if g, g , and gd are given for a positive divisor d of p - 1, we can compute the secret in O(log p
We present an algorithm for generating elliptic curves of prime order over Optimal Extension Fields suitable for use in cryptography. The algorithm is based on the theory of Comple...