On the Function Field Sieve and the Impact of Higher Splitting Probabilities

Application to Discrete Logarithms in \(\mathbb{F}_{2^{1971}}\) and \(\mathbb{F}_{2^{3164}}\)
  • Faruk Göloğlu
  • Robert Granger
  • Gary McGuire
  • Jens Zumbrägel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8043)


In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as \(L_{q^n}(1/3,(4/9)^{1/3})\) for computing arbitrary logarithms, but also in an heuristic polynomial time algorithm for finding the discrete logarithms of degree one and two elements when the field has a subfield of an appropriate size. To illustrate the efficiency of the method, we have successfully solved the DLP in the finite fields with 21971 and 23164 elements, setting a record for binary fields.


Discrete logarithm problem function field sieve 


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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

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

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