Improving the Polynomial time Precomputation of Frobenius Representation Discrete Logarithm Algorithms

Simplified Setting for Small Characteristic Finite Fields
  • Antoine Joux
  • Cécile Pierrot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8873)


In this paper, we revisit the recent small characteristic discrete logarithm algorithms. We show that a simplified description of the algorithm, together with some additional ideas, permits to obtain an improved complexity for the polynomial time precomputation that arises during the discrete logarithm computation. With our new improvements, this is reduced to O(q 6), where q is the cardinality of the basefield we are considering. This should be compared to the best currently documented complexity for this part, namely O(q 7). With our simplified setting, the complexity of the precomputation in the general case becomes similar to the complexity known for Kummer (or twisted Kummer) extensions.


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Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Antoine Joux
    • 1
    • 2
  • Cécile Pierrot
    • 2
    • 3
  1. 1.CryptoExperts, France and Chaire de Cryptologie de la Fondation de l’UPMCParisFrance
  2. 2.Laboratoire d’Informatique de Paris 6, UPMC Sorbonnes UniversitésParisFrance
  3. 3.CNRS and Direction Générale de l’ArmementFrance

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