El Gamal Cryptosystem on a Montgomery Curves Over Non Local Ring-Reference-Cited by-同舟云学术

El Gamal Cryptosystem on a Montgomery Curves Over Non Local Ring

Published:2022-03-02 Issue: Volume:21 Page:85-89
ISSN:2224-2880
Container-title:WSEAS TRANSACTIONS ON MATHEMATICS
language:en
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Author:

Elhamam Moha Ben Taleb¹,Grini Abdelali¹,Chillali Abdelhakim²,El Fadil Lhoussain¹

Affiliation:

1. Sidi Mohamed Ben Abdellah University, Faculty of Science Dhar El Mahraz, Atlas, Fez, postcode 1796, Fez, Morocco, MOROCCO

2. Sidi Mohamed Ben Abdellah University, FP, LSI, Taza, Atlas, Fez, postcode 1796, Fez, Morocco, MOROCCO

Abstract

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.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Mathematics

Reference10 articles.

1. Ben Taleb, E.M., Chillali, A., El Fadil, L., Twisted Hessian curves over the Ring Fq[e], e 2 = e, Bol. Soc. Paran, (3s.) v.(40), doi:10.52699/bspm.15867, (2022).

2. Boulbot, A., Chillali, A., Mouhib, A., ”Elliptic Curves Over the Ring R”, Bol. Soc. Paran., Vol.38, No.3, 2020, 193-201.

3. ElGamal, T., A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms, In Proceedings of CRYPTO 84 on Advances in cryptology. Springer-Verlag New York, Inc, 1985, pp. 10-18.

4. Grini, A., Chillali, A., Mouanis, H., The Binary Operations Calculus in H 2 a,d . Bol. Soc. Paran, Vol.40, 2020, 1-6.

5. Grini, A., Chillali, A., Mouanis, H., Cryptography over twisted Hessian curves of the ring Fq[ε] , ε 2 = 0. Adv. Math.: Sci. J., vol.10 , no.1, 2021, 235-243.

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