-\begin{thebibliography}{10}
-\expandafter\ifx\csname url\endcsname\relax
- \def\url#1{\texttt{#1}}\fi
-\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi
-\expandafter\ifx\csname href\endcsname\relax
- \def\href#1#2{#2} \def\path#1{#1}\fi
-
-\bibitem{915396}
-T.~Stojanovski, J.~Pihl, L.~Kocarev, Chaos-based random number generators. part
- ii: practical realization, Circuits and Systems I: Fundamental Theory and
- Applications, IEEE Transactions on 48~(3) (2001) 382--385.
-
-\bibitem{915385}
-T.~Stojanovski, L.~Kocarev, Chaos-based random number generators-part i:
- analysis [cryptography], Circuits and Systems I: Fundamental Theory and
- Applications, IEEE Transactions on 48~(3) (2001) 281--288.
-
-\bibitem{5376454}
-L.~Cao, L.~Min, H.~Zang, A chaos-based pseudorandom number generator and
- performance analysis, in: Computational Intelligence and Security, 2009. CIS
- '09. International Conference on, Vol.~1, IEEE, 2009, pp. 494--498.
-
-\bibitem{Marsaglia1996}
-G.~Marsaglia, Diehard: a battery of tests of randomness,
- http://stat.fsu.edu/~geo/diehard.html.
-
-\bibitem{Nist10}
-E.~Barker, A.~Roginsky, Draft {N}{I}{S}{T} special publication 800-131
- recommendation for the transitioning of cryptographic algorithms and key
- sizes (2010).
-
-\bibitem{LEcuyerS07}
-P.~L'Ecuyer, R.~J. Simard, Test{U01}: {A} {C} library for empirical testing of
- random number generators, ACM Trans. Math. Softw 33~(4).
-
-\bibitem{Devaney}
-R.~L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd Edition,
- Addison-Wesley, Redwood City, CA, 1989.
-
-\bibitem{guyeuxTaiwan10}
-C.~Guyeux, Q.~Wang, J.~Bahi, Improving random number generators by chaotic
- iterations application in data hiding, in: Computer Application and System
- Modeling (ICCASM), 2010 International Conference on, Vol.~13, IEEE, 2010, pp.
- V13--643--V13--647.
-
-\bibitem{bcgr11:ip}
-J.~Bahi, J.-F. Couchot, C.~Guyeux, A.~Richard, On the link between strongly
- connected iteration graphs and chaotic boolean discrete-time dynamical
- systems, in: FCT'11, 18th Int. Symp. on Fundamentals of Computation Theory,
- Vol. 6914 of LNCS, Oslo, Norway, 2011, pp. 126--137.
-
-\bibitem{wbg10ip}
-Q.~Wang, J.~Bahi, C.~Guyeux, X.~Fang, Randomness quality of {CI} chaotic
- generators. application to internet security, in: INTERNET'2010. The 2nd Int.
- Conf. on Evolving Internet, IEEE Computer Society Press, Valencia, Spain,
- 2010, pp. 125--130, best Paper award.
-
-\bibitem{DBLP:conf/secrypt/CouchotHGWB14}
-J.~Couchot, P.~H{\'{e}}am, C.~Guyeux, Q.~Wang, J.~M. Bahi, Pseudorandom number
- generators with balanced gray codes, in: M.~S. Obaidat, A.~Holzinger,
- P.~Samarati (Eds.), {SECRYPT} 2014 - Proceedings of the 11th International
- Conference on Security and Cryptography, Vienna, Austria, 28-30 August, 2014,
- SciTePress, 2014, pp. 469--475.
-
-\bibitem{Banks92}
-J.~Banks, J.~Brooks, G.~Cairns, P.~Stacey, On {D}evaney's definition of chaos,
- Amer. Math. Monthly 99 (1992) 332--334.
-
-\bibitem{wbg10:ip}
-Q.~Wang, J.~Bahi, C.~Guyeux, X.~Fang, Randomness quality of {CI} chaotic
- generators. application to internet security, in: INTERNET'2010. The 2nd Int.
