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Strategies in Filtering in the Number Field Sieve
 In preparation
, 2000
"... 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 nonzero elements) of the matrix critically affect the running time of Block ..."
Abstract

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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 nonzero 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 discusses several possible filter strategies and their use in the recent record factorizations of RSA140, R211 and RSA155. 2000 Mathematics Subject Classification: Primary 11Y05. Secondary 11A51. 1999 ACM Computing Classification System: F.2.1. Keywords and Phrases: Number Field Sieve, factoring, filtering, Structured Gaussian elimination, Block Lanczos, RSA. Note: Work carried out under project MAS2.2 "Computational number theory and data security". This report will appear in the proceed...