Writing Fermat's parallelization paragraph.

.. and removing some useless shit here and there.

book/fermat.tex

@@ -90,13 +90,15 @@ some practical tets.
 
 \section{Thoughts about parallelization}
 
-During each single iteration, the computational complexity is dominated by the
-quare root's $\dsqrt$ function, which belongs to the class
-\bigO{lg^2 N}, as we saw in section ~\ref{sec:preq:sqrt}.
-
-Even if at first sight might seem plausible to split
-
-As we saw in Chapter ~\ref{chap:preq}, th
+At first glance we might be willing to split the entire interval
+$\{ \ceil{\sqrt{N}}, \ldots, N-1 \}$ in equal parts, one assigned to per each
+node. Hovever, this would not be any more efficient than the trial division
+algorithm, and nevertheless it is woth noting that during each single iteration,
+the computational complexity is dominated by the quare root $\dsqrt$ function,
+which belongs to the class \bigO{\log^2 N}, as we saw in section
+~\ref{sec:preq:sqrt}. Computing separatedly $x^2$ would add an overhead of the
+same order of magnitude \bigO{\log^2 N}, and thus result in a complete waste of
+resources.
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book/library.bib

@@ -113,7 +113,7 @@
 }
 
 
-@article{William:p+1,
+@article{Williams:p+1,
   title = {A $p + 1$ Method of Factoring},
   author = {Williams, H. C.},
   journal = {Mathematics of Computation},

book/math_prequisites.tex

@@ -30,7 +30,7 @@ $$
 With $f(n) = \bigO{g(n)}$ we actually mean
 $f(n) \in \bigO{g(n)}$.
 
-\section{Euclid's Greatest Common Divisor}
+\section{Euclid's Greatest Common Divisor \label{sec:preq:gcd}}
 
 Being the greatest common divisor a foundamental algebraic operation in the TLS
 protocol, \openssl implemented it with the following signature:

book/ssl_prequisites.tex

@@ -43,9 +43,7 @@ close of the connection
 
 \section{Remarks among SSL/TLS versions}
 
-cos'e
-differenze tra le varie versioni
-la certification autority
+
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book/wiener.tex

@@ -1,4 +1,4 @@
-\chapter{Wiener's Attack}
+\chapter{Wiener's Attack \label{chap:wiener}}
 
 Wiener's attack was first published in 1989 as a result of cryptanalysis on the
 use of short RSA secret keys ~\cite{wiener}. It exploited the fact that it is