Prime generation with the Demytko–Miller–Trbovich algorithm

Abstract

Prime numbers satisying certain constraints are used in publickey cryptosystems. Consequently, some attention has been paid to algorithms which allow large, cryptographically useful, primes to be created. One algorithm, devised by Miller and Trbovich, was neglected until Nick Demytko of Telecom Research Laboratories published a theoretical examination of it in 1988. At Telecom's invitation the following practical analysis of the method was undertaken. An implementation of the algorithm was written, and nearly one million primes generated, and analysed. This paper gives details of the algorithm, implementation, experiments and results, and draws conclusions about the applicability of the algorithm.