Cryptography Over Twisted Hessian Curves of the Ring ${F}_{q}[epsilon]$

Grini, Abdelâli; Chillali, Abdelhakim; Mouanis, Hakima

doi:10.37418/amsj.10.1.24

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2024

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“…An elliptic curve E a,b over F q is given by the Weierstrass equation Y 2 Z = X 3 + aXZ 2 + bZ 3 , where the coefficients a, b are in F q . It is well known that elliptic curves are a versatile cryptographic tool [2,4,6,19,20,21,22,25], and in particular, that their group structure plays a crucial role in such applications, see [13,14,18,23]. This work follows the series of works that study elliptic curves on finite rings.…”

Section: Introductionmentioning

confidence: 99%

Elliptic curves over a finite ring

Zakariae,

Abdelhakim,

Ali

2023

AUCMCS

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Let Fq be a finite field, where q is a power of a prime p such that p>5. Let \alpha be a root of a monic polynomial of a minimal degree over Fq. In this paper, we will study elliptic curves over (Fq[\alpha],+,*), where + is the usual addition and * represent a non-standard product law over Fq[\alpha]. Elliptic curves over this ring can be used to create a new type of cryptography. The method is fast, simple, and secure.

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