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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.