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Abstract: . The Number Field Sieve is expected to be the fastest among the recent major factoring methods. Keywords: Factoring Method, Sieving Method, NFS, SNFS, GNFS, DLP Recent developments of computational number theory have been very much infuenced by cryptography. In particular, several methods have been introduced to factor a large natural number. In this note, a survey on the Number Field Sieve, or NFS, will be given as one of the most important of these methods. In x 1, we shall see that the NFS... (Update)
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BibTeX entry: (Update)
@misc{ nakamula-survey,
author = "Ken Nakamula",
title = "A Survey on the Number Field Sieve",
url = "citeseer.ist.psu.edu/312752.html" }
Citations (may not include all citations):134 Factoring integers with elliptic curves (context) - Lenstra - 1987
55 Theorems on factorization and primality testing (context) - Pollard - 1974
37 Analysis and comparison of some integer factoring algorithms (context) - Pomerance - 1982
35 The discrete logarithm problem (context) - McCurley - 1990
32 Factoring by electronic mail (context) - Lenstra, Manasse - 1990
32 A Monte-Carlo method for factorization (context) - Pollard - 1975
29 The factorization of the ninth Fermat number (context) - Lenstra, Lenstra et al. - 1993
25 Solving sparse linear equations over nite elds (context) - Wiedemann - 1986
24 A rigorous time bound for factoring integers (context) - Lenstra, Pomerance - 1992
24 a theory of factorization and genera (context) - Shanks, Number - 1971
22 The development of the number eld sieve (context) - Lenstra, Lenstra et al. - 1993
20 NFS with four large primes: an explosive experiment (context) - Dodson, Lenstra - 1995
16 method of factoring (context) - Williams - 1982
12 Factoring integers with large-prime variations of the quadra.. - Boender, Riele - 1996
12 A tale of two sieves (context) - Pomerance - 1996
11 Square Roots of Products of Algebraic Numbers (context) - Montgomery - 1994
7 Modications to the number eld sieve (context) - Coppersmith - 1993
6 A block Lanczos algorithm for nding dependencies over GF (context) - Montgomery - 1995
6 A world wide number eld sieve factoring record: on to 512 bi.. (context) - Cowie, Dodson et al. - 1996
3 An implementation of the number eld sieve (context) - Elkenbracht-Huizing - 1996
3 Computing discrete logarithms with the general number eld si.. - Weber - 1996
3 An implementation of the general number eld sieve (context) - Buchmann, Loho et al. - 1994
3 Old and new deterministic Factoring Algorithms - McKee, Pinch - 1996
2 information available by sending electronic mail to challeng.. (context) - Security, Inc et al. - 1991
2 A new world record for the special number eld sieve factorin.. (context) - Montgomery, Cavalla et al. - 1997
2 A multiple polynomial general number elds sieve (context) - Elkenbracht-Huizing - 1996
2 On factoring large numbers (context) - Lehmer, Powers - 1931
2 Quadratic elds and factorization (context) - Schoof - 1982
1 Number Theory List (context) - Miller
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