Chaotic cryptosystems: Cryptanalysis and identifiability

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 53, Issue 12, 2006, Pages 2673-2680

  Anstett, Floriane ^a   Millerioux, Gilles ^a   Bloch, Gérard ^a  

^a CENTRE DE RECHERCHE EN AUTOMATIQUE DE NANCY   (France)

Author keywords

Algebraic attack; Brute force attack; Chaotic cryptosystems; Cryptanalysis; Identifiability; Known plaintext attack

Indexed keywords

ALGEBRA; IDENTIFICATION (CONTROL SYSTEMS); ROBUSTNESS (CONTROL SYSTEMS); SYSTEM THEORY;

ALGEBRAIC ATTACK; BRUTE FORCE ATTACKS; CHAOTIC CRYPTOSYSTEMS; CRYPTANALYSIS; IDENTIFIABILITY; KNOWN PLAINTEXT ATTACK;

CRYPTOGRAPHY;

EID: 33845908263     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2006.885979     Document Type: Article

References (43)

1. T. L. Carroll and L. M. Pecora, "Synchronizing chaotic circuits," IEEE Trans. Circuits Syst., vol. 38, no. 4, pp. 453-456, Apr. 1991.
2. M. J. Ogorzalek, "Taming chaos - Part 1: Synchronization," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 10, pp. 693-699, Oct. 1993.
3. M. Hasler, "Synchronization of chaotic systems and transmission of information," Int. J. Bifurc. Chaos, vol. 8, no. 4, pp. 647-659, Apr. 1998.
4. T. Yang, "A survey of chaotic secure communication systems," Int. J. Comput. Cogn., vol. 2, no. 2, pp. 81-130, 2004.
5. G. Millérioux, A. Hernandez, and J. Amigó, "Conventional cryptography and message-embedding," in Proc. 2005 Int. Symp. Nonlinear Theory and its Applications (NOLTA 2005), Bruges, Belgium, Oct. 18-21, 2005.
6. G. Alvarez and S. Li, "Some basic cryptographic requirements for chaos-based cryptosystems," Int. J. Bifurc. Chaos, 2006.
7. H. Delfs and H. Knebl, Introduction to Cryptography. Berlin, Germany: Springer-Verlag, 2002.
8. X. Wang, M. Zhan, and C. H. Lai, "Error function attack of chaos synchronization based encryption schemes," Chaos, vol. 14, no. 1, pp. 128-137, 2004.
9. S. Li, G. Alvarez, G. Chen, and X. Mou, "Breaking a chaos-noise-based secure communication scheme," Chaos, vol. 15, no. 1, 2005.
10. G. Alvarez, F. Montoya, M. Romera, and G. Pastor, "Cryptanalyzing a discrete-time chaos synchronization secure communication system," Chaos, Solitons, Fractals, vol. 21, pp. 689-694, 2004.
11. G. Alvarez, S. Li, F. Montoya, G. Pastor, and M. Romera, "Breaking projective chaos synchronization secure communication using filtering and generalized synchronization," Chaos, Solitons, Fractals, vol. 24, pp.775-783, 2005.
12. R. Marino and P. Tomei, "Global adaptive observers for nonlinear systems via filtered transformations," IEEE Trans. Autom. Contr., vol. 37, no. 8, pp. 1239-1245, 1992.
13. A. Fradkov, H. Nijmeijer, and A. Markov, "Adaptive observer-based synchronization for communication," Int. J. Bifurc. Chaos, vol. 10, no. 12, pp. 2807-2813, 2000.
14. Q. Zhang and A. Xu, "Global adaptive observer for a class of nonlinear systems," in Proc. 40th IEEE Conf. Decision and Control, Orlando, FL, Dec. 4-7, 2001, vol. 4, pp. 3360-3365.
15. A. Guyader and Q. Zhang, "Adaptive observer for discrete time linear time varying systems," in Proc. 3rd IFAC/IFORS Symp. Identification and System Parameter Estimation, SYSID'2003, Rotterdam, The Netherlands, Aug. 2003.
16. F. Anstett, G. Millerioux, and G. Bloch, "Global adaptive synchronization based upon polytopic observers," in Proc. IEEE Int. Symp. Circuits Syst., Vancouver, BC, Canada, May 2004, pp. 728-731.
17. G. Millerioux, F. Anstett, and G. Bloch, "Considering the attractor structure of chaotic maps for observer-based synchronization problems," Math. Comput. Simulation, vol. 68, no. 1, pp. 67-85, 2005.
