NDLI: SMP Based Solver for Large Binary Systems

Content Provider	IEEE Xplore Digital Library
Author	Jain, N. Pande, B. Gupta, P.
Copyright Year	2009
Abstract	Solving a large sparse system of linear equations (SSLE)over the binary field is an important step in the general number field seive (GNFS) algorithm that is often used to factorize large integers used in the RSA algorithm. Block Lanczos method proposed by Montgomery is an efficient and reliable method for solving such systems. A number of implementations of Block Lanczos method on distributed systems have been proposed in past. This paper discusses the parallel Montgomery’s Block Lanczos method for solving binary system of equations on shared multiprocessors(SMP). A simple experiment shows that the speed of convergence of this algorithm is dependent on a wise choice of initial guess for kick-starting the algorithm. A somewhat dense choice of the initial guess is suggested rather than a random choice for faster convergence. Devoid of any communication overheads of a loosely coupled system, the improved method gives good performance on SMP systems which can provide an able alternative to the more popular distributed systems. Details of implementation of this algorithm on SMP and experimental results are also provided in the paper.
Starting Page	426
Ending Page	431
File Size	671516
Page Count	6
File Format	PDF
ISBN	9780769539140
DOI	10.1109/PDCAT.2009.70
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-12-08
Publisher Place	Japan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Equations Linear systems Convergence Iterative algorithms Distributed computing Protocols Cryptography Security Polynomials Nonlinear filters openmp parallel algorithm sparse linear systems binary fields Galois Field GF(2) SMP RSA GNFS integer factorization
Content Type	Text
Resource Type	Article

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