Proving knowledge of isogenies: a survey

Ward Beullens; Luca De Feo; Steven D. Galbraith; Christophe Petit

doi:10.1007/s10623-023-01243-3

Proving knowledge of isogenies: a survey

Ward Beullens, Luca De Feo, Steven D. Galbraith^*, Christophe Petit

^*Corresponding author for this work

Computer Science

Research output: Contribution to journal › Article › peer-review

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Abstract

Isogeny-based cryptography is an active area of research in post-quantum public key cryptography. The problem of proving knowledge of an isogeny is a natural problem that has several applications in isogeny-based cryptography, such as allowing users to demonstrate that they are behaving honestly in a protocol. It is also related to isogeny-based digital signatures. Over the last few years, there have been a number of advances in this area, but there are still many open problems. This paper aims to give an overview of the topic and highlight some open problems and directions for future research.

Original language	English
Journal	Designs, Codes and Cryptography
Early online date	2 Jun 2023
DOIs	https://doi.org/10.1007/s10623-023-01243-3
Publication status	E-pub ahead of print - 2 Jun 2023

Bibliographical note

Funding Information:
Steven Galbraith is funded by NZ Government MBIE Catalyst Fund UOAX1933. Ward Beullens holds a Junior Post-Doctoral fellowship 1S95620N from the Research Foundation Flanders (FWO). Christophe Petit was supported by EPSRC award EP/V011324/1.

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

isogeny
post-quantum cryptography
zero-knowledge

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science Applications
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1007/s10623-023-01243-3

PetitC2023Proving
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10623-023-01243-3.
Accepted author manuscript, 515 KBLicence: Other (please specify with Rights Statement)

Post-Quantum Cryptography: a Cryptanalysis Approach
Petit, C. (Principal Investigator)
Engineering & Physical Science Research Council
1/10/21 → 30/09/26
Project: Research Councils

Cite this

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Proving knowledge of isogenies: a survey

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Projects

Post-Quantum Cryptography: a Cryptanalysis Approach

Cite this