Bucket Sieving

Kazumaro AOKI  Hiroki UEDA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.8   pp.1845-1850
Publication Date: 2009/08/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.1845
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: Theory
integer factoring,  sieving algorithm,  number field sieve,  largish prime,  bucket sort,  radix sort,  

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This paper proposes a new sieving algorithm that employs a bucket sort as a part of a factoring algorithm such as the number field sieve. The sieving step requires an enormous number of memory updates; however, these updates usually cause cache hit misses. The proposed algorithm significantly reduces the number of cache hit misses when the size of the sieving region is roughly less than the square of the cache size, and the memory updates are several times faster than the straightforward implementation according to the PC experiments.