J. H. Holland, Emergence: From Chaos to Order, 2000.

W. Perruquetti and J. Barbot, Chaos in Automatic Control (Automation and Control Engineering ), 2005.

S. Banerjee, Chaos Synchronization and Cryptography for Secure Communications: Applications for Encryption, 2010.
DOI : 10.4018/978-1-61520-737-4

C. Cruz-hernandez and A. A. Martynyuk, Advances in Chaotic Dynamics and Applications, 2010.

C. Shannon, Communication Theory of Secrecy Systems*, Bell System Technical Journal, vol.28, issue.4, pp.656-715, 1949.
DOI : 10.1002/j.1538-7305.1949.tb00928.x

F. Dachselt, K. Kelber, J. Vandewalle, and W. Schwarz, Chaotic versus classical stream ciphers-a comparative study, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187), pp.518-521, 1998.
DOI : 10.1109/ISCAS.1998.698969

L. Kocarev, Chaos-based cryptography: a brief overview, IEEE Circuits and Systems Magazine, vol.1, issue.3, pp.6-21, 2001.
DOI : 10.1109/7384.963463

G. Millérioux, J. M. Amigó, and J. Daafouz, A connection between chaotic and conventional cryptography . IEEE Trans. On Circuits and Systems I: Regular Papers, 2008.

J. Fridrich, Symmetric Ciphers Based on Two-Dimensional Chaotic Maps, International Journal of Bifurcation and Chaos, vol.08, issue.06, pp.1259-1284, 1998.
DOI : 10.1142/S021812749800098X

R. Schmitz, Use of chaotic dynamical systems in cryptography, Journal of the Franklin Institute, vol.338, issue.4, pp.429-441, 2001.
DOI : 10.1016/S0016-0032(00)00087-9

J. Szczepanski, J. M. Amigó, T. Michalek, and L. Kocarev, Cryptographically secure substitutions based on the approximation of mixing maps, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.52, issue.2, pp.443-453, 2005.
DOI : 10.1109/TCSI.2004.841602

J. M. Amigó, J. Szczepanski, and L. Kocarev, A chaos-based approach to the design of cryptographically secure substitutions, Physics Letters A, vol.343, issue.1-3, pp.55-60, 2005.
DOI : 10.1016/j.physleta.2005.05.057

K. M. Cuomo, A. V. Oppenheim, and S. H. Strogatz, Synchronization of Lorenz-based chaotic circuits with applications to communications, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol.40, issue.10, pp.40626-633, 1993.
DOI : 10.1109/82.246163

C. W. Wu and L. O. Chua, A SIMPLE WAY TO SYNCHRONIZE CHAOTIC SYSTEMS WITH APPLICATIONS TO SECURE COMMUNICATION SYSTEMS, International Journal of Bifurcation and Chaos, vol.03, issue.06, pp.1619-1627, 1993.
DOI : 10.1142/S0218127493001288

G. Kolumban, M. P. Kennedy, and C. L. , The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.45, issue.11, pp.1129-1140, 1998.
DOI : 10.1109/81.735435

H. Dedieu, M. P. Kennedy, and M. Hasler, Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua's circuits, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol.40, issue.10, pp.634-642, 1993.
DOI : 10.1109/82.246164

U. Parlitz, L. O. Chua, L. Kocarev, K. S. Halle, and A. Shang, Transmission of digital signals by chaotic synchronization, International Journal of Bifurcation and Chaos, vol.3, issue.2, pp.973-977, 1993.

A. L. Fradkov and A. Y. Markov, Adaptive synchronization of chaotic systems based on speedgradient method and passification, IEEE Trans. Circuits. Syst. I: Fundamental Theo. Appl, issue.10, pp.44905-912, 1997.

H. J. Huijberts, H. Nijmeijer, and R. Willems, System identification in communication with chaotic systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.47, issue.6, pp.47800-808, 2000.
DOI : 10.1109/81.852932

H. Dedieu and M. Ogorzalek, Identifiability and identification of chaotic systems based on adaptive synchronization, Proc. ECCTD'97, pp.290-295, 1997.
DOI : 10.1109/81.633884

F. Anstett, G. Millérioux, and G. Bloch, Global adaptive synchronization based upon polytopic observers, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), pp.728-731, 2004.
DOI : 10.1109/ISCAS.2004.1329107

URL : https://hal.archives-ouvertes.fr/hal-00120386

G. Millérioux and C. Mira, Coding Scheme Based on Chaos Synchronization from Noninvertible Maps, International Journal of Bifurcation and Chaos, vol.08, issue.10, pp.2019-2029, 1998.
DOI : 10.1142/S0218127498001674

Z. P. Jiang, A note on chaotic secure communication systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.49, issue.1, pp.92-96, 2002.
DOI : 10.1109/81.974882

K. Lian and P. Liu, Synchronization with message embedded for generalized lorenz chaotic circuits and its error analysis, IEEE Trans. Circuits. Syst. I: Fundamental Theo. Appl, vol.47, issue.9, pp.1418-1424, 2000.

