\newcommand{\alert}[1]{\begin{color}{blue}\textit{#1}\end{color}}
+
+\newcommand{\PCH}[1]{\begin{color}{blue}#1\end{color}}
+
\title{Efficient and Cryptographically Secure Generation of Chaotic Pseudorandom Numbers on GPU}
\begin{document}
\section{Security Analysis}
\label{sec:security analysis}
-
+\PCH{This section is dedicated to the analysis of the security of the
+ proposed PRNGs from a theoretical point of view. The standard definition
+ of {\it indistinguishability} used is the classical one as defined for
+ instance in~\cite[chapter~3]{Goldreich}. It is important to emphasize that
+ this property shows that predicting the future results of the PRNG's
+ cannot be done in a reasonable time compared to the generation time. This
+ is a relative notion between breaking time and the sizes of the
+ keys/seeds. Of course, if small keys or seeds are chosen, the system can
+ be broken in practice. But it also means that if the keys/seeds are large
+ enough, the system is secured.}
In this section the concatenation of two strings $u$ and $v$ is classically
denoted by $uv$.
