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The function field sieve

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Algorithmic Number Theory (ANTS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 877))

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Abstract

The fastest method known for factoring integers is the ‘number field sieve’. An analogous method over function fields is developed, the ‘function field sieve’, and applied to calculating discrete logarithms over GF(p n). An heuristic analysis shows that there exists a cε ℜ>0 such that the function field sieve computes discrete logarithms within random time: L p n[1/3, c] when log(p) ≤ n 9(n) where g is any function such that g: N → ℜ <.98>0 approaches zero as n → ∞.

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Authors and Affiliations

  1. Department of Computer Science, University of Southern California, 90089, Los Angeles, California

    Leonard M. Adleman

Authors
  1. Leonard M. Adleman
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Leonard M. Adleman Ming-Deh Huang

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© 1994 Springer-Verlag Berlin Heidelberg

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Adleman, L.M. (1994). The function field sieve. In: Adleman, L.M., Huang, MD. (eds) Algorithmic Number Theory. ANTS 1994. Lecture Notes in Computer Science, vol 877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58691-1_48

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  • DOI: https://doi.org/10.1007/3-540-58691-1_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58691-3

  • Online ISBN: 978-3-540-49044-9

  • eBook Packages: Springer Book Archive

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