Solving a \(6120\)-bit DLP on a Desktop Computer

  • Faruk Göloğlu
  • Robert Granger
  • Gary McGuire
  • Jens Zumbrägel
Conference paper

DOI: 10.1007/978-3-662-43414-7_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8282)
Cite this paper as:
Göloğlu F., Granger R., McGuire G., Zumbrägel J. (2014) Solving a \(6120\)-bit DLP on a Desktop Computer. In: Lange T., Lauter K., Lisoněk P. (eds) Selected Areas in Cryptography -- SAC 2013. SAC 2013. Lecture Notes in Computer Science, vol 8282. Springer, Berlin, Heidelberg

Abstract

In this paper we show how some recent ideas regarding the discrete logarithm problem (DLP) in finite fields of small characteristic may be applied to compute logarithms in some very large fields extremely efficiently. By combining the polynomial time relation generation from the authors’ CRYPTO 2013 paper, an improved degree two elimination technique, and an analogue of Joux’s recent small-degree elimination method, we solved a DLP in the record-sized finite field of \(2^{6120}\) elements, using just a single core-month. Relative to the previous record set by Joux in the field of \(2^{4080}\) elements, this represents a \(50\,\%\) increase in the bitlength, using just \(5\,\%\) of the core-hours. We also show that for the fields considered, the parameters for Joux’s \(L_Q(1/4 + o(1))\) algorithm may be optimised to produce an \(L_Q(1/4)\) algorithm.

Keywords

Discrete logarithm problem Binary finite fields 

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Faruk Göloğlu
    • 1
  • Robert Granger
    • 1
  • Gary McGuire
    • 1
  • Jens Zumbrägel
    • 1
  1. 1.Complex and Adaptive Systems Laboratory, School of Mathematical SciencesUniversity College DublinDublinIreland

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