Fast algorithms for the generation of large primes for the RSA cryptosystem

Abstract

The generation of large primes is of particular importance in the context of public key cryptography. The Miller-Rabin test is currently one of the most efficient ways of determining whether a given odd integer is composite. Repeated use of this test allows one to certify an integer as 'probable' prime with an arbitrary small probability of error. Based on the observation that prime numbers tend to occur in clusters, or constellations, an algorithm is proposed for the efficient generation of large primes. It is readily implementable on an IBM-PC.<>