- Conf. on Evolving Internet, IEEE Computer Society Press, Valencia, Spain,
- 2010, pp. 125--130, best Paper award.
-
-\bibitem{bfgw11:ip}
-J.~Bahi, X.~Fang, C.~Guyeux, Q.~Wang, On the design of a family of {CI}
- pseudo-random number generators, in: WICOM'11, 7th Int. IEEE Conf. on
- Wireless Communications, Networking and Mobile Computing, Wuhan, China, 2011,
- pp. 1--4.
-
-\bibitem{Robinson:1981:CS}
-J.~P. Robinson, M.~Cohn,
- \href{http://dl.acm.org/citation.cfm?id=1963620.1963622}{Counting sequences},
- IEEE Trans. Comput. 30~(1) (1981) 17--23.
-\newline\urlprefix\url{http://dl.acm.org/citation.cfm?id=1963620.1963622}
-
-\bibitem{DBLP:journals/combinatorics/BhatS96}
-G.~S. Bhat, C.~D. Savage,
- \href{http://www.combinatorics.org/Volume_3/Abstracts/v3i1r25.html}{Balanced
- gray codes}, Electr. J. Comb. 3~(1).
-\newline\urlprefix\url{http://www.combinatorics.org/Volume_3/Abstracts/v3i1r25.html}
-
-\bibitem{ZanSup04}
-I.~Suparta, A.~v. Zanten, Totally balanced and exponentially balanced gray
- codes, Discrete Analysis and Operation Research (Russia) 11~(4) (2004)
- 81--98.
-
-\bibitem{Bykov2016}
-I.~S. Bykov, On locally balanced gray codes, Journal of Applied and Industrial
- Mathematics 10~(1) (2016) 78--85.
-
-\bibitem{LevinPeresWilmer2006}
-D.~A. Levin, Y.~Peres, E.~L. Wilmer,
- \href{http://scholar.google.com/scholar.bib?q=info:3wf9IU94tyMJ:scholar.google.com/&output=citation&hl=en&as_sdt=2000&ct=citation&cd=0}{{Markov
- chains and mixing times}}, American Mathematical Society, 2006.
-\newline\urlprefix\url{http://scholar.google.com/scholar.bib?q=info:3wf9IU94tyMJ:scholar.google.com/&output=citation&hl=en&as_sdt=2000&ct=citation&cd=0}
-
-\bibitem{proba}
-M.~Mitzenmacher, E.~Upfal, Probability and Computing, Cambridge University
- Press, 2005.
-
-\bibitem{matsumoto1998mersenne}
-M.~Matsumoto, T.~Nishimura, Mersenne twister: a 623-dimensionally
- equidistributed uniform pseudo-random number generator, ACM Transactions on
- Modeling and Computer Simulation (TOMACS) 8~(1) (1998) 3--30.
+\begin{thebibliography}{21}
+\newcommand{\enquote}[1]{``#1''}
+\providecommand{\natexlab}[1]{#1}
+\providecommand{\url}[1]{\texttt{#1}}
+\providecommand{\urlprefix}{URL }
+\expandafter\ifx\csname urlstyle\endcsname\relax
+ \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else
+ \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup
+ \urlstyle{rm}\Url}\fi
+
+\bibitem[{Bahi \emph{et~al.}(2011{\natexlab{a}})Bahi, Couchot, Guyeux \&
+ Richard}]{bcgr11:ip}
+Bahi, J., Couchot, J.-F., Guyeux, C. \& Richard, A. [2011{\natexlab{a}}]
+ \enquote{On the link between strongly connected iteration graphs and chaotic
+ boolean discrete-time dynamical systems,} \emph{FCT'11, 18th Int. Symp. on
+ Fundamentals of Computation Theory} (Oslo, Norway), pp. 126--137.
