Tbilisi Mathematical Journal

ECC over the ring F₃^d[ε], ε⁴=0 by using two methods

B. Selikh, A. Chillali, D. Mihoubi, N. Ghadbane

Let F₃^d is the finite field of order 3^d with d be a positive integer, we consider A₄=F₃^d[ε]=F_3^d[X]/(X⁴) is a finite quotient ring, where ε⁴=0. In this paper, we will show an example of encryption and decryption. Firstly, we will present the elliptic curve over this ring. In addition, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. Precisely, we give a numerical example of cryptography (encryption and decryption) by using two methods with a secret key.


Tbilisi Mathematical Journal, Vol. 14(3) (2021), pp. 213-223

ECC over the ring F3d[ε], ε4=0 by using two methods

B. Selikh, A. Chillali, D. Mihoubi, N. Ghadbane

ECC over the ring F₃^d[ε], ε⁴=0 by using two methods