Implementation of the CSIDH Algorithm Model on Supersingular Twisted and Quadratic Edwards Curves

Bessalov, Anatoly and Sokolov, Volodymyr and Skladannyi, Pavlo and Mazur, Nataliia and Ageyev, Dmytro (2021) Implementation of the CSIDH Algorithm Model on Supersingular Twisted and Quadratic Edwards Curves Cybersecurity Providing in Information and Telecommunication Systems II 2021, 3187 (1). pp. 302-309. ISSN 1613-0073

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Abstract

The properties of twisted and quadratic supersingular Edwards curves forming pairs of quadratic torsion with the order p + 1 over the simple field Fp are considered. A modification of the CSIDH algorithm using the isogenies of these curves in replacement of the extended arithmetic’s of the isogenies of curves in the Montgomery form is presented. The isogeny parameters of the CSIDH algorithm model are calculated and tabulated on the basis of the theorems proved in the previous work. The example of Alice’s and Bob’s calculations according to the non-interactive Diffy-Hellman circuit, illustrating the separation of their secrets, is considered. The use of the known projective (W:Z)-coordinates for the given classes of curves provides the fastest execution of the CSIDH algorithm to-date.

Item Type: Article
Uncontrolled Keywords: Generalized Edwards form curve; complete Edwards curve; twisted Edwards curve; quadratic Edwards curve; curve order; point order; isomorphism, isogeny; w-coordinates; quadratic residue; quadratic non-residue
Subjects: Статті у наукометричних базах > Scopus
Divisions: Факультет інформаційних технологій та математики > Кафедра інформаційної та кібернетичної безпеки імені професора Володимира Бурячка
Depositing User: Павло Миколайович Складанний
Date Deposited: 30 Sep 2022 06:35
Last Modified: 18 Oct 2022 18:09
URI: https://elibrary.kubg.edu.ua/id/eprint/41867

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