Identification protocols and signature schemes based on supersingular isogeny problems

Steven D. Galbraith, Christophe Petit, Javier Silva

Research output: Chapter in Book/Report/Conference proceedingConference contribution

44 Citations (Scopus)
347 Downloads (Pure)

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 Plut) relied on potentially easier problems. The protocol makesnovel use of an algorithm of Kohel-Lauter-Petit-Tignol for the quaternion version of the l -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.
Original languageEnglish
Title of host publicationAdvances in Cryptology – ASIACRYPT 2017
Subtitle of host publication23rd International Conference on the Theory and Applications of Cryptology and Information Security, Hong Kong, China, December 3-7, 2017, Proceedings, Part I
EditorsTsuyoshi Takagi, Thomas Peyrin
PublisherSpringer
Pages3-33
Number of pages30
ISBN (Electronic)9783319706948
ISBN (Print)9783319706931
DOIs
Publication statusPublished - 30 Nov 2017
Event23rd Annual International Conference on the Theory and Applications of Cryptology and Information Security (ASIACRYPT 2017) - Hong Kong
Duration: 3 Dec 20177 Dec 2017

Publication series

Name Lecture Notes in Computer Science (LNCS)
PublisherSpringer
Volume10624
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd Annual International Conference on the Theory and Applications of Cryptology and Information Security (ASIACRYPT 2017)
CityHong Kong
Period3/12/177/12/17

Bibliographical note

Winner of the Best Paper Award of ASIACRYPT 2017 conference.

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