Fin

diff --git a/mabase.bib b/mabase.bib
index de477419a55a48103059e038a5c74b2a952f6b89..41edde2ca723423c57c23395ded7c5e7389df0bb 100644 (file)
--- a/mabase.bib
+++ b/mabase.bib
@@ -14,6 +14,20 @@
   timestamp = {2009.06.29}
 }
 
   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},
 @inproceedings{bfg12a:ip,
 inhal = {no},
 domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO},

diff --git a/prng_gpu.tex b/prng_gpu.tex
index f985e035f107aadeff3efa6d9babd9d65576a2be..f7499d98f7ab03016283032fde07ffb32364b842 100644 (file)
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -1040,7 +1040,7 @@ not only sought in general to obtain chaos, but they are also required for rando
 \end{itemize}
 
 
 \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.
 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.

diff --git a/reponse.tex b/reponse.tex
index 97e39a2ff4a85410e07100ea15e522f1ea59a3ba..e8a1acf9e75f27480b8870ddb4e1e1650ba95097 100644 (file)
--- a/reponse.tex
+++ b/reponse.tex
@@ -95,7 +95,8 @@ A sentence has been added to clarify this point at the end of Section 5.4.
 
 
 \bigskip
 
 
 \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
 
 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


@@ -105,23 +106,23 @@ cryptographically secure, but whatever the size of the keys, a brute force attac
 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
 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.} 
 
 
 
 \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.}
 
 \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{Typos and other nitpicks:\\


@@ -135,4 +136,8 @@ These misspells have been corrected (sorry for that).
 \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. }
 
 \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}
 \end{document}