Article
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Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves
Version 1
: Received: 22 June 2024 / Approved: 22 June 2024 / Online: 24 June 2024 (08:15:23 CEST)
How to cite: Bessalov, A.; Sokolov, V.; Abramov, S. Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves. Preprints 2024, 2024061600. https://doi.org/10.20944/preprints202406.1600.v1 Bessalov, A.; Sokolov, V.; Abramov, S. Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves. Preprints 2024, 2024061600. https://doi.org/10.20944/preprints202406.1600.v1
Abstract
The article presents the author’s works in the field of modifications and modeling of the PQC CSIDH algorithm on non-cyclic supersingular Edwards curves and its predecessor CRS scheme on ordinary non-cyclic Edwards curves are reviewed. Lower estimates of the computational speed gains of the modified algorithms over the original ones are obtained. The most significant results were obtained by choosing classes of non-cyclic Edwards curves connected as quadratic twist pairs instead of cyclic complete Edwards curves, as well as the method of algorithm randomization as an alternative to “constant time CSIDH.” It is shown that in the CSIDH and CSIKE algorithms, there are two independent cryptosystems with the possibility of parallel computation, eliminating the threat of side-channel attacks. For the CRS scheme, there are four such cryptosystems. Integral lower bound estimates of the performance gain of the modified CSIDH algorithm are obtained at 1.5 ∙ 29, and for the CRS scheme are 3 ∙ 29.
Keywords
post-quantum cryptography; isogeny-based cryptography; isogeny; supersingular Edwards curve; quadratic Edwards curve; twisted Edwards curve; complete Edwards curve; CSIDH; CSIKE; CRS
Subject
Computer Science and Mathematics, Other
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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