Computing of Odd Degree Isogenies on Supersingular Twisted Edwards Curves

Bessalov, Anatoly and Sokolov, V. Y. and Skladannyi, Pavlo and Zhyltsov, Oleksii (2021) Computing of Odd Degree Isogenies on Supersingular Twisted Edwards Curves Cybersecurity Providing in Information and Telecommunication Systems, 2923. pp. 1-11. ISSN 1613-0073

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Abstract

An overview of the properties of three classes of curves in generalized Edwards form Ea,d with two parameters is given. The known formulas for the odd degree isogenies on curves Ed with one parameter are generalized to all classes of curves in Edwards form, and Theorem 1 on the isogenic mapping of the points of these curves is proved. The analysis of the known effective method for computing isogenies in Farashahi-Hosseini w-coordinates, justified for the curve Ed, is given. Theorem 2 proves the applicability of this method to the class of twisted Edwards curves. Examples of 3- and 5-isogenies of twisted Edwards curves are given. Methods for bypassing the exceptional points of such curves in PQC cryptosystems like CSIDH are proposed.

Item Type:	Article
Additional Information:	EID: 2-s2.0-85112376265
Uncontrolled Keywords:	Generalized Edwards form curve; complete Edwards curve; twisted Edwards curve; quadratic Edwards curve; curve order; points order; isomorphism; isogeny; w-coordinate; quadratic residue; quadratic nonresidue
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:	Volodymyr Sokolov
Date Deposited:	20 Aug 2021 11:54
Last Modified:	27 Aug 2021 06:21
URI:	https://elibrary.kubg.edu.ua/id/eprint/36994

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