18. H. Dedieu and M. Ogorzalek, "Identifiability and identification of chaotic systems based on adaptative synchronization," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 44, no. 10, pp. 948-962, Oct. 1997.
19. H. Guojie, F. Zhengjin, and M. Ruiling, "Chosen ciphertext attack on chaos communication based on chaotic synchronization," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 2, pp. 275-279, Feb. 2003.
20. H. Guojie, F. Zhengjin, and W. Lin, "Analysis of a type digital chaotic cryptosystem," in Proc. IEEE Int. Symp. Circuits Syst., Scottsdale, AZ, May 26-29, 2002, vol. 3, pp. III-473-III-475.
21. P. G. Vaidya and S. Angadi, "Decoding chaotic cryptography without access to the superkey," Chaos, Solitons, Fractals, vol. 17, pp. 379-386, 2003.
22. E. Solak, "On the security of a class of discrete-time chaotic cryptosystems," Phys. Lett. A, no. 320, pp. 389-395, 2004.
23. E. Solak, "Cryptanalysis of observer based discrete-time chaotic encryption schemes," Int. J. Bifurc. Chaos, vol. 15, no. 2, pp. 653-658, 2005.
24. T. Beth, D. E. Lazic, and A. Mathias, Cryptanalysis of Cryptosystems Based on Remote Chaos Replication. New York: Springer-Verlag, 1994.
25. F. Anstett, G. Millerioux, and G. Bloch, "Message-embedded cryptosystems: Cryptanalysis and identifiability," in Proc. 44th IEEE Conf. Decision and Control, Sevilla, Spain, Dec. 12-15, 2005.
26. M. Hénon, "A two-dimensional mapping with a strange attractor," Commun. Math. Phys., vol. 50, pp. 69-77, 1976.
27. R. May, "Simple mathematical models with complicated dynamics," Nature, vol. 261, pp. 459-470, 1976.
28. B. Mandelbrot, Les Objets Fractals: Forme, Hasard et Dimension. Paris, France: Flammarion, 1975.
29. H. G. Schuster, Deterministic Chaos. New York: Wiley-VCH, 1988.
30. G. Millerioux and J. Daafouz, "Unknown input observers for message-embedded chaos synchronization of discrete-time systems," Int. J. Bifurc. Chaos, vol. 14, no. 4, pp. 1357-1368, Apr. 2004.
31. G. Millerioux and J. Daafouz, "Input independent chaos synchronization of switched systems," IEEE Trans. Autom. Contr., vol. 49, no. 7, pp. 1182-1187, Jul. 2004.
32. A. Menezes, P. V. Oorschot, and S. Vanstone, Handbook of Applied Cryptography. Boca Raton, FL: CRC, 1996.
33. E. Walter and L. Pronzato, Identification of Parametric Models From Experimental Data. New York: Springer-Verlag, 1997.
34. S. Nõmm and C. H. Moog, "Identifiability of discrete-time nonlinear systems," in Proc. 6th IFAC Symp. Nonlinear Control Systems, NOLCOS, Stuttgart, Germany, Sep. 1-3, 2004, pp. 477-489.
35. L. Ljung and T. Glad, "On global identifiability for arbitrary model parametrizations," Automatica, vol. 30, no. 2, pp. 265-276, 1994.
36. S. Diop and M. Fliess, "Nonlinear observability, identifiability and persistent trajectories," in Proc. 30th Conf. Decision and Control, Brighton, U.K., Dec. 1991, pp. 714-718.
37. H. Pohjanpalo, "System identifiability based on the power series expansion of the solution," Math. Biosci., vol. 41, pp. 21-33, 1978.
38. H. Nijmeijer and A. J. van der Schaft, Nonlinear Dynamical Control Systems. New York: Springer, 1990.
39. B. Buchberger, "An algorithm for finding a basis for the residue class ring of zero-dimensional polynomial ideal," Ph.D. dissertation, Dept. of Math., Math. Inst. Univ. of Innsbrück, Innsbruck, Austria, 1965.
40. E. Kolchin, Differential Algebra and Algebraic Groups. New York: Academic, 1973.
41. E. Frisk, "Residual generation for fault diagnosis," Ph.D. dissertation, Dept. of Elect. Eng., Linköpings Universitet, Linkoping, Sweden, 2001.
42. J. F. Ritt, Differential Algebra. Providence, RI: American Mathematical Society, 1950.
43. J.-P. Barbot, "Observability bifurcations: Application to cryptography," in Proc. 4ème Ecole Internationale d'Automatique de Lille, 2003, pp. 1-19.