Anzeige
Erschienen in:
29.09.2021 | Original Research
A new cryptosystem based on a twisted Hessian curve \(H^{4}_{a,d}\)
Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 4/2022
EinloggenAktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
In this paper, we are going to study the twisted Hessian curves on the local ring \(\mathbb {F}_{q}[\epsilon ]\), \(\epsilon ^{4}=0\), with \(\mathbb {F}_{q}\) is a finite field of order \(q=p^{b}\), where p is a prime number \( \ge 5\) and \(b\in \mathbb {N}^{*}\). In a first time, we study the arithmetic of the ring \(\mathbb {F}_{q}[\epsilon ]\), \(\epsilon ^{4}=0\), which will be used in the remainder of this work. After, we define the twisted Hessian curves \(H^{4}_{a,d}\) over this ring and we give essential properties and the classification of these elements. In addition, we define the group extension \(H^{4}_{a,d}\) of \(H_{a_{0},d_{0}}\) by \(Ker \ \tilde{\pi }\). We finish this work by introducing a new public key cryptosystem which is a variant of Cramer-Shoup public key cryptosystem on a twisted Hessian curves and study its security and efficiency. Our future work will focus on the generalist these studies for all integers \(n>4\), \(\epsilon ^{n}=0\), which is beneficial and interesting in cryptography.