Paper 2016/124

Collecting relations for the Number Field Sieve in $GF(p^6)$

Pierrick Gaudry, Laurent Grémy, and Marion Videau


In order to assess the security of cryptosystems based on the discrete logarithm problem in non-prime finite fields, as are the torus-based or pairing-based ones, we investigate thoroughly the case in $GF(p^6)$ with the Number Field Sieve. We provide new insights, improvements, and comparisons between different methods to select polynomials intended for a sieve in dimension 3 using a special-q strategy. We also take into account the Galois action to increase the relation productivity of the sieving phase. To validate our results, we ran several experiments and real computations for various selection methods and field sizes with our publicly available implementation of the sieve in dimension 3, with special-q and various enumeration strategies.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
Contact author(s)
laurent gremy @ inria fr
2016-05-30: last of 2 revisions
2016-02-14: received
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Creative Commons Attribution


      author = {Pierrick Gaudry and Laurent Grémy and Marion Videau},
      title = {Collecting relations for the Number Field Sieve in $GF(p^6)$},
      howpublished = {Cryptology ePrint Archive, Paper 2016/124},
      year = {2016},
      note = {\url{}},
      url = {}
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