+
+\bibitem[{Bahi \emph{et~al.}(2011{\natexlab{b}})Bahi, Fang, Guyeux \&
+ Wang}]{bfgw11:ip}
+Bahi, J., Fang, X., Guyeux, C. \& Wang, Q. [2011{\natexlab{b}}] \enquote{On the
+ design of a family of {CI} pseudo-random number generators,} \emph{WICOM'11,
+ 7th Int. IEEE Conf. on Wireless Communications, Networking and Mobile
+ Computing} (Wuhan, China), pp. 1--4.
+
+\bibitem[{Banks \emph{et~al.}(1992)Banks, Brooks, Cairns \& Stacey}]{Banks92}
+Banks, J., Brooks, J., Cairns, G. \& Stacey, P. [1992] \enquote{On {D}evaney's
+ definition of chaos,} \emph{Amer. Math. Monthly} \textbf{99}, 332--334.
+
+\bibitem[{Barker \& Roginsky(2010)}]{Nist10}
+Barker, E. \& Roginsky, A. [2010] \enquote{Draft {N}{I}{S}{T} special
+ publication 800-131 recommendation for the transitioning of cryptographic
+ algorithms and key sizes,} .
+
+\bibitem[{Bhat \& Savage(1996)}]{DBLP:journals/combinatorics/BhatS96}
+Bhat, G.~S. \& Savage, C.~D. [1996] \enquote{Balanced gray codes,}
+ \emph{Electr. J. Comb.} \textbf{3},
+ \urlprefix\url{http://www.combinatorics.org/Volume_3/Abstracts/v3i1r25.html}.
+
+\bibitem[{Bykov(2016)}]{Bykov2016}
+Bykov, I.~S. [2016] \enquote{On locally balanced gray codes,} \emph{Journal of
+ Applied and Industrial Mathematics} \textbf{10}, 78--85.
+
+\bibitem[{Cao \emph{et~al.}(2009)Cao, Min \& Zang}]{5376454}
+Cao, L., Min, L. \& Zang, H. [2009] \enquote{A chaos-based pseudorandom number
+ generator and performance analysis,} \emph{Computational Intelligence and
+ Security, 2009. CIS '09. International Conference on} (IEEE), pp. 494--498.
+
+\bibitem[{Couchot \emph{et~al.}(2014)Couchot, H{\'{e}}am, Guyeux, Wang \&
+ Bahi}]{DBLP:conf/secrypt/CouchotHGWB14}
+Couchot, J., H{\'{e}}am, P., Guyeux, C., Wang, Q. \& Bahi, J.~M. [2014]
+ \enquote{Pseudorandom number generators with balanced gray codes,}
+ \emph{{SECRYPT} 2014 - Proceedings of the 11th International Conference on
+ Security and Cryptography, Vienna, Austria, 28-30 August, 2014}, eds.
+ Obaidat, M.~S., Holzinger, A. \& Samarati, P. (SciTePress), ISBN
+ 978-989-758-045-1, pp. 469--475.
+
+\bibitem[{Devaney(1989)}]{Devaney}
+Devaney, R.~L. [1989] \emph{An Introduction to Chaotic Dynamical Systems}, 2nd
+ ed. (Addison-Wesley, Redwood City, CA).
+
+\bibitem[{Guyeux \emph{et~al.}(2010)Guyeux, Wang \& Bahi}]{guyeuxTaiwan10}
+Guyeux, C., Wang, Q. \& Bahi, J. [2010] \enquote{Improving random number
+ generators by chaotic iterations application in data hiding,} \emph{Computer
+ Application and System Modeling (ICCASM), 2010 International Conference on}
+ (IEEE), pp. V13--643--V13--647.
+
+\bibitem[{L'Ecuyer \& Simard(2007)}]{LEcuyerS07}
+L'Ecuyer, P. \& Simard, R.~J. [2007] \enquote{Test{U01}: {A} {C} library for
+ empirical testing of random number generators,} \emph{ACM Trans. Math. Softw}
+ \textbf{33}.