G. Millérioux and J. Daafouz, UNKNOWN INPUT OBSERVERS FOR MESSAGE-EMBEDDED CHAOS SYNCHRONIZATION OF DISCRETE-TIME SYSTEMS, International Journal of Bifurcation and Chaos, vol.14, issue.04, pp.1357-1368, 2004.
DOI : 10.1142/S0218127404009831

T. Yang, A survey of chaotic secure communication systems, Int. J. of Computational Cognition, 2004.

M. Hasler, Synchronization of Chaotic Systems and Transmission of Information, International Journal of Bifurcation and Chaos, vol.08, issue.04, pp.647-659, 1998.
DOI : 10.1142/S0218127498000450

T. Yang, C. W. Wu, and L. O. Chua, Cryptography based on chaotic systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.44, issue.5, pp.469-472, 1997.
DOI : 10.1109/81.572346

A. T. Parker and K. M. Short, Reconstructing the keystream from a chaotic encryption scheme, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.48, issue.5, pp.624-630, 2001.
DOI : 10.1109/81.922466

F. Robert, Les Systèmes Dynamiques Discrets, 1995.

J. Gleick, Chaos: Making a New Science, Vintage, 1997.

H. Poincaré, Les nouvelles méthodes de la mécanique céleste. Gauthier-Villars, 1967.

E. N. Lorenz36-]-t, J. A. Li, R. L. Yorke, A. L. Devaney, . Fradkov et al., Deterministic nonperiodic flow Period three implies chaos An Introduction to Chaotic Dynamical Systems On self-synchronization and controlled synchronization, Systems and Control letters, pp.130-141985, 1963.

A. Kerckhoffs, La cryptographie militaire, Journal des sciences militaires, vol.IX, pp.5-83, 1883.

C. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol.27, issue.3, pp.379-423, 1948.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

D. Whitfield and M. Hellman, New directions in cryptography, IEEE Transactions on Information Theory, vol.22, pp.644-654, 1976.

R. L. Rivest, A. Shamir, and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, vol.21, issue.2, pp.120-126, 1978.
DOI : 10.1145/359340.359342

B. Schneier, Applied Cryptography, 1996.

J. Daemen, Cipher and Hash function design, strategies based on linear and differential cryptanalysis, 1995.

J. Daemen and V. Rijmen, The design of Rijndael: AES ? the Advanced Encryption Standard, 2002.
DOI : 10.1007/978-3-662-04722-4

M. Dworkin, Recommendation for block cipher modes of operations, NIST Special Publication, pp.800-838, 2001.

G. S. Vernam, Secret signaling system. patent 1,310, p.719

J. Daemen, R. Govaerts, and J. Vandewalle, A practical approach to the design of high speed selfsynchronizing stream-ciphers, pp.279-283, 1992.

A. Joux and F. Muller, Loosening the knot. Fast Software Encryption, Lecture Note in Computer Science, pp.87-99, 2003.

P. Sarkar, Hiji-bij-bij: A New Stream Cipher with a Self-synchronizing Mode of Operation, 2003.
DOI : 10.1007/978-3-540-24582-7_3

A. Joux and F. Muller, Two Attacks Against the HBB Stream Cipher, 2004.
DOI : 10.1007/11502760_22

]. V. Klíma, Cryptanalysis of hiji-bij-bij (hbb), 2005.

P. Hawkes, M. Paddon, G. R. Gregory, and W. V. Miriam, Primitive specification for sss. eSTREAM, ECRYPT Stream Cipher Project, Report, vol.028, 2005.

J. Daemen and P. Kitsos, The self-synchronizing stream cipher mosquito: estream documentation , version 2. eSTREAM, ECRYPT Stream Cipher Project, Report, 2005.

