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A World Wide Number Field Sieve factoring record: On to 512 bits
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A World Wide Number Field Sieve factoring record: On to 512 bits
James Cowie1 , Bruce Dodson2 , R. Marije Elkenbracht-Huizing3 , Arjen K. Lenstra4 , Peter L. Montgomery5 and Jörg Zayer6 
| (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.
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