Abstract: In this paper, we will give a cryptographic application
over the integral closure O_Lof sextic extension L, namely L is an
extension of Q of degree 6 in the form Q(a,b), which is a rational
quadratic and monogenic extension over a pure monogenic cubic
subfield K generated by a who is a root of monic irreducible
polynomial of degree 2 andb is a root of irreducible polynomial of
degree 3.
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.