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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Improved Primality Proving with Eisenstein Pseudocubes
verfasst von : Kjell Wooding, H. C. Williams
Erschienen in: Algorithmic Number Theory
Verlag: Springer Berlin Heidelberg
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In August 2002, Agrawal, Kayal, and Saxena described an unconditional, deterministic algorithm for proving the primality of an integer
N
. Though of immense theoretical interest, their technique, even incorporating the many improvements that have been proposed since its publication, remains somewhat slow for practical application. This paper describes a new, highly efficient method for certifying the primality of an integer
$N \equiv 1 \pmod 3$
, making use of quantities known as Eisenstein pseudocubes. This improves on previous attempts, including the peudosquare-based approach of Lukes
et al.
, and the pseudosquare improvement proposed by Berrizbeitia,
et al.