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Abstract: The Special Number Field Sieve factoring algorithm has a large number of parametric choices, each of which can affect its run time. We give guidelines for these choices along with a discussion of useful coding optimizations. We also give a theoretical argument which proves that the choice of sieving region that has been used so far in successful factorizations is not optimal and show how to obtain an improved sieve region. The improvement has yielded a 15% speed increase in practice. (Update)
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BibTeX entry: (Update)
@misc{ factoring, time, space, Number Field Sieve, NFS, SNFS, parameter selection,
author = "Robert D. Silverman",
title = "Optimal Parameterization of SNFS",
url = "citeseer.ist.psu.edu/silverman03optimal.html" }
Citations (may not include all citations):124 The Art of Computer Programming Vol (context) - Knuth - 1981
72 The Development of the Number Field Sieve (context) - Lenstra, Lenstra - 1993
43 Factoring with two large primes (context) - Lenstra, Manasse - 1990
30 factorisatio numerorum (context) - Canfield, Erdos et al. - 1983
25 up to High Powers (context) - Brillhart, Lehmer et al. - 1987
23 Asymptotic semi-smoothness probabilities - Bach, Peralta - 1996
21 Computational Aspects of Discrete Logarithms (context) - Lambert - 1996
15 The Lattice Sieve (context) - Pollard
11 Square roots of products of algebraic numbers (context) - Montgomery - 1993
9 Polynomial selection for the number field sieve integer fact.. - Murphy - 1999
3 Factoring integers with the Number Field Sieve (context) - Elkenbracht-Huizing - 1996
2 Advances in Cryptology-EUROCRYPT (context) - Cavallar, of et al. - 2000
2 Lectures on the Calculus of Variations (context) - Bolza - 1961
1 A block Lanczos algorithm for finding dependncies over GF (context) - Montgomery - 1995
1 The number field sieve on many computers (context) - Elkenbracht-Huizing, Montgomery et al. - 1996
1 Theory of random graphs (context) - Kovalenko - 1970
1 Factorizations of Cunningham numbers with bases 13 to 99: Mi.. - Brent, Montgomery et al. - 2000
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