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Doubly-Focused Enumeration of Pseudosquares and Pseudocubes

  • Kjell Wooding
  • Hugh C. Williams
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4076)

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.

Keywords

Arithmetic Progression Residue Class Primality Test Chinese Remainder Theorem General Purpose Computer 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kjell Wooding
    • 1
  • Hugh C. Williams
    • 1
  1. 1.Centre for Information Security and CryptographyUniversity of CalgaryCalgary, AlbertaCanada

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