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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Richard 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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