Abstract
The Number Field Sieve (NFS) is the asymptotically fastest factoring algorithm known. It had spectacular successes in factoring numbers of a special form. Then the method was adapted for general numbers, and recently applied to the RSA-130 number [6], setting a new world record in factorization. The NFS has undergone several modifications since its appearance. One of these modifications concerns the last stage: the computation of the square root of a huge algebraic number given as a product of hundreds of thousands of small ones. This problem was not satisfactorily solved until the appearance of an algorithm by Peter Montgomery. Unfortunately, Montgomery only published a preliminary version of his algorithm [15], while a description of his own implementation can be found in [7]. In this paper, we present a variant of the algorithm, compare it with the original algorithm, and discuss its complexity.
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Nguyen, P. (1998). A Montgomery-like square root for the Number Field Sieve. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054859
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DOI: https://doi.org/10.1007/BFb0054859
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