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Paper 2021/1462

Prime pairing in algorithms searching for smooth group order

Pavel Atnashev and George Woltman

Abstract

Factorization methods like P−1, P+1, ECM have a stage which deals with primes of $a ± b$ form, where $a + b$ and $a − b$ are processed by a single operation. Selecting $a$ and $b$ such that both $a + b$ and $a − b$ are prime is called `prime pairing` and can significantly improve performance of the stage. This paper introduces new methods of pairing, which in some cases find pairs for up to 99.9% of primes in a range. A practical algorithm and its implementations are presented.

Metadata
Available format(s)
PDF
Publication info
Preprint. MINOR revision.
Keywords
factoring
Contact author(s)
patnashev @ gmail com
History
2021-11-06: received
Short URL
https://ia.cr/2021/1462
License
Creative Commons Attribution
CC BY
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