Improved of Elliptic Curves Cryptography over a Ring

Authors: A. Chillali, A. Tadmori, M. Ziane

Abstract:

In this article we will study the elliptic curve defined over the ring An and we define the mathematical operations of ECC, which provides a high security and advantage for wireless applications compared to other asymmetric key cryptosystem.

Keywords: Elliptic Curves, Finite Ring, Cryptography.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100472

References:

[1] A. Chillali, The j-invariant over E3dn, Int.j.Open problems Compt. Math.Vol.5, No 4,December 2012,ISSN 1998-6262, Copyright ICSRS Publication, (WWW.i-csrs.org,pp.106-111, 2012).
[2] A. Chillali, Cryptography over elliptic curve of the ring, World Academy of science Engineering and Technology, 78 (2011), pp.848-850
[3] A. Chillali, Elliptic curve over ring, International Mathematical Forum, Vol.6, no.31, 2011 pp.1501-1505
[4] A. Tadmori, A. Chillali and M. Ziane, Elliptic Curves over SPIR of characteristic Two, proceeding of the 2013 international conference on applied mathematics and Computational Methode, www.europment.org/library/2013/AMCM-05.
[5] A. Tadmori, A. Chillali and M. Ziane, Normal Form of the elliptic Curves over the finite ring, Journal of Mathematics and system Sience, 4 (2014) 194-196.
[6] A. Tadmori, A. Chillali and M. Ziane, Coding over elliptic curves in the ring of characteristic two, International journal of Applied Mathemathics and Informatics, (Volume 8. 2014).
[7] A. Tadmori, A. Chillali and M. Ziane, The binary operations calculus in Ea,b,c, International Journal of Mathematical Models and Methods in Applied Sciences, Volume 9, p:171-175,( 2015 ).
[8] W. Bosma and H. Lenstra, Complete system of two addition laws for elliptic curved, Journal of Number theory, (1995).