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)


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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