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Mathematics of Computation

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An FFT extension to the $P-1$ factoring algorithm

Authors: Peter L. Montgomery and Robert D. Silverman
Journal: Math. Comp. 54 (1990), 839-854
MSC: Primary 11Y05
MathSciNet review: 1011444
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Abstract: J. M. Pollard, in 1974, presented the $P - 1$ 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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Keywords: Convolutions, FFT, residue number systems, smooth groups, factorization
Article copyright: © Copyright 1990 American Mathematical Society