A Parallel GNFS Algorithm Based on a Reliable Look-Ahead Block Lanczos Method for Integer Factorization

Abstract

The Rivest-Shamir-Adleman (RSA) algorithm is a very popular and secure public key cryptosystem, but its security relies on the difficulty of factoring large integers. The General Number Field Sieve (GNFS) algorithm is currently the best known method for factoring large integers over 110 digits. Our previous work on the parallel GNFS algorithm, which integrated the Montgomery's block Lanczos method to solve large and sparse linear systems over GF(2), is less reliable. In this paper, we have successfully implemented and integrated the parallel General Number Field Sieve (GNFS) algorithm with the new look-ahead block Lanczos method for solving large and sparse linear systems generated by the GNFS algorithm. This new look-ahead block Lanczos method is based on the look-ahead technique, which is more reliable, avoiding the break-down of the algorithm due to the domain of GF(2). The algorithm can find more dependencies than Montgomery's block Lanczos method with less iterations. The detailed experimental results on a SUN cluster will be presented in this paper as well