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Improved Stage 2 to P ± 1 Factoring Algorithms

  • Peter L. Montgomery
  • Alexander Kruppa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5011)

Abstract

Some implementations of stage 2 of the P–1 method of factorization use convolutions. We describe a space-efficient implementation, allowing convolution lengths around 223 and stage 2 limit around 1016 while attempting to factor 230-digit numbers on modern PC’s. We describe arithmetic algorithms on reciprocal polynomials. We present adjustments for the P+1 algorithm. We list some new findings.

Keywords

Integer factorization convolution discrete Fourier transform number theoretic transform P–1 P+1 multipoint polynomial evaluation reciprocal polynomials 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Peter L. Montgomery
    • 1
  • Alexander Kruppa
    • 2
  1. 1.Microsoft Research, One Microsoft WayRedmondUSA
  2. 2.LORIA, Campus ScientifiqueVandœuvre-lès-Nancy CedexFrance

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