Open AccessEl Gamal Cryptosystem on a Montgomery Curves Over Non Local Ring
Author(s) -
Moha ben taleb Elhamam,
Abdelâli Grini,
Abdelhakim Chillali,
Lhoussain El Fadil
Publication year - 2022
Publication title -
wseas transactions on mathematics
Language(s) - English
Resource type - Journals
eISSN - 2224-2880
pISSN - 1109-2769
DOI - 10.37394/23206.2022.21.13
Subject(s) - mathematics , ring (chemistry) , prime (order theory) , bijection , cryptosystem , finite field , elliptic curve , discrete mathematics , combinatorics , pure mathematics , cryptography , algorithm , chemistry , organic chemistry
Let Fq be the finite field of q elements, where q is a prime power. In this paper, we study the Montgomery curves over the ring Fq[X]/(X^2−X), denoted by MA,B(Fq[X]/(X^2−X) ); (A,B) ∈ (Fq[X]/(X^2−X))^2. Using the Montgomery equation, we define the Montgomery curves MA,B(Fq[X]/X^2−X) and we give a bijection between this curve and product of two Montgomery curves defined on Fq. Furthermore, we study the addition law of Montgomery curves over the ring Fq[X]/X^2−X. We close this paper by introducing a public key cryptosystem which is a variant of the ElGamal cryptosystem on a Montgomery curves over the same ring.