Cryptology ePrint Archive: Report 2021/1462

Prime pairing in algorithms searching for smooth group order

Pavel Atnashev and George Woltman

Abstract: Factorization methods like Pāˆ’1, P+1, ECM have a stage which deals with primes of $a Ā± b$ form, where $a + b$ and $a āˆ’ b$ are processed by a single operation. Selecting $a$ and $b$ such that both $a + b$ and $a āˆ’ b$ 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.

Category / Keywords: factoring

Date: received 1 Nov 2021

Contact author: patnashev at gmail com

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Version: 20211106:154632 (All versions of this report)

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