Probabilistic Analysis on JPV Algorithm and Improving It using GCD Function

Abstract

JPV algorithm, proposed by Joye et al. was predicted to be faster than the combined prime generation algorithm but it runs slower in practice. This discrepancy is because only the number of Fermat test calls was compared in estimating its total running time. We present a probabilistic analysis on the total running time of JPV algorithm. This analysis is very accurate and corresponds to the experiment with only 1-2% error. Furthermore, we propose an improved JPV algorithm that uses GCD function. It is faster than JPV algorithm and similar to the combined algorithm with the same space requirement.