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Title:
Prime pairing in algorithms searching for smooth group order
Authors: Pavel Atnashev, 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.
ePrint: https://eprint.iacr.org/2021/1462
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