An FFT extension to the factoring algorithm

Authors:
Peter L. Montgomery and Robert D. Silverman

Journal:
Math. Comp. **54** (1990), 839-854

MSC:
Primary 11Y05

DOI:
https://doi.org/10.1090/S0025-5718-1990-1011444-3

MathSciNet review:
1011444

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Abstract | References | Similar Articles | Additional Information

Abstract: J. M. Pollard, in 1974, presented the integer factoring algorithm. His paper couched the algorithm in theoretical terms based upon use of Fast Fourier Transform techniques, but he was unable to say whether the method could be made practical. We discuss the mathematical basis of the algorithm and show how it can work in practice. The practical implementation depends, for its success, upon the use of Residue Number Systems. We also present an open problem as to how the method could be made to work for the Elliptic Curve factoring algorithm.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1990-1011444-3

Keywords:
Convolutions,
FFT,
residue number systems,
smooth groups,
factorization

Article copyright:
© Copyright 1990
American Mathematical Society