Improved of Elliptic Curves Cryptography over a Ring

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.





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).