J. Daemen, J. Lano, and B. Preneel, Chosen ciphertext attack on sss. eSTREAM, ECRYPT Stream Cipher Project, 2005.

A. Joux and F. Muller, Chosen-ciphertext attacks against mosquito. Fast Software Encryption, Lecture Note in Computer Science, vol.4047, 2006.

J. Daemen and P. Kitsos, The Self-synchronizing Stream Cipher Moustique, New Stream Cipher Designs, pp.210-223978, 2008.
DOI : 10.1007/978-3-540-68351-3_16

E. Käsper, V. Rijmen, T. Bjørstad, C. Rechberger, M. Robshaw et al., Correlated Keystreams in Moustique, Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology, AFRICACRYPT'08, pp.246-257, 2008.
DOI : 10.1007/978-3-540-68164-9_17

A. Klimov and A. Shamir, New applications of t-functions in block ciphers and hash functions. Fast Software Encryption, pp.18-31, 2005.

S. Khazaei and W. Meier, New Directions in Cryptanalysis of Self-Synchronizing Stream Ciphers, 2008.
DOI : 10.1007/3-540-45661-9_9

F. Arnault, T. Berger, and A. Necer, A New Class of Stream Ciphers Combining LFSR and FCSR Architectures, Progress in Cryptology ? INDOCRYPT 2002, pp.22-33, 2002.
DOI : 10.1007/3-540-36231-2_3

URL : https://hal.archives-ouvertes.fr/hal-00068427

B. Zhang, H. Wu, D. Feng, and F. Bao, Chosen Ciphertext Attack on a New Class of Self-Synchronizing Stream Ciphers, Progress in Cryptology -INDOCRYPT 2004, pp.1219-1221, 2005.
DOI : 10.1007/978-3-540-30556-9_7

A. Klimov and A. Shamir, A New Class of Invertible Mappings, Cryptographic Hardware and Embedded Systems -CHES 2002, pp.470-483, 2003.
DOI : 10.1007/3-540-36400-5_34

A. Klimov and A. Shamir, Cryptographic Applications of T-Functions, Mitsuru Matsui and Robert Zuccherato, pp.248-261978, 1007.
DOI : 10.1007/978-3-540-24654-1_18

U. Maurer, New Approaches to the Design of Self-Synchronizing Stream Ciphers, pp.458-471, 1991.
DOI : 10.1007/3-540-46416-6_39

O. Jung and C. Ruland, Encryption with Statistical Self-Synchronization in Synchronous Broadband Networks, Cryptographic Hardware and Embedded Systems, pp.74-74, 1999.
DOI : 10.1007/3-540-48059-5_29

H. M. Heys, An analysis of the statistical self-synchronization of stream ciphers, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213), pp.897-904, 2001.
DOI : 10.1109/INFCOM.2001.916281

A. Alkassar, A. Geraldy, B. Pfitzmann, and A. Sadeghi, Optimized Self-Synchronizing Mode of Operation, IN PROCEEDINGS OF THE 8TH INTERNATIONAL WORKSHOP ON FAST SOFTWARE ENCRYPTION, 2001.
DOI : 10.1007/3-540-45473-X_7

F. Yang, H. M. Heys, M. Fliess, J. Lévine, and P. Rouchon, Comparison of two self-synchronizing cipher modes. Queen's 22nd Biennial Symposium on Communications Flatness and defect of nonlinear systems: Introductory theory and examples, International Journal of Control, vol.61, pp.1327-1361, 1995.

H. Sira-ramirez and S. K. , Differentially Flat Systems, 2004.

R. Nitsche, M. Bitzer, M. Khaldi, and G. Bloch, Fault Tolerant Oxygen Control of a Diesel Engine Air System, IFAC Proceedings Volumes, vol.43, issue.7, 2010.
DOI : 10.3182/20100712-3-DE-2013.00036

URL : https://hal.archives-ouvertes.fr/hal-00475414

F. Cazaurang, Commande robuste des systèmes plats application à la commande d'une machine synchrone, 1997.

G. Millérioux and J. Daafouz, Flatness of Switched Linear Discrete-Time Systems, IEEE Transactions on Automatic Control, vol.54, issue.3, pp.615-619, 2009.
DOI : 10.1109/TAC.2008.2009589

J. Parriaux and G. Millérioux, A constructive approach for the design of self-synchronizing dynamical systems: an application to communications*, IFAC Proceedings Volumes, vol.44, issue.1, 2011.
DOI : 10.3182/20110828-6-IT-1002.02124

