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Book Sections Year : 2017

FFT extension for algebraic-group factorization algorithms

Abstract

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.
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Dates and versions

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

Identifiers

  • HAL Id : hal-01630907 , version 1

Cite

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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