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Starfish on Strike

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Progress in Cryptology – LATINCRYPT 2010 (LATINCRYPT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6212))

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Abstract

This paper improves the price-performance ratio of ECM, the elliptic-curve method of integer factorization. In particular, this paper constructs “a = − 1” twisted Edwards curves having Q-torsion group Z/2×Z/4, Z/8, or Z/6 and having a known non-torsion point; demonstrates that, compared to the curves used in previous ECM implementations, some of the new curves are more effective at finding small primes despite being faster; and precomputes particularly effective curves for several specific sizes of primes.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, Chicago, IL, 60607–7045, USA

    Daniel J. Bernstein

  2. Laboratoire PRiSM, Université de Versailles Saint-Quentin-en-Yvelines, France

    Peter Birkner

  3. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600, MB, Eindhoven, Netherlands

    Tanja Lange

Authors
  1. Daniel J. Bernstein
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  2. Peter Birkner
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  3. Tanja Lange
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Editor information

Editors and Affiliations

  1. Computer Science Department, École Normale Supérieure, 45 Rue d’Ulm, 75230, Paris Cedex 05, France

    Michel Abdalla

  2. Computer Architecture and Networking Laboratory (LARC), Universidade de Sáo Paulo, Av. Prof. Luciano Gualberto, trav.3, n.158, 05508-900, Sáo Paulo (SP), Brazil

    Paulo S. L. M. Barreto

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Bernstein, D.J., Birkner, P., Lange, T. (2010). Starfish on Strike. In: Abdalla, M., Barreto, P.S.L.M. (eds) Progress in Cryptology – LATINCRYPT 2010. LATINCRYPT 2010. Lecture Notes in Computer Science, vol 6212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14712-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-14712-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14711-1

  • Online ISBN: 978-3-642-14712-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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