A kilobit special number field sieve factorization

Authors:
Kazumaro Aoki;Jens Franke;Thorsten Kleinjung;Arjen K. Lenstra;Dag Arne Osvik
Affiliations:
NTT, Musashino-shi, Tokyo, Japan;University of Bonn, Department of Mathematics, Bonn, Germany;University of Bonn, Department of Mathematics, Bonn, Germany;EPFL, IC LACAL, Lausanne, Switzerland and Alcatel-Lucent Bell Laboratories, Murray Hill, NJ;EPFL, IC LACAL, Lausanne, Switzerland
Venue:
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
Year:
2007

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Abstract

We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 21039 - 1. Although this factorization is orders of magnitude 'easier' than a factorization of a 1024-bit RSA modulus is believed to be, the methods we used to obtain our result shed new light on the feasibility of the latter computation.