Patent ID: 8229113

Claim:
A computer-based method of establishing a session key for encryption of data between a pair of correspondents in a data communication system in which data is exchanged between the correspondents utilising public key cryptographic system, said method performed in a cryptographic unit having a hardware processor including: one of said correspondents selecting a finite group G, establishing a subgroup S, having an order q, of the group G, determining an element α of the subgroup S to generate greater than a predetermined number of the q elements of the subgroup S sufficiently large to render a brute force attack impractical, and said cryptographic unit utilising said hardware processor and said element α to generate a session key at said one correspondent, and said cryptographic unit utilising said session key in a cryptographic operation performed by said one correspondent, wherein said order of said subgroup is of the form nrr′, where n, r and r′ are each integers and r and r′ are each prime numbers, and said element α is a generator of a subgroup of an order of one of said primes r,r′.