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Solving Discrete Logarithms on a 170-Bit MNT Curve by Pairing Reduction

  • Aurore GuillevicEmail author
  • François Morain
  • Emmanuel Thomé
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10532)

Abstract

Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances are built over finite fields of large characteristic and their security relies on the fact the embedding field of the underlying curve is relatively large. How large is debatable. The aim of our work is to sustain the claim that the combination of degree 3 embedding and too small finite fields obviously does not provide enough security. As a computational example, we solve the DLP on a 170-bit MNT curve, by exploiting the pairing embedding to a 508-bit, degree-3 extension of the base field.

Keywords

Discrete logarithm Finite field Number Field Sieve MNT elliptic curve 

Notes

Acknowledgements

The authors are grateful to Pierrick Gaudry for his help in running the computations.

Supplementary material

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Aurore Guillevic
    • 5
    • 6
    Email author
  • François Morain
    • 1
    • 4
  • Emmanuel Thomé
    • 1
    • 2
    • 3
  1. 1.Institut National de Recherche en Informatique et en Automatique (INRIA)Villers-lès-Nancy and SaclayFrance
  2. 2.Université de Lorraine, Loria, UMR 7503Vandoeuvre-lès-NancyFrance
  3. 3.CNRS, Loria, UMR 7503Vandoeuvre-lès-NancyFrance
  4. 4.École Polytechnique/LIX, CNRS UMR 7161PalaiseauFrance
  5. 5.University of CalgaryAlbertaCanada
  6. 6.Pacific Institute for the Mathematical Sciences, CNRS UMI 3069VancouverCanada

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