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BY-NC-ND 3.0 license Open Access Published by De Gruyter June 11, 2014

Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies

  • Luca De Feo EMAIL logo , David Jao and Jérôme Plût

Abstract

We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases under the isogeny in order to allow the parties to construct a shared commutative square despite the non-commutativity of the endomorphism ring. We give a precise formulation of the necessary computational assumptions along with a discussion of their validity, and prove the security of our protocols under these assumptions. In addition, we present implementation results showing that our protocols are multiple orders of magnitude faster than previous isogeny-based cryptosystems over ordinary curves. This paper is an extended version of [Lecture Notes in Comput. Sci. 7071, Springer (2011), 19–34]. We add a new zero-knowledge identification scheme and detailed security proofs for the protocols. We also present a new, asymptotically faster, algorithm for key generation, a thorough study of its optimization, and new experimental data.

Funding source: NSERC CRD

Award Identifier / Grant number: CRDPJ 405857-10

Funding source: Agence Nationale de la Recherche, ECLIPSES project

Award Identifier / Grant number: Contract ANR-09-VERS-018

We would like to thank Gaëtan Bisson, Andrew M. Childs, Alfred Menezes, Vladimir Soukharev, and the anonymous reviewers for helpful comments and suggestions.

Received: 2012-6-29
Revised: 2014-5-14
Accepted: 2014-5-16
Published Online: 2014-6-11
Published in Print: 2014-9-1

© 2014 by De Gruyter

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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