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FactInt

Advanced Methods for Factoring Integers

1.6.2

18 February 2018

Stefan Kohl
Email: stefan@gap-system.org
Homepage: https://stefan-kohl.github.io/

Alexander Konovalov
Email: alexander.konovalov@st-andrews.ac.uk
Homepage: https://alexk.host.cs.st-andrews.ac.uk
Address:
School of Computer Science
University of St Andrews
Jack Cole Building, North Haugh,
St Andrews, Fife, KY16 9SX, Scotland

Abstract

This package for GAP 4 provides a general-purpose integer factorization routine, which makes use of a combination of factoring methods. In particular it contains implementations of the following algorithms:

• Pollard's p-1

• Williams' p+1

• Elliptic Curves Method (ECM)

• Continued Fraction Algorithm (CFRAC)

• Multiple Polynomial Quadratic Sieve (MPQS)

It also contains code by Frank Lübeck for making use of Richard P. Brent's tables of factors of integers of the form b^k ± 1. FactInt is completely written in the GAP language and contains / requires no external binaries. It needs GAPDoc 1.6 [LN17] or higher. FactInt must be installed in the pkg subdirectory of the GAP distribution.

Copyright

© 1999 - 2017 by Stefan Kohl.

FactInt is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.

FactInt is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

For a copy of the GNU General Public License, see the file GPL in the etc directory of the GAP distribution or see http://www.gnu.org/licenses/gpl.html.

Acknowledgements

I would like to thank Bettina Eick and Steve Linton for their support and many interesting discussions.

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