URL : https://hal.archives-ouvertes.fr/hal-00655582

J. Parriaux and G. Millérioux, Designing self-synchronizing switched linear systems: An application to communications, <ce:title>IFAC World Congress 2011</ce:title>, pp.68-79, 2013.
DOI : 10.1016/j.nahs.2012.05.001

URL : https://hal.archives-ouvertes.fr/hal-00709227

J. Parriaux and G. Millérioux, Nilpotent semigroups for the characterization of flat outputs of discrete-time switched linear and lpv systems, Conference on Decision and Control, p.2012
URL : https://hal.archives-ouvertes.fr/hal-00735068

R. W. Brockett and M. D. Mesarovic, The reproducibility of multivariable systems, Journal of Mathematical Analysis and Applications, vol.11, pp.548-563, 1965.
DOI : 10.1016/0022-247X(65)90104-6

L. Vu and D. Liberzon, Invertibility of switched linear systems, Automatica, vol.44, issue.4, pp.949-958, 2008.
DOI : 10.1016/j.automatica.2007.08.015

T. Floquet and J. Barbot, State and unknown input estimation for linear discrete-time systems, Automatica, vol.42, issue.11, pp.1883-1889, 2006.
DOI : 10.1016/j.automatica.2006.05.030

URL : https://hal.archives-ouvertes.fr/hal-00757977

S. Sundaram and C. Hadjicostis, Designing Stable Inverters and State Observers for Switched Linear Systems with Unknown Inputs, Proceedings of the 45th IEEE Conference on Decision and Control, 2006.
DOI : 10.1109/CDC.2006.376891

M. K. Sain and J. L. Massey, Invertibility of linear time-invariant dynamical systems, IEEE Transactions on Automatic Control, vol.14, issue.2, pp.141-149, 1969.
DOI : 10.1109/TAC.1969.1099133

R. M. Hirschorn, Invertibility of Nonlinear Control Systems, SIAM Journal on Control and Optimization, vol.17, issue.2, 1979.
DOI : 10.1137/0317022

A. Ben-israel and T. N. Greville, Generalized inverses: Theory and applications, 1980.

J. Lévine and D. V. Nguyen, Flat output characterization for linear systems using polynomial matrices, Systems & Control Letters, vol.48, issue.1, pp.69-75, 2003.
DOI : 10.1016/S0167-6911(02)00257-8

H. Radjavi and P. Rosenthal, Simultaneous Triangularization, 2000.
DOI : 10.1007/978-1-4612-1200-3

C. Dubi, An algorithmic approach to simultaneous triangularization, Linear Algebra and its Applications, vol.430, issue.11-12, pp.2975-2981, 2009.
DOI : 10.1016/j.laa.2008.05.037

D. Liberzon, J. P. Hespanha, and A. S. Morse, Stability of switched systems: a Lie-algebraic condition, Systems & Control Letters, vol.37, issue.3, pp.117-122, 1999.
DOI : 10.1016/S0167-6911(99)00012-2

Y. Mori, A solution to the common Lyapunov function problem for continuous-time systems, Proceedings of the 36th IEEE Conference on Decision and Control, pp.3530-3531, 1997.
DOI : 10.1109/CDC.1997.652397

C. B. Schrader and M. K. Sain, Research on system zeros: a survey, International Journal of Control, vol.28, issue.4, pp.1407-1433, 1989.
DOI : 10.1137/0326021

D. Baji? and C. Stefanovi?, Statistical Analysis of Search for Set of Sequences in Random and Framed Data, Sequences and Their Applications ? SETA 2010, pp.320-332, 2010.
DOI : 10.1007/978-3-642-15874-2_28

C. Carlet, Computer Science, and Engineering, chapter Boolean Functions for Cryptography and Error-Correcting Codes, Boolean Models and Methods in Mathematics, 2010.

C. Carlet and P. Guillot, A new representation of boolean functions Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lecture Notes in Computer Science, vol.1719, pp.731-731, 1999.

C. Carlet, Boolean Models and Methods in Mathematics, Computer Science, and Engineering, chapter Vectorial Boolean Functions for Cryptography, 2010.

J. Daemen, R. Govaerts, and J. Vandewalle, Correlation matrices, Fast Software Encryption : Second International Workshop, pp.275-285, 1994.

