}
@INPROCEEDINGS{bcgr11:ip,
- author = {Bahi, Jacques and Couchot, Jean-fran\c{c}ois and Guyeux, Christophe
+ author = {Bahi, Jacques M. and Couchot, Jean-fran\c{c}ois and Guyeux, Christophe
and Richard, Adrien},
title = {On the Link Between Strongly Connected Iteration Graphs and Chaotic
Boolean Discrete-Time Dynamical Systems},
}
@ARTICLE{bg10:ij,
- author = {Bahi, Jacques and Guyeux, Christophe},
+ author = {Bahi, Jacques M. and Guyeux, Christophe},
title = {Hash Functions Using Chaotic Iterations},
journal = {Journal of Algorithms \& Computational Technology},
year = {2010},
}
@INPROCEEDINGS{guyeux10ter,
- author = {Bahi, Jacques and Guyeux, Christophe},
+ author = {Bahi, Jacques M. and Guyeux, Christophe},
title = {A new chaos-based watermarking algorithm},
booktitle = {SECRYPT'10, Int. conf. on security and cryptography},
year = {2010},
}
@INPROCEEDINGS{bgc11:ip,
- author = {Bahi, Jacques and Guyeux, Christophe and Cote, Nathalie},
+ author = {Bahi, Jacques M. and Guyeux, Christophe and Cote, Nathalie},
title = {Chaos of Protein Folding},
booktitle = {IJCNN 2011, Int. Joint Conf. on Neural Networks},
year = {2011},
}
@INPROCEEDINGS{guyeux10bis,
- author = {Bahi, Jacques and Guyeux, Christophe and Makhoul, Abdallah},
+ author = {Bahi, Jacques M. and Guyeux, Christophe and Makhoul, Abdallah},
title = {Efficient and Robust Secure Aggregation of Encrypted Data in Sensor
Networks},
booktitle = {SENSORCOMM'10, 4-th Int. Conf. on Sensor Technologies and Applications},
}
@INPROCEEDINGS{guyeuxVictoria,
- author = {Bahi, Jacques and Guyeux, Christophe and Makhoul, Abdallah},
+ author = {Bahi, Jacques M. and Guyeux, Christophe and Makhoul, Abdallah},
title = {Secure Data Aggregation in Wireless Sensor Networks. Homomorphism
versus Watermarking Approach},
booktitle = {ADHOCNETS 2010, 2nd Int. Conf. on Ad Hoc Networks},
}
@INPROCEEDINGS{bgs11:ip,
- author = {Bahi, Jacques and Guyeux, Christophe and Salomon, Michel},
+ author = {Bahi, Jacques M. and Guyeux, Christophe and Salomon, Michel},
title = {Building a Chaotic Proven Neural Network},
booktitle = {ICCANS 2011, IEEE Int. Conf. on Computer Applications and Network
Security},
}
@INPROCEEDINGS{bgw10:ip,
- author = {Bahi, Jacques and Guyeux, Christophe and Wang, Qianxue},
+ author = {Bahi, Jacques M. and Guyeux, Christophe and Wang, Qianxue},
title = {A Pseudo Random Numbers Generator Based on Chaotic Iterations. Application
to Watermarking},
booktitle = {WISM 2010, Int. Conf. on Web Information Systems and Mining},
}
@INPROCEEDINGS{bgw09:ip,
- author = {Bahi, Jacques and Guyeux, Christophe and Wang, Qianxue},
+ author = {Bahi, Jacques M. and Guyeux, Christophe and Wang, Qianxue},
title = {A novel pseudo-random generator based on discrete chaotic iterations},
booktitle = {INTERNET'09, 1-st Int. Conf. on Evolving Internet},
year = {2009},
}
@INPROCEEDINGS{bmg10:onp,
- author = {Bahi, Jacques and Makhoul, Abdallah and Guyeux, Christophe},
+ author = {Bahi, Jacques M. and Makhoul, Abdallah and Guyeux, Christophe},
title = {Efficient and Robust Secure Aggregation of Encrypted Data in Sensor
Networks for critical applications},
booktitle = {RESSACS, Journ\'ee th\'ematique PHC/ResCom sur RESeaux de capteurS
}
@INPROCEEDINGS{guyeuxBayonne,
- author = {Bahi, Jacques and Makhoul, Abdallah and Guyeux, Christophe},
+ author = {Bahi, Jacques M. and Makhoul, Abdallah and Guyeux, Christophe},
title = {Efficient and Robust Secure Aggregation of Encrypted Data in Sensor
Networks for critical applications},
