deletions | additions       diff --git a/section_Bytes_The_polynomials_in__.tex b/section_Bytes_The_polynomials_in__.tex  index 93059e3..d82b906 100644  --- a/section_Bytes_The_polynomials_in__.tex  +++ b/section_Bytes_The_polynomials_in__.tex 
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$$  A \,=\, \{ 0,1,x,x+1,\ldots,x^{n-1},x^{n-1}+1,\ldots,x^{n-1}+x^{n-2}+\cdots+x+1\} \,.  $$  We will denote $A=\FF_{2^n}$.\\  Also in this general setting, we can sum and multiply. The sum is obvious, the multiplication  may require some divisions by $g$ before we can arrive at a small-degree polynomial.  For cryptographic reasons we are especially interested in the case of $g=x^8 + x^4 + x^3 + x^2 + 1\in \Fb[x]$.   We define $\FF_{256}:=\{p \in \Fb[x] \vert \deg(p) <8\}$.  As explained above $\FF_{256}$ is the set of the remainders of divisions by $g$, i.e.  $\FF_{256}=\{0,1,,x,x+1,\ldots,x^5+x^4+x^3+x^2+x+1\}. $  Moreover the $\\  It is possible to prove that for each $n$, $\FF_{2^n}$ is a field, i.e. that for each $f\in \FF_{2^n}$, $f \neq 0$, there is an element $h \in \FF_{2^n}$ such that $hf=fh = 1$ in $\FF_{2^n}$. Such an element $h$ is called \emph{inverse} of $f$.  The  following fact holds \begin{Theorem}  The finite set $A$ $A=\FF_{2^n}$  is a field if and only if $p$ is an irreducible polynomial. \end{Theorem}  \begin{Example}