A practical “perfect” pseudo-random number generator

The “x2 mod N” generator, also known as the BBS generator [2], has a strong theoretical foundation from the computational complexity theory and the number theory. Proofs were given that, under certain reasonable assumptions on which modern cryptography heavily relies, the BBS pseudo-random sequences would pass any feasible statistical test. Unfortunately, the algorithm was found to be too slow for computer simulation applications. In this article, we present a practical implementation of the “x2 mod N” generator. We show a variant of the Montgomery modular multiplication algorithm [21] tailored to the typical computer environment used for computer simulations. We observed an adequate level of performance for the “x2 mod N” generator to be seriously considered whenever an otherwise “good” pseudo-random generator casts a doubt about the results of a sensitive simulation.