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: The paper provides an in-depth tutorial of mathematical
construction of maximal length sequences (m-sequences) via primitive
polynomials and how to map the same when implemented in
shift registers. It is equally important to check whether a polynomial
is primitive or not so as to get proper m-sequences. A fast method to
identify primitive polynomials over binary fields is proposed where
the complexity is considerably less in comparison with the standard
procedures for the same purpose.