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Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms

  • Antoine Joux
  • Reynald Lercier
  • David Naccache
  • Emmanuel Thomé
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5921)

Abstract

This paper extends Joux-Naccache-Thomé’s e-th root algorithm to the static Diffie-Hellman problem (sdhp).

The new algorithm can be adapted to diverse finite fields by customizing it with an nfs-like core or an ffs-like core.

In both cases, after a number of non-adaptive sdhp oracle queries, the attacker builds-up the ability to solve new sdhp instances unknown before the query phase.

While sub-exponential, the algorithm is still significantly faster than all currently known dlp and sdhp resolution methods.

We explore the applicability of the technique to various cryptosystems.The attacks were implemented in \({\mathbb F}_{2^{1025}}\) and also in \({\mathbb F}_{p}\), for a 516-bit p.

Keywords

dlp sdhp ffs nfs 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Antoine Joux
    • 1
  • Reynald Lercier
    • 2
  • David Naccache
    • 3
  • Emmanuel Thomé
    • 4
  1. 1.DGA and Université de Versailles, UVSQ PRISMVersailles CEDEXFrance
  2. 2.DGA/CELAR, La Roche Marguerite, F-35174 Bruz, France and, IRMAR, Université de Rennes 1RennesFrance
  3. 3.École normale supérieure, Équipe de cryptographieParis CEDEX 05France
  4. 4.LORIA, CACAO – bâtiment AINRIA LorraineVilliers-lès-Nancy CEDEXFrance

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