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

Abramov, Serhii та Sokolov, Volodymyr та 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. с. 174-181. ISSN 1613-0073

Текст S_Abramov_V_Sokolov_V_Abramov_CPITS_2024_3826.pdf Download (3MB)

Анотація

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.

Тип елементу :	Стаття
Ключові слова:	post-quantum cryptography; elliptic curve; point exponentiation; exponentiation graph; point reconstruction; reconstruction pattern
Типологія:	Статті у базах даних > Scopus
Підрозділи:	Факультет інформаційних технологій та математики > Кафедра інформаційної та кібернетичної безпеки ім. професора Володимира Бурячка
Користувач, що депонує:	Павло Миколайович Складанний
Дата внесення:	06 Груд 2024 08:14
Останні зміни:	06 Груд 2024 08:14
URI:	https://elibrary.kubg.edu.ua/id/eprint/50154

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