The lattice sieve

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


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!).


Algebraic Number Field Short Vector Computational Number Theory Number Field Sieve Primary 11Y05 
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    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
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    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
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    J. M. Pollard, Factoring with cubic integers, unpublished manuscript, 1988; this volume, pp. 4–10.Google Scholar
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    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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