Properties of Isogeny Graph of Non-Cyclic Edwards Curves

Abramov, Serhii and Bessalov, Anatoly and Sokolov, Volodymyr (2023) Properties of Isogeny Graph of Non-Cyclic Edwards Curves Cybersecurity Providing in Information and Telecommunication Systems, 3550. pp. 234-239. ISSN 1613-0073

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Abstract

Some properties of isogenies of non-cyclic supersingular Edwards curves, which are used in the implementation of the CSIDH algorithm, are considered. This article continues the consideration of properties using the example of these classes of supersingular Edwards curves from previous work. All isogeny calculations are performed using one parameter of the curve equation d. Isogeny properties are modeled on an isogeny graph and are considered graph properties. Recommendations are given for selecting some cryptosystem parameters. It is shown which parameters d are prohibited for use in CSIDH algorithms and that the transition from one isogeny to another is not always possible.

Item Type: Article
Uncontrolled Keywords: Post-quantum cryptography; commutative supersingular isogeny Diffie-Hellman algorithm; curve in generalized Edwards form; non-cyclic Edwards curve; curve order; point order; graph of isogeny
Subjects: Це архівна тематика Київського університету імені Бориса Грінченка > Статті у наукометричних базах > Scopus
Divisions: Це архівні підрозділи Київського університету імені Бориса Грінченка > Факультет інформаційних технологій та математики > Кафедра інформаційної та кібернетичної безпеки імені професора Володимира Бурячка
Depositing User: Павло Миколайович Складанний
Date Deposited: 11 Dec 2023 12:25
Last Modified: 11 Dec 2023 12:25
URI: https://elibrary.kubg.edu.ua/id/eprint/47363

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