Cryptography, the science of encrypting and deciphering messages written in secret codes,
has played a vital role in securing information since ancient times. In classical cryptography …

Let Fq be a finite field of order q= pd where d is a positive integer and p≥ 5 is a prime
number. M. Virat see ([9]) has studied the elliptic curve Ea, b (Fp [ǫ]) defined over the local …

The Binary Operations Calculus in H2 Key Words: Finite field, Finite ring, Local ring, Twisted
Hessian curve. Contents 1 Introdu Page 1 Bol. Soc. Paran. Mat. (3s.) v. 2022 (40) : 1–6. c …

Fully homomorphic encryption scheme on a nonCommutative ring R Page 1 978-1-7281-4813-7/19/$31.00
©2019 IEEE Fully homomorphic encryption scheme on a nonCommutative ring R Mustapha …

In this paper, we are going to study the twisted Hessian curves on the local ring F _ q ϵ F q
ϵ, ϵ^ 4= 0 ϵ 4= 0, with F _ q F q is a finite field of order q= p^ bq= pb, where p is a prime …

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 …

In this work, we will present an example of encryption and decryption, by using the elliptic
curve defined over the ring A 2= F 2 d [ε], where d is a positive integer and ε 2= 0. The …

The goal of this work is to study some arithmetic proprieties of the twisted Hessian curves
defined by a equation of type: aX 3+ Y 3+ Z 3= dXYZ on the local ring R 2= 𝔽 q [X]/(X 2) …

The goal of this chapter is to study some arithmetic proprieties of an elliptic curve defined by
a Weierstrass equation on the local ring Rn X []/(Xn), where n≥ 1 is an integer. It consists of …

In this work, we came to present the elliptic curves over a nonlocal ring A= 2 d [X](X 2− X),
where 2 d is a finite field of characteristic 2, and d is a prime integer. We consider an elliptic …