J. Parriaux, P. Guillot, and G. Millérioux, Towards a spectral approach for the design of self-synchronizing stream ciphers, Cryptography and Communications, vol.430, issue.11???12, pp.259-274, 2011.
DOI : 10.1007/s12095-011-0046-2

URL : https://hal.archives-ouvertes.fr/hal-00540853

K. Nyberg and M. Hermelin, Multidimensional Walsh Transform and a Characterization of Bent Functions, 2007 IEEE Information Theory Workshop on Information Theory for Wireless Networks, 2007.
DOI : 10.1109/ITWITWN.2007.4318037

C. Godsil and G. Royle, Algebraic Graph Theory, 2001.
DOI : 10.1007/978-1-4613-0163-9

P. Guillot, Fonctions courbes binaires et transformation de Möbius, 1999.

C. Shannon, The Synthesis of Two-Terminal Switching Circuits, Bell System Technical Journal, vol.28, issue.1, pp.59-98, 1949.
DOI : 10.1002/j.1538-7305.1949.tb03624.x

J. Kahn, G. Kalai, and N. Linial, The influence of variables on Boolean functions, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science, pp.68-80, 1988.
DOI : 10.1109/SFCS.1988.21923

G. Kindler and S. Safra, Noise-resistant boolean-functions are juntas, 2003.

J. Parriaux, P. Guillot, and G. Millérioux, Synchronization of Boolean Dynamical Systems: A Spectral Characterization, Sequences and Their Applications, pp.373-386, 2010.
DOI : 10.1007/978-3-642-15874-2_32

URL : https://hal.archives-ouvertes.fr/hal-00540855

A. Cayley, A theorem on trees, Quaterly Journal of Pure and Applied Mathematics, pp.376-378, 1889.
DOI : 10.1017/CBO9780511703799.010

S. Goldwasser and S. Micali, Probabilistic encryption, Journal of Computer and System Sciences, vol.28, issue.2, pp.270-299, 1984.
DOI : 10.1016/0022-0000(84)90070-9

URL : http://doi.org/10.1016/0022-0000(84)90070-9

E. Biham and A. Shamir, Differential Cryptanalysis of DES-like Cryptosystems, Lecture Notes in Computer Science, vol.537, pp.2-21, 1991.
DOI : 10.1007/3-540-38424-3_1

]. F. Muller, Differential attacks and stream ciphers, ECRYPT Network of Excellence in Cryptology, 2004.

M. Matsui, Linear Cryptanalysis Method for DES Cipher, Advances in Cryptology ? EUROCRYPT 93, pp.386-397
DOI : 10.1007/3-540-48285-7_33

. Altera, Fpga architecture, 2006.

. Xilinx, Xilinx 7 series fpgas embedded memory advantages, 2012.

. Altera, Stratix v device handbook, 2012.

. Xilinx, Spartan-6 family overview, 2011.

. Xilinx, 7 series fpgas overview, 2012.

A. Tridgell and P. Mackerras, The rsync algorithm, 1996.

M. R. Titchener, Generalised T-codes: extended construction algorithm for self-synchronising codes, IEE Proceedings - Communications, vol.143, issue.3, pp.122-128, 1996.
DOI : 10.1049/ip-com:19960551

B. Stigler, Polynomial dynamical systems in biology, Modeling and Simulation of Biological Networks, pp.59-84, 2006.

M. L. Borgne, A. Benveniste, and P. L. Guernic, Polynomial dynamical systems over finite fields, Algebraic Computing in Control, pp.212-222, 1007.
DOI : 10.1007/BFb0006940

O. Colón-reyes, A. Jarrah, R. Laubenbacher, and B. Sturmfels, Monomial dynamical systems over finite fields, 2006.

L. Misiurewicz, G. Stevens-john-diana, and M. T. , Iterations of linear maps over finite fields, Linear Algebra and its Applications, vol.413, issue.1, pp.218-234, 2006.
DOI : 10.1016/j.laa.2005.09.002

M. and L. Borgne, Dynamical systems over galois fields: Applications to des and to the SIGNAL language, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00544352

J. Reger, Linear Systems over Finite Fields ??? Modeling, Analysis, and Synthesis, at - Automatisierungstechnik, vol.53, issue.1-2005, 2004.
DOI : 10.1524/auto.53.1.45.56703

J. Gunnarsson, Algebraic methods for discrete event systems -a tutorial, 1996.

Y. Crama, Boolean Models and Methods in Mathematics, Computer Science, and Engineering, 2010.