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Abstract: The Number Field Sieve (NFS) is the asymptotically fastest known factoring algorithm for large integers. This article describes an implementation of the NFS, including the choice of two quadratic polynomials, both classical and lattice sieving, the block Lanczos method and a new square root algorithm. Finally some data on factorizations obtained with this implementation are listed, including the record factorization of 12 151 \Gamma 1. AMS Subject Classification (1991): 11Y05, 11Y40 Keywords ... (Update)
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.... were factored using the Quadratic Sieve (QS) For additional information, implementations and previous large NFS factorizations, see [15 17, 19, 32]. This paper reports on the factorization of RSA 155 by NFS and the implications for RSA. The number RSA 155 was taken from...
.... [21] For information about NFS, see [13] For additional information, implementations and previous large NFS factorizations, see [9, 10, 11, 12]. In this paper, we report on the factoring of RSA 140 by NFS and the implications for RSA. The number RSA 140 was taken from the...
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BibTeX entry: (Update)
M Elkenbracht-Huizing, "An Implementation of the Number Field Sieve", Experimental Mathematics 5(3) (1996) pp 375--389. http://citeseer.ist.psu.edu/huizing95implementation.html More
@techreport{ huizing95implementation,
author = "R. M. Huizing",
title = "An implementation of the number field sieve",
number = "NM-R9511",
year = "1995",
url = "citeseer.ist.psu.edu/huizing95implementation.html" }
Citations (may not include all citations):2003 The Art of Computer Programming (context) - Knuth - 1981
352 A Course in Computational Algebraic Number Theory (context) - Cohen - 1993
227 Factoring polynomials with rational coefficients (context) - Lenstra, Lenstra et al. - 1982
68 Prime Numbers and Computer Methods for Factorization (context) - Riesel - 1985
59 Algebraic Number Theory (context) - Lang - 1970
50 The number field sieve - Lenstra, Lenstra et al.
39 Data Structure Techniques (context) - Standish - 1980
39 The quadratic sieve factoring algorithm (context) - Pomerance - 1985
35 Factoring integers with the number field sieve (context) - Buhler, Lenstra et al.
29 The factorization of the ninth Fermat number (context) - Lenstra, Lenstra et al. - 1993
27 A block Lanczos algorithm for finding dependencies over GF (context) - Montgomery - 1995
23 Algebraische Zahlentheorie (context) - Neukirch - 1992
22 Solving linear equations over GF (context) - Coppersmith - 1993
19 volume 1554 of Lecture Notes in Mathematics (context) - Lenstra, Lenstra et al. - 1993
15 The lattice sieve (context) - Pollard
11 Factoring numbers using singular integers (context) - Adleman - 1991
8 Factoring with cubic integers (context) - Pollard
4 Factoring with elliptic curves (context) - Lenstra - 1987
4 Computing a square root for the number field sieve - Couveignes
2 Can be obtained by ftp at megrez (context) - Batut, Bernardi et al.
1 Technical report implementing the number field sieve (context) - Buhler, Montgomery et al.
1 Uber Beziehungen zwischen den Primidealen eines algebraische.. (context) - Frobenius - 1968
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Documents on the same site (http://www.uk.pgp.net/pgpnet/pgp-faq/faq-appendix2.html):
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