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The Special Number Field Sieve in \(\mathbb{F}_{p^{n}}\)

Application to Pairing-Friendly Constructions
  • Antoine Joux
  • Cécile Pierrot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8365)

Abstract

In this paper, we study the discrete logarithm problem in finite fields related to pairing-based curves. We start with a precise analysis of the state-of-the-art algorithms for computing discrete logarithms that are suitable for finite fields related to pairing-friendly constructions. To improve upon these algorithms, we extend the Special Number Field Sieve to compute discrete logarithms in \(\mathbb{F}_{p^{n}}\), where p has an adequate sparse representation. Our improved algorithm works for the whole range of applicability of the Number Field Sieve.

Keywords

Elliptic Curve Elliptic Curf Discrete Logarithm Problem Linear Polynomial High Security Level 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Antoine Joux
    • 1
    • 2
    • 4
    • 5
    • 6
  • Cécile Pierrot
    • 3
    • 4
    • 5
    • 6
  1. 1.CryptoExpertsFrance
  2. 2.Chaire de Cryptologie de la Fondation de l’UPMCParisFrance
  3. 3.Laboratoire PRISMUniversité de Versailles Saint-QuentinVersaillesFrance
  4. 4.UPMC, Univ Paris 06, LIP6France
  5. 5.PolSys ProjectINRIA, Paris-Rocquencourt CenterFrance
  6. 6.CNRS, UMR 7606, LIP6France

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