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Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti

CiteScore 2017: 1.43

SCImago Journal Rank (SJR) 2017: 0.293
Source Normalized Impact per Paper (SNIP) 2017: 1.117

Mathematical Citation Quotient (MCQ) 2017: 0.51

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Volume 8, Issue 3


Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies

Luca De Feo / David Jao / Jérôme Plût
Published Online: 2014-06-11 | DOI: https://doi.org/10.1515/jmc-2012-0015


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.

Keywords: Elliptic curves; isogenies; quantum-resistant cryptosystems

MSC: 94A60; 14G50; 11Y16; 14K02

About the article

Received: 2012-06-29

Revised: 2014-05-14

Accepted: 2014-05-16

Published Online: 2014-06-11

Published in Print: 2014-09-01

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

Citation Information: Journal of Mathematical Cryptology, Volume 8, Issue 3, Pages 209–247, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc-2012-0015.

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