A Load-Balanced Parallelization of AKS Algorithm

Abstract

The best known deterministic polynomial-time algorithm for primality testing right now is due to Agrawal, Kayal, and Saxena. This algorithm has a time complexity O (log^{ 15 / 2} ( n )) . Although this algorithm is polynomial, its reliance on the congruence of large polynomials results in enormous computational requirement. In this paper, we propose a parallelization technique for this algorithm based on message-passing parallelism together with four workload-distribution strategies. We perform a series of experiments on an implementation of this algorithm in a high-performance computing system consisting of 15 nodes, each with 4 CPU cores. The experiments indicate that our proposed parallelization technique introduce a significant speedup on existing implementations. Furthermore, the dynamic workload-distribution strategy performs better than the others. Overall, the experiments show that the parallelization obtains up to 36 times speedup.