Doubly-Focused enumeration of pseudosquares and pseudocubes

Authors:
Kjell Wooding;Hugh C. Williams
Affiliations:
Centre for Information Security and Cryptography, University of Calgary, Calgary, Alberta, Canada;Centre for Information Security and Cryptography, University of Calgary, Calgary, Alberta, Canada
Venue:
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Year:
2006

Citing 4
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ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory

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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.