ECC over the ring F_{s^d}[X]/(X^2) by using a password

Abstract

In this work, we will present an example of encryption and decryption, by using the elliptic curve defined over the ring A₂ = F_2^d[ε], where d is a positive integer and ε² = 0. The motivation for this work came from the observation that communications, industrial automation and many more. For majority of these applications, security is a vital issue. Cryptography plays an important role in providing data security. In a first time, we describe these curves defined over this ring. Then, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. In other we give an example of encrypted message with a secret key.