Research of the graphic model of the points of the elliptic curve in the Edward form

Abramov, Serhii and Sokolov, Volodymyr and Abramov, Vadym (2024) Research of the graphic model of the points of the elliptic curve in the Edward form Cybersecurity Providing in Information and Telecommunication Systems II 2024, 3826. pp. 174-181. ISSN 1613-0073

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Abstract

Elliptic curves in Edwards form, known for their speed and efficiency, are highly promising for asymmetric cryptosystems. The CSIDH protocol is particularly notable for post-quantum cryptography. Recent studies classify these curves and demonstrate CSIDH’s implementation on quadratic and twisted Edwards curves, highlighting their unique properties through graphical models like the wheel representation of point exponentiation. The model in the form of a graph of points of an elliptic curve in the form of Edwards was studied. The algorithm for the reconstruction of the series of points kP of all groups of points of the Edwards curve without the use of a group operation for 1/8 of the known points has been refined. The possibility of reconstructing the order of these points is also shown.

Item Type: Article
Uncontrolled Keywords: post-quantum cryptography; elliptic curve; point exponentiation; exponentiation graph; point reconstruction; reconstruction pattern
Subjects: Статті у базах даних > Scopus
Divisions: Факультет інформаційних технологій та математики > Кафедра інформаційної та кібернетичної безпеки ім. професора Володимира Бурячка
Depositing User: Павло Миколайович Складанний
Date Deposited: 06 Dec 2024 08:14
Last Modified: 06 Dec 2024 08:14
URI: https://elibrary.kubg.edu.ua/id/eprint/50154

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