Patent ID: 8588409

Claim:
A method of establishing an order p of a finite field Z p , and an order n of a subgroup of a multiplicative group Z p * of said finite field Z p , the method being performed by a correspondent in a data communication system, the correspondent having a cryptographic unit for performing cryptographic operations, the method comprising the steps of: i) the cryptographic unit obtaining a value of n of the form n=hr+1 where h is an integer, r is a prime integer, r is greater than n 2/3 , and all factors of n−1 are significantly smaller or bigger than n 1/3 ; ii) the cryptographic unit obtaining an even integer t and computing tn+1to produce a computed value; iii) the cryptographic unit checking whether the computed value is prime; and iv) the cryptographic unit utilizing the computed value as the prime order p of the finite field if said computed value is prime, and the cryptographic unit utilizing the value n as the order n of the subgroup of the multiplicative group.