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A Montgomery-like Square Root for the Number Field Sieve (1998) [8 citations — 3 self]

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@INPROCEEDINGS{Nguyen98amontgomery-like,
    author = {Phong Nguyen and Ecole Normale Sup'erieure},
    title = {A Montgomery-like Square Root for the Number Field Sieve},
    booktitle = {In Proc. of ANTS-III, volume 1423 of LNCS},
    year = {1998},
    pages = {151--168},
    publisher = {Springer-Verlag}
}

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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. 1 Introduction The number field sieve [8] is the most powerful known factoring method...

Citations

540	A course in computational algebraic number theory – Cohen - 1995
416	Factoring polynomials with rational coefficients – Lenstra, Lenstra, et al. - 1982
215	Modern Heuristic Techniques for Combinatorial Problems – Reeves - 1993
157	Factoring integers with elliptic curves – LENSTRA - 1957
73	Computational Algebraic Number Theory – Pohst - 1994
53	The number field sieve – Lenstra, Lenstra, et al. - 1990
43	Factoring integers with the number field sieve – Buhler, Jr, et al. - 1993
42	The factorization of the ninth Fermat number – Lenstra, Lenstra, et al. - 1993
22	A world wide number field sieve factoring record: on to 512 bits – Cowie, Dodson, et al. - 1996
19	Algorithms in algebraic number theory – Lenstra - 1992
18	Square roots of products of algebraic numbers – Montgomery - 1993
12	An implementation of the number field sieve – Elkenbracht-Huizing - 1996
10	Approximating rings of integers in number fields – Buchmann, Lenstra - 1994
9	Computing a square root for the number field sieve – Couveignes - 1993
7	Factoring with cubic integers – Pollard - 1993
2	PARI-GP computer package. Can be obtained by ftp at megrez.math.u-bordeaux.fr – Batut, Bernardi, et al.
1	The development of the Number – Lenstra, Lenstra - 1993