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A World Wide Number Field Sieve factoring record: On to 512 bits

James CowieContact Information, Bruce DodsonContact Information, R. Marije Elkenbracht-HuizingContact Information, Arjen K. LenstraContact Information, Peter L. MontgomeryContact Information and Jörg ZayerContact Information

(1)  Cooperating Systems Corporation, 12 Hollywood Drive, 02167 Chestnut Hill, MA, USA
(2)  Department of Mathematics, Lehigh University, 18015-3174 Bethlehem, PA, USA
(3)  Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
(4)  Citibank, N.A., 4 Sylvan Way, 07054 Parsippany, NJ, USA
(5)  780 Las Colindas Road, 94903-2346 San Rafael, CA, USA
(6)  Gartenstrasse 13, 66352 Dorf im Warndt, Germany
Abstract
We present data concerning the factorization of the 130-digit number RSA130 which we factored on April 10, 1996, using the Number Field Sieve factoring method. This factorization beats the 129-digit record that was set on April 2, 1994, by the Quadratic Sieve method. The amount of computer time spent on our new record factorization is only a fraction of what was spent on the previous record. We also discuss a World Wide Web interface to our sieving program that we have developed to facilitate contributing to the sieving stage of future large scale factoring efforts. These developments have a serious impact on the security of RSA public key cryptosystems with small moduli. We present a conservative extrapolation to estimate the difficulty of factoring 512-bit numbers.

Contact Information James Cowie
Email: cowie@mumonkan.cooperate.com

Contact Information Bruce Dodson
Email: bad0@lehigh.edu

Contact Information R. Marije Elkenbracht-Huizing
Email: marije@cwi.nl

Contact Information Arjen K. Lenstra
Email: arjen.lenstra@citicorp.com

Contact Information Peter L. Montgomery
Email: pmontgom@cwi.nl

Contact Information Jörg Zayer
Email: j.zayer@ids-scheer.de
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