Evaluation and comparison of two efficient probabilistic primality testing algorithms

Abstract

We analyse two recent probabilistic primality testing algorithms; the first one is derived from Miller [6] in a formulation given by Rabin [7], and the second one is from Solovay and Strassen [9]. Both decide whether or not an odd number n is prime in time O( m, log n M( n)) with an error probability less than α m , for some 0≤a< 1 2 . Our comparison shows that the first algorithm is always more efficient than the second, both in probabilistic and algorithmic terms.