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Abstract: A critical step when factoring large integers by the Number Field Sieve [8] consists of finding dependencies in a huge sparse matrix over the field F2 , using a Block Lanczos algorithm. Both size and weight (the number of non-zero elements) of the matrix critically affect the running time of Block Lanczos. In order to keep size and weight small the relations coming out of the siever do not flow directly into the matrix, but are filtered first in order to reduce the matrix size. This paper... (Update)
Context of citations to this paper: More
.... by algorithmic improvements, mainly in the polynomial generation step [28, 31, 32] and to a lesser extent in the filter step of NFS [9]. The complete project to factor RSA 155 took seven calendar months. The polynomial generation step took about one month on several fast...
...of John Cannon at the University of Sydney, the Medicis Center at Ecole Polytechnique (Palaiseau, France) and Microsoft Research Ltd (Cambridge, UK) for the use of their computing resources. 2 The criterion used for this filter step will be described in a forthcoming report...
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The Three-Large-Primes Variant of the Number Field Sieve - Cavallar (Correct)
Factorization of a 512-bit RSA Modulus - Cavallar, Lioen, Riele, Dodson.. (2000) (Correct)
Factorization of RSA-140 Using the Number Field Sieve - Cavallar, Dodson.. (Correct)
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0.2: Some Parallel Algorithms for Integer Factorisation - Brent (1999) (Correct)
0.2: Recent Progress and Prospects for Integer Factorisation Algorithms - Brent (2000) (Correct)
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4: NFS with four large primes: an explosive experiment (context) - Dodson, Lenstra
3: The quadratic sieve factoring algorithm (context) - Pomerance - 1985
3: Improved Polynomial Selection for the Number Field Sieve (context) - Montgomery, Murphy - 1999
BibTeX entry: (Update)
S. Cavallar. Strategies for filtering in the Number Field Sieve. Preprint, to appear in the Proceedings of ANTS-IV (Algorithmic Number Theory Symposium IV, Leiden, The Netherlands, July 2--7, 2000), Lecture Notes in Computer Science, SpringerVerlag, Berlin, 2000. http://citeseer.ist.psu.edu/cavallar00strategies.html More
@inproceedings{ cavallar00strategies,
author = "Stefania Cavallar",
title = "Strategies in Filtering in the Number Field Sieve",
booktitle = "{ANTS}",
pages = "209-232",
year = "2000",
url = "citeseer.ist.psu.edu/cavallar00strategies.html" }
Citations (may not include all citations):105 volume 3 of The Art of Computer Programming (context) - Knuth, Searching - 1998
87 The Stanford GraphBase: A Platform for Combinatorial computi.. (context) - Knuth - 1993
59 Algebraic Number Theory (context) - Lang - 1986
35 Factoring integers with the number field sieve (context) - Buhler, Lenstra et al. - 1993
33 the history of the minimum spanning tree problem (context) - Graham, Hell - 1985
28 Solving large sparse linear systems over finite fields - LaMacchia, Odlyzko - 1991
27 A block Lanczos algorithm for finding dependencies over GF (context) - Montgomery - 1995
23 Algebraische Zahlentheorie (context) - Neukirch - 1992
15 The lattice sieve (context) - Pollard - 1993
14 Factorization of a 512-bit RSA modulus - Cavallar, Dodson et al. - 2000
7 sparse matrices over finite fields via created catastrophes (context) - Pomerance, Smith et al. - 1992
5 digit SNFS factorization (context) - Cavallar, Dodson et al. - 1999
5 A Montgomery-like square root for the number field sieve - Nguyen - 1998
3 Factoring Large Integers with the Quadratic Sieve (context) - Boender - 1997
1 An implementation of the number field sieve - Elkenbracht-Huizing - 1996
1 Solving large sparse systems of linear equations over finite.. (context) - Denny - 1995
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