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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)
- 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
-
CC BY