Performance evaluation of long integer multiplication using OpenMP and MPI on shared memory architecture

Abstract

Multiplying long integers is an operation that has many applications in Computational Science and arbitrary arithmetic computation. Many cryptographic algorithms such as Diffe-Hellman key exchange [1], RSA, ECC and etc. require operations on very large subsets of the integer numbers. These algorithms use security key size of 1024 bits and more for secure message encryption, decryption and, key exchange. To perform encryption, decryption and key exchange we are required to perform a series of exponentiation and multiplication operations. In this paper, we propose the parallel multiplication algorithms for long integers on multiple core processors using parallel programming languages such as OpenMP and MPI. The OpenMP and MPI are most common parallel languages for programming and provide different performances characteristics. We also target to analyze and compare the OpenMP and MPI implementations on multi-core processors. The new proposed parallel algorithm achieves better performance than the basic serial implementations. The achieved speedup by OpenMP and MPI on serial implementation are 12.62x and 10.72x using school-book, 49.95x and 37.26x using Karatsuba on school-book, 66.11x and 31.47x using Toom-Cook on school-book. We have observed, as bit-length are increased the parallel algorithms exhibits better speedup performance on utilizing more cores available.