The "Elliptic" matrices and a new kind of cryptography

Abstract

In [17], A. chillali et al introduce a new cryptographic method based on matrices over a finite field Fpn , where p is a prime number. In this paper, we will generate this method in a new group of square block matrices based on an elliptic curve, called "elliptic" matrices.

Elliptic curves over a finite ring

“…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.…”