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Identification Protocols and Signature Schemes Based on Supersingular Isogeny Problems

  • Steven D. GalbraithEmail author
  • Christophe Petit
  • Javier Silva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10624)

Abstract

We provide a new identification protocol and new signature schemes based on isogeny problems. Our identification protocol relies on the hardness of the endomorphism ring computation problem, arguably the hardest of all problems in this area, whereas the only previous scheme based on isogenies (due to De Feo, Jao and Plût) relied on potentially easier problems. The protocol makes novel use of an algorithm of Kohel-Lauter-Petit-Tignol for the quaternion version of the \(\ell \)-isogeny problem, for which we provide a more complete description and analysis. Our new signature schemes are derived from the identification protocols using the Fiat-Shamir (respectively, Unruh) transforms for classical (respectively, post-quantum) security. We study their efficiency, highlighting very small key sizes and reasonably efficient signing and verification algorithms.

Notes

Acknowledgement

We thank Dominique Unruh, David Pointcheval and Ali El Kaafarani for discussions related to this paper. Research from the second author was supported by a research grant from the UK government.

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Copyright information

© International Association for Cryptologic Research 2017

Authors and Affiliations

  • Steven D. Galbraith
    • 1
    Email author
  • Christophe Petit
    • 2
  • Javier Silva
    • 3
  1. 1.Mathematics DepartmentUniversity of AucklandAucklandNew Zealand
  2. 2.School of Computer ScienceUniversity of BirminghamBirminghamUK
  3. 3.Universitat Pompeu FabraBarcelonaSpain

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