Chapter

Advances in Cryptology – ASIACRYPT 2007

Volume 4833 of the series Lecture Notes in Computer Science pp 1-12

A Kilobit Special Number Field Sieve Factorization

  • Kazumaro AokiAffiliated withNTT, 3-9-11 Midori-cho, Musashino-shi, Tokyo, 180-8585
  • , Jens FrankeAffiliated withUniversity of Bonn, Department of Mathematics, Beringstraße 1, D-53115 Bonn
  • , Thorsten KleinjungAffiliated withUniversity of Bonn, Department of Mathematics, Beringstraße 1, D-53115 Bonn
  • , Arjen K. LenstraAffiliated withEPFL IC LACAL, INJ 330, Station 14, 1015-LausanneAlcatel-Lucent Bell Laboratories, Murray Hill, NJ
  • , Dag Arne OsvikAffiliated withEPFL IC LACAL, INJ 330, Station 14, 1015-Lausanne

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.