Twisted Hessian curves over the ring 𝔽<i><SUB align="right">q</i>[<i>∈</i>], <i>∈</i><SUP align="right">2</SUP> = 0

Abstract

No AccessTwisted Hessian curves over the ring 𝔽q[∈], ∈2 = 0Abdelâli Grini, Abdelhakim Chillali, Lhoussain El Fadil and Hakima MouanisAbdelâli GriniDepartment of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, Morocco, Abdelhakim ChillaliDepartment of Mathematics, Physical and Computer Sciences, FP, LSI, Taza, S.M. Ben Abdellah University, Fez, Morocco, Lhoussain El FadilDepartment of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, Morocco and Hakima MouanisDepartment of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, MoroccoPublished Online:November 28, 2022pp 181-189https://doi.org/10.1504/IJCAET.2023.127795PDF ToolsAdd to FavouritesDownload CitationsTrack Citations Share this article on social mediaShareShare onFacebookTwitterLinkedInReddit AboutAbstractThe goal of this work is to study some arithmetic proprieties of the twisted Hessian curves defined by a equation of type: aX3 + Y3 + Z3 = dXYZ on the local ring R2 = 𝔽q[X]/(X2), where p ≥ 5 is a prime number, q = pd and d ∈ ℕ*, such that -3 is not a square in 𝔽q. This paper consists of an introduction, section, and a conclusion. In the introduction, we review some fundamental arithmetic proprieties of finite local rings R2, which will be used in the remainder of this article. The section is devoted to the study the above mentioned twisted Hessian curves on these finite local rings for restriction to some specific characteristic p ≥ 5. Using these studies, we give essential properties and we define the group H2a,d, these properties, the classification of these elements and a bijection between the sets H2a,d and Ha0,d0 × 𝔽q, where Ha0,d0 is the twisted Hessian curve over the finite field 𝔽q.Keywordstwisted Hessian curves, finite over ring, cryptography, elliptic curves, local ring Previous article Next article FiguresReferencesRelatedDetails Volume 18Issue 1-32023 ISSN: 1757-2657eISSN: 1757-2665 HistoryPublished onlineNovember 28, 2022 Copyright © 2023 Inderscience Enterprises Ltd.Keywordstwisted Hessian curvesfinite over ringcryptographyelliptic curveslocal ringAuthors and AffiliationsAbdelâli Grini1 Abdelhakim Chillali2 Lhoussain El Fadil3 Hakima Mouanis4 1. Department of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, Morocco2. Department of Mathematics, Physical and Computer Sciences, FP, LSI, Taza, S.M. Ben Abdellah University, Fez, Morocco3. Department of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, Morocco4. Department of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, MoroccoPDF download