FFT extension for algebraic-group factorization algorithms (original) (raw)

Chapitre D'ouvrage Année : 2017

Résumé

It is well known that the second stage of factoring methods that exploit smoothness of group orders can be implemented efficiently using the fast Fourier transform (FFT). For Pollard's p−1 method [17] this originated with the Mont-gomery and Silverman paper [16], and for the elliptic curve factoring method [12] it was the subject of Peter Montgomery's PhD dissertation [14]. Along with Peter's most recent work on this subject [15], these developments are presented in this chapter.

DOI

Cite 10.1017/9781316271575.009 Autre Brent, R. P., Kruppa, A., & Zimmermann, P. (n.d.). FFT Extension for Algebraic-Group Factorization Algorithms. In Topics in Computational Number Theory Inspired by Peter L. Montgomery (pp. 189–205). Cambridge University Press. https://doi.org/10.1017/9781316271575.009

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Soumis le : jeudi 9 novembre 2017-12:01:42

Dernière modification le : mercredi 28 janvier 2026-10:52:04

Archivage à long terme le : samedi 10 février 2018-14:56:22

Dates et versions

hal-01630907 , version 1 (09-11-2017)

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Identifiants

Citer

Richard P. Brent, Alexander Kruppa, Paul Zimmermann. FFT extension for algebraic-group factorization algorithms. Joppe W. Bos; Arjen K. Lenstra. Topics in Computational Number Theory Inspired by Peter L. Montgomery, Cambridge University Press, pp.189-205, 2017, 978-1-107-10935-3. ⟨hal-01630907⟩

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