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The lattice sieve

  • J. M. Pollard
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1554)

Abstract

We describe a possible improvement to the Number Field Sieve. In theory we can reduce the time for the sieve stage by a factor comparable with log(B1). In the real world, where much factoring takes place, the advantage will be less. We used the method to repeat the factorisation of F7 on an 8-bit computer (yet again!).

Keywords

Algebraic Number Field Short Vector Computational Number Theory Number Field Sieve Primary 11Y05 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. K. Lenstra, H. W. Lenstra, Jr., M. S. Manasse, J. M. Pollard, The number field sieve, this volume, pp. 11–42; extended abstract: Proc. 22nd Annual ACM Symp. on Theory of Computing (STOC), Baltimore, May 14–16, 1990, 564–572.Google Scholar
  2. 2.
    A. K. Lenstra, H. W. Lenstra, Jr., M. S. Manasse, J. M. Pollard, The factorization of the ninth Fermat number, Math. Comp. 61 (1993), to appear.Google Scholar
  3. 3.
    J. M. Pollard, Factoring with cubic integers, unpublished manuscript, 1988; this volume, pp. 4–10.Google Scholar
  4. 4.
    C. Pomerance, Factoring, pp. 27–47 in: C. Pomerance (ed.), Cryptology and computational number theory, Proc. Sympos. Appl. Math. 42, Amer. Math. Soc., Providence, 1990.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • J. M. Pollard
    • 1
  1. 1.Tidmarsh CottageReadingEngland

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