Identification protocols and signature schemes based on supersingular isogeny problems

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• dc.contributor.author Galbraith, Steven D.
• dc.contributor.author Petit, Christophe
• dc.contributor.author Silva, Javier
• dc.date.accessioned 2020-11-02T08:51:34Z
• dc.date.available 2020-11-02T08:51:34Z
• dc.date.issued 2020
• dc.description.abstract We present signature schemes whose security relies on computational assumptions relating to isogeny graphs of supersingular elliptic curves. We give two schemes, both of them based on interactive identification protocols. The first identification protocol is due to De Feo, Jao and Plût. The second one, and the main contribution of the paper, makes novel use of an algorithm of Kohel, Lauter, Petit and Tignol for the quaternion version of the ℓ-isogeny problem, for which we provide a more complete description and analysis, and is based on a more standard and potentially stronger computational problem. Both identification protocols lead to signatures that are existentially unforgeable under chosen message attacks in the random oracle model using the well-known Fiat-Shamir transform, and in the quantum random oracle model using another transform due to Unruh. A version of the first signature scheme was independently published by Yoo, Azarderakhsh, Jalali, Jao and Soukharev. This is the full version of a paper published at ASIACRYPT 2017.en
• dc.description.sponsorship Research from the second author was supported by a research grant from the UK government. The third author was supported by a PhD formation grant from the Spanish government, co-financed by the ESF (Ayudas para contratos predoctorales para la formación de doctores 2016).
• dc.format.mimetype application/pdf
• dc.identifier.citation Galbraith SD, Petit C, Silva J. Identification protocols and signature schemes based on supersingular isogeny problems. Journal of Cryptology. 2020;33:130-75. DOI: 10.1007/s00145-019-09316-0
• dc.identifier.doi http://dx.doi.org/10.1007/s00145-019-09316-0
• dc.identifier.issn 0933-2790
• dc.identifier.uri http://hdl.handle.net/10230/45635
• dc.language.iso eng
• dc.publisher Springer
• dc.relation.ispartof Journal of Cryptology. 2020;33:130-75
• dc.rights This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Isogeniesen
• dc.subject.keyword Public key signaturesen
• dc.subject.keyword Post-quantum cryptographyen
• dc.title Identification protocols and signature schemes based on supersingular isogeny problemsen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion