timestamp = {2009.06.29}
}
+@book{guyeux12:bc,
+inhal = {no},
+domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO},
+equipe = {and},
+classement = {OS},
+author = {Guyeux, Christophe},
+title = {Le d\'esordre des it\'erations chaotiques - Applications aux r\'eseaux de capteurs, \`a la dissimulation d'information, et aux fonctions de hachage},
+abstract = {Les itérations chaotiques, un outil issu des mathématiques discrètes, sont pour la première fois étudiées pour obtenir de la divergence et du désordre. Après avoir utilisé les mathématiques discrètes pour en déduire des situations de non convergence, ces itérations sont modélisées sous la forme d'un système dynamique et sont étudiées topologiquement dans le cadre de la théorie mathématique du chaos. Nous prouvons que leur adjectif « chaotique » a été bien choisi : ces itérations sont du chaos aux sens de Devaney, Li-Yorke, l'expansivité, l'entropie topologique et l'exposant de Lyapunov, etc. Ces propriétés ayant été établies pour une topologie autre que la topologie de l'ordre, les conséquences de ce choix sont discutées. Nous montrons alors que ces itérations chaotiques peuvent être portées telles quelles sur ordinateur, sans perte de propriétés, et qu'il est possible de contourner le problème de la finitude des ordinateurs pour obtenir des programmes aux comportements prouvés chaotiques selon Devaney, etc. Cette manière de faire est respectée pour générer des algorithmes de tatouage numérique et des fonction de hachage chaotiques au sens le plus fort qui soit.},
+publisher = {\'Editions Universitaires Europ\'eennes},
+isbn = {978-3-8417-9417-8},
+year = 2012,
+note = {ISBN 978-3-8417-9417-8. 362 pages. Publication de la thèse de doctorat.},
+}
+
@inproceedings{bfg12a:ip,
inhal = {no},
domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO},
\end{itemize}
-We have proven in our previous works~\cite{} that chaotic iterations satisfying Theorem~\ref{Th:Caractérisation des IC chaotiques} are, among other
+We have proven in our previous works~\cite{guyeux12:bc} that chaotic iterations satisfying Theorem~\ref{Th:Caractérisation des IC chaotiques} are, among other
things, strongly transitive, topologically mixing, chaotic as defined by Li and Yorke,
and that they have a topological entropy and an exponent of Lyapunov both equal to $ln(\mathsf{N})$,
where $\mathsf{N}$ is the size of the iterated vector.
\bigskip
-\textit{The BBS-based generator of section 9 is anything but cryptographically secure.}
+\textit{The BBS-based generator of section 9 is anything but cryptographically secure. A 16-bit modulus (trivially factorable) gives out a period of at most $2^{16}$, which is neither useful nor secure. Its speed is irrelevant, as this generator as no practical applications whatsoever (a larger modulus, at least 1024-bit long, might be useful in some situations, but it will be a terrible GPU performer, of course).}
+
This claim is surprising, as this result is mathematically proven in the article:
either there is something wrong in the proof, or the generator is cryptographically
achieve to break it. It is only a question of time: with sufficiently large primes,
the time required to break it is astronomically large, making this attack completely
impracticable in practice. To sum up, being cryptographically secure is not a
-question of key size,
-
-
-
-\bigskip
-\textit{A 16-bit modulus (trivially factorable) gives out a period of at most $2^{16}$, which is neither useful nor secure. Its speed is irrelevant, as this generator as no practical applications whatsoever (a larger modulus, at least 1024-bit long, might be useful in some situations, but it will be a terrible GPU performer, of course).}
-
+question of key size.
+\begin{color}{green}
+PCH, tu peux broder là-dessus?
+\end{color}
\bigskip
\textit{To sum it up, while the theoretical part of the paper is interesting, the practical results leave much to be desired, and do not back the thesis that chaos improves some quality metric of the generators.}
+We hope now that, with the new sections added to the document, we have convinced the reviewers that to add chaotic properties in
+existing generators can be of interest.
+
\bigskip
\textit{On the theoretical side, you may be interested in Vladimir Anashin's work on ergodic theory on p-adic (specifically, 2-adic) numbers to prove uniform distribution and maximal period of generators. The $d_s(S, \check{S})$ distance loosely resembles the p-adic norm.}
-We have already established the uniform distribution in \cite{FCt}.
+Thank you for this information. However, we have already established the uniform distribution in \cite{bcgr11:ip} (recalled in Theorem 2).
\bigskip
\textit{Typos and other nitpicks:\\
\bigskip
\textit{ [1] Howes, L., and Thomas, D. "Efficient random number generation and application using CUDA." In GPU Gems 3, H. Nguyen, Ed. NVIDIA, 2007, Ch. 37. }
+
+\bibliographystyle{plain}
+\bibliography{mabase}
+
\end{document}
