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\section{Polynomials on bits}\label{Sec:Polynomials}  In many algorithms, cryptographic applications,  as for example in Linear Feedback Shift Registers (LFSRs for short), cryptographers have to deal with polynomials whose coefficients are \emph{bits}.\\  In this section we will introduce these polynomials, together with the   operations on them. \\ polynomials.\\  Let us start with \emph{terms} and \emph{monomials}.\\ \emph{terms}.\\  A \emph{term} in the variable $x$ is a power of $x$, so it is i.e.  $x^a$ for some natural number $a\in \NN$. For example, $x^2$ or $x^{100}$, but also $x=x^1$ and $1=x^0$.  \\  A \emph{monomial} in the variable $x$ and coefficients in $\Fb$, roughly speaking, is "a term with a coefficient".  It is an expression of the form $bx^a$, where $b \in \Fb$