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Doubly-Focused Enumeration of Pseudosquares and Pseudocubes

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Algorithmic Number Theory (ANTS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4076))

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Abstract

This paper offers numerical evidence for a conjecture that primality proving may be done in (logN)3 + o(1) operations by examining the growth rate of quantities known as pseudosquares and pseudocubes. In the process, a novel method of solving simultaneous congruences—doubly-focused enumeration— is examined. This technique, first described by D. J. Bernstein, allowed us to obtain record-setting sieve computations in software on general purpose computers.

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Author information

Authors and Affiliations

  1. Centre for Information Security and Cryptography, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, T2N 1N4, Canada

    Kjell Wooding & Hugh C. Williams

Authors
  1. Kjell Wooding
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  2. Hugh C. Williams
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Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Florian Hess

  2. Institut für Mathematik, MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Sebastian Pauli

  3. Institut für Mathematik, Technische Universität Berlin, Fakultät II, MA 8-1, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Michael Pohst

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© 2006 Springer-Verlag Berlin Heidelberg

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Wooding, K., Williams, H.C. (2006). Doubly-Focused Enumeration of Pseudosquares and Pseudocubes. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_16

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  • DOI: https://doi.org/10.1007/11792086_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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