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The lattice sieve

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(B 1). In the real world, where much factoring takes place, the advantage will be less. We used the method to repeat the factorisation of F 7 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. 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.

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  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.

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  3. J. M. Pollard, Factoring with cubic integers, unpublished manuscript, 1988; this volume, pp. 4–10.

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  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.

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© 1993 Springer-Verlag

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Pollard, J.M. (1993). The lattice sieve. In: Lenstra, A.K., Lenstra, H.W. (eds) The development of the number field sieve. Lecture Notes in Mathematics, vol 1554. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091538

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  • DOI: https://doi.org/10.1007/BFb0091538

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57013-4

  • Online ISBN: 978-3-540-47892-8

  • eBook Packages: Springer Book Archive