A kilobit special number field sieve factorization

Kazumaro Aoki; Jens Franke; Thorsten Kleinjung; Arjen Lenstra; Dag Arne Osvik

Paper 2007/205

A kilobit special number field sieve factorization

Kazumaro Aoki, Jens Franke, Thorsten Kleinjung, Arjen Lenstra, and Dag Arne Osvik

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 $2^{1039} - 1$ . 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.

Metadata

Available format(s): PDF PS
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: factoring number field sieve block Wiedemann
Contact author(s): akl @ epfl ch
History: 2007-05-31: received
Short URL: https://ia.cr/2007/205
License: CC BY

BibTeX

@misc{cryptoeprint:2007/205,
      author = {Kazumaro Aoki and Jens Franke and Thorsten Kleinjung and Arjen Lenstra and Dag Arne Osvik},
      title = {A kilobit special number field sieve factorization},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/205},
      year = {2007},
      url = {https://eprint.iacr.org/2007/205}
}