Custom static diffie-hellman groups

Abstract

Methods for choosing groups for a static Diffie-Hellman key agreement protocol to inhibit active attacks by an adversary are provided. In mod p groups, an even h is chosen of value approximately ( 9/16)(logn), values r and n are determined using sieving and primality testing on r and n, and a value t is found to compute p=tn+1 wherein p is prime. In elliptic curve groups defined over a binary filed, a random curve is chosen, the number of points on the curve is counted and this number is checked for value of 2n wherein n is prime and n−1 meets preferred criteria. In elliptic curve groups defined over a prime field of order q, a value n=hr+1 is computed, wherein n is prime and n−1 meets preferred criteria, and a complex multiplication method is applied on n to produce a value q and an elliptic curve E defined over q and having an order n.