A Kilobit Special Number Field Sieve Factorization

  • Kazumaro Aoki
  • Jens Franke
  • Thorsten Kleinjung
  • Arjen K. Lenstra
  • Dag Arne Osvik
Conference paper

DOI: 10.1007/978-3-540-76900-2_1

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4833)
Cite this paper as:
Aoki K., Franke J., Kleinjung T., Lenstra A.K., Osvik D.A. (2007) A Kilobit Special Number Field Sieve Factorization. In: Kurosawa K. (eds) Advances in Cryptology – ASIACRYPT 2007. ASIACRYPT 2007. Lecture Notes in Computer Science, vol 4833. Springer, Berlin, Heidelberg

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Kazumaro Aoki
    • 1
  • Jens Franke
    • 2
  • Thorsten Kleinjung
    • 2
  • Arjen K. Lenstra
    • 3
    • 4
  • Dag Arne Osvik
    • 3
  1. 1.NTT, 3-9-11 Midori-cho, Musashino-shi, Tokyo, 180-8585Japan
  2. 2.University of Bonn, Department of Mathematics, Beringstraße 1, D-53115 BonnGermany
  3. 3.EPFL IC LACAL, INJ 330, Station 14, 1015-LausanneSwitzerland
  4. 4.Alcatel-Lucent Bell Laboratories, Murray Hill, NJUSA

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