Paper 2013/197

Discrete logarithm in GF(2^809) with FFS

Razvan Barbulescu, Cyril Bouvier, Jérémie Detrey, Pierrick Gaudry, Hamza Jeljeli, Emmanuel Thomé, Marion Videau, and Paul Zimmermann


The year 2013 has seen several major complexity advances for the discrete logarithm problem in multiplicative groups of small characteristic finite fields. These outmatch, asymptotically, the Function Field Sieve (FFS) approach, which was so far the most efficient algorithm known for this task. Yet, on the practical side, it is not clear whether the new algorithms are uniformly better than FFS. This article presents the state of the art with regard to the FFS algorithm, and reports data from a record-sized discrete logarithm computation in a prime-degree extension field.

Note: Version expanded from preliminary announcement draft.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown status
discrete logarithm problemnumber field sievefunction field sieve
Contact author(s)
Emmanuel Thome @ gmail com
2013-11-05: last of 2 revisions
2013-04-09: received
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Creative Commons Attribution


      author = {Razvan Barbulescu and Cyril Bouvier and Jérémie Detrey and Pierrick Gaudry and Hamza Jeljeli and Emmanuel Thomé and Marion Videau and Paul Zimmermann},
      title = {Discrete logarithm in GF(2^809) with FFS},
      howpublished = {Cryptology ePrint Archive, Paper 2013/197},
      year = {2013},
      note = {\url{}},
      url = {}
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