Prime pairing in algorithms searching for smooth group order

Pavel Atnashev; George Woltman

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: CC BY

BibTeX

@misc{cryptoeprint:2021/1462,
      author = {Pavel Atnashev and George Woltman},
      title = {Prime pairing in algorithms searching for smooth group order},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/1462},
      year = {2021},
      url = {https://eprint.iacr.org/2021/1462}
}