+
+\bibitem[{Levin \emph{et~al.}(2006)Levin, Peres \&
+ Wilmer}]{LevinPeresWilmer2006}
+Levin, D.~A., Peres, Y. \& Wilmer, E.~L. [2006] \emph{{Markov chains and mixing
+ times}} (American Mathematical Society),
+ \urlprefix\url{http://scholar.google.com/scholar.bib?q=info:3wf9IU94tyMJ:scholar.google.com/&output=citation&hl=en&as_sdt=2000&ct=citation&cd=0}.
+
+\bibitem[{Marsaglia(1996)}]{Marsaglia1996}
+Marsaglia, G. [1996] \enquote{Diehard: a battery of tests of randomness,}
+ \emph{http://stat.fsu.edu/~geo/diehard.html} .
+
+\bibitem[{Matsumoto \& Nishimura(1998)}]{matsumoto1998mersenne}
+Matsumoto, M. \& Nishimura, T. [1998] \enquote{Mersenne twister: a
+ 623-dimensionally equidistributed uniform pseudo-random number generator,}
+ \emph{ACM Transactions on Modeling and Computer Simulation (TOMACS)}
+ \textbf{8}, 3--30.
+
+\bibitem[{Mitzenmacher \& Upfal(2005)}]{proba}
+Mitzenmacher, M. \& Upfal, E. [2005] \emph{Probability and Computing}
+ (Cambridge University Press).
+
+\bibitem[{Robinson \& Cohn(1981)}]{Robinson:1981:CS}
+Robinson, J.~P. \& Cohn, M. [1981] \enquote{Counting sequences,} \emph{IEEE
+ Trans. Comput.} \textbf{30}, 17--23,
+ \urlprefix\url{http://dl.acm.org/citation.cfm?id=1963620.1963622}.
+
+\bibitem[{Stojanovski \& Kocarev(2001)}]{915385}
+Stojanovski, T. \& Kocarev, L. [2001] \enquote{Chaos-based random number
+ generators-part i: analysis [cryptography],} \emph{Circuits and Systems I:
+ Fundamental Theory and Applications, IEEE Transactions on} \textbf{48},
+ 281--288.
+
+\bibitem[{Stojanovski \emph{et~al.}(2001)Stojanovski, Pihl \& Kocarev}]{915396}
+Stojanovski, T., Pihl, J. \& Kocarev, L. [2001] \enquote{Chaos-based random
+ number generators. part ii: practical realization,} \emph{Circuits and
+ Systems I: Fundamental Theory and Applications, IEEE Transactions on}
+ \textbf{48}, 382--385.
+
+\bibitem[{Suparta \& Zanten(2004)}]{ZanSup04}
+Suparta, I. \& Zanten, A.~v. [2004] \enquote{Totally balanced and exponentially
+ balanced gray codes,} \emph{Discrete Analysis and Operation Research
+ (Russia)} \textbf{11}, 81--98.
+
+\bibitem[{Wang \emph{et~al.}(2010{\natexlab{a}})Wang, Bahi, Guyeux \&
+ Fang}]{wbg10ip}
+Wang, Q., Bahi, J., Guyeux, C. \& Fang, X. [2010{\natexlab{a}}]
+ \enquote{Randomness quality of {CI} chaotic generators. application to
+ internet security,} \emph{INTERNET'2010. The 2nd Int. Conf. on Evolving
+ Internet} (IEEE Computer Society Press, Valencia, Spain), pp. 125--130, best
+ Paper award.
+
+\bibitem[{Wang \emph{et~al.}(2010{\natexlab{b}})Wang, Bahi, Guyeux \&
+ Fang}]{wbg10:ip}
+Wang, Q., Bahi, J., Guyeux, C. \& Fang, X. [2010{\natexlab{b}}]
+ \enquote{Randomness quality of {CI} chaotic generators. application to
+ internet security,} \emph{INTERNET'2010. The 2nd Int. Conf. on Evolving
+ Internet} (IEEE Computer Society Press, Valencia, Spain), pp. 125--130, best
+ Paper award.