booktitle = {RESSACS, Journ\'ee th\'ematique PHC/ResCom sur RESeaux de capteurS
}
@ARTICLE{bs10:ij,
- author = {Bahi, Jacques and Salomon, Michel},
+ author = {Bahi, Jacques M. and Salomon, Michel},
title = {A Decentralized Energy-based Diffusion Algorithm to Increase the
Lifetime of {MANETs}},
journal = {Computer Networks Journal},
timestamp = {2009.11.09}
}
+@ARTICLE{Simard07testu01:a,
+ author = {Richard Simard and Université De Montréal},
+ title = {TestU01: A C library for empirical testing of random number generators},
+ journal = {ACM Transactions on Mathematical Software},
+ year = {2007},
+ pages = {2007}
+}
+
@ARTICLE{DefiningChaos,
author = {M. Martelli and M. Dang and T. Seph},
title = {Defining chaos},
}
@INPROCEEDINGS{wbg10:ip,
- author = {Wang, Qianxue and Bahi, Jacques and Guyeux, Christophe and Fang,
+ author = {Wang, Qianxue and Bahi, Jacques M. and Guyeux, Christophe and Fang,
Xiaole},
title = {Randomness quality of {CI} chaotic generators. Application to Internet
security},
statistical perfection refers to the ability to pass the whole
{\it BigCrush} battery of tests, which is widely considered as the most
stringent statistical evaluation of a sequence claimed as random.
-This battery can be found into the well-known TestU01 package.
+This battery can be found into the well-known TestU01 package~\cite{LEcuyerS07}.
Chaos, for its part, refers to the well-established definition of a
chaotic dynamical system proposed by Devaney~\cite{Devaney}.
as a chaotic dynamical system. Such a post-treatment leads to a new category of
PRNGs. We have shown that proofs of Devaney's chaos can be established for this
family, and that the sequence obtained after this post-treatment can pass the
-NIST, DieHARD, and TestU01 batteries of tests, even if the inputted generators
+NIST~\cite{Nist10}, DieHARD~\cite{Marsaglia1996}, and TestU01~\cite{LEcuyerS07} batteries of tests, even if the inputted generators
cannot.
The proposition of this paper is to improve widely the speed of the formerly
proposed generator, without any lack of chaos or statistical properties.
\rightarrow \mathds{B}^\mathsf{N}$, we can preserve the theoretical properties on $G_f$
during implementations (due to the discrete nature of $f$). It is as if
$\mathds{B}^\mathsf{N}$ represents the memory of the computer whereas $\llbracket 1 ; \mathsf{N}
-\rrbracket^{\mathds{N}}$ is its input stream (the seeds, for instance).
+\rrbracket^{\mathds{N}}$ is its input stream (the seeds, for instance, in PRNG, or a physical noise in TRNG).
\section{Application to pseudorandomness}
\label{sec:pseudorandom}
+
\subsection{A First pseudorandom Number Generator}
We have proposed in~\cite{bgw09:ip} a new family of generators that receives
This generator is synthesized in Algorithm~\ref{CI Algorithm}.
-It takes as input: a function $f$;
+It takes as input: a Boolean function $f$ satisfying Theorem~\ref{Th:Caractérisation des IC chaotiques};
an integer $b$, ensuring that the number of executed iterations is at least $b$
and at most $2b+1$; and an initial configuration $x^0$.
It returns the new generated configuration $x$. Internally, it embeds two
if and only if $M$ is a double stochastic matrix.
\end{theorem}
-This former generator as successively passed various batteries of statistical tests, as the NIST tests~\cite{bcgr11:ip}.
+This former generator as successively passed various batteries of statistical tests, as the NIST~\cite{bcgr11:ip}, DieHARD~\cite{Marsaglia1996}, and TestU01~\cite{LEcuyerS07}.
\subsection{Improving the Speed of the Former Generator}
