Special ideal ring A3 and cryptography

Abstract

In [1] and [2] we defined the elliptic curve over the ring F₃d[ε],ε² = 0. In this work we will give some properties of the elliptic curve over the special ideal ring of characteristic 3, A₃ = F₃d[ε],ε³ = 0, and an application in cryptography. Our future work will focus on the study of the general case of these rings, which seem to be beneficial and interesting in cryptography, specially the one based on the identity (IBE) [6]. [7], [8].