A Block Lanczos Algorithm for Finding Dependencies over GF(2)

  • Peter L. Montgomery
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 921)

Abstract

Some integer factorization algorithms require several vectors in the null space of a sparse m × n matrix over the field GF(2). We modify the Lanczos algorithm to produce a sequence of orthogonal subspaces of GF(2)n, each having dimension almost N, where N is the computer word size, by applying the given matrix and its transpose to N binary vectors at once. The resulting algorithm takes about n/(N − 0.76) iterations. It was applied to matrices larger than 106 × 106 during the factorizations of 105-digit and 119-digit numbers via the general number field sieve.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Peter L. Montgomery
    • 1
  1. 1.San RafaelUSA

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