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Discontinuity, Nonlinearity, and Complexity 2(4) (2013) 333--343 | DOI:10.5890/DNC.2013.11.003

Massimiliano Zanin$^{1}$,$^{2}$,$^{3}$; J. Ricardo Sevilla-Escoboza$^{4}$; Rider Jaimes-Reátegui$^{4}$; J. Hugo García-López$^{4}$; Guillermo Huerta-Cuellar$^{4}$; Alexander N. Pisarchik$^{2}$,$^{5}$

$^{1}$ Innaxis Foundation & Research Institute, José Ortega y Gasset 20, 28006, Madrid, Spain

$^{2}$ Centre for Biomedical Technology, Polytechnical University ofMadrid, Pozuelo de Alarcón, 28223Madrid, Spain

$^{3}$ Faculdade de Ciências e Tecnologia, Departamento de Engenharia Electrotécnica, Universidade Nova de Lisboa, Portugal

$^{4}$ Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco, Mexico

$^{5}$ Centro de Investigaciones en Optica, Loma del Bosque 115, Lomas del Campestre, 37150 Leon, Guanajuato, Mexico

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Abstract

Synchronization of chaotic oscillators has an important application in cryptography. When two identical oscillators are coupled, they can be completely synchronized and the chaotic output of the transmitter oscillator can be used to mask a message. Although the oscillator parameters are usually used as secret keys, the sensitivity of such cryptosystems to parameter changes has never been systematically analyzed. To cryptanalyze a communication system based on synchro- nization of chaotic oscillators, we use a synchronization attack that allows estimating all unknown parameters by minimizing the synchronization error. Using this attack we cryptanalyze popular communication systems based on the Rössler and Chua chaotic electronic circuits. We suggest to include this attack as a standard security test for crypt-analysis of chaotic communication systems.

Acknowledgments

J.R.S.E. acknowledges Universidad de Guadalajara, CU Lagos (Mexico) for the financial support through project PROINPEP 2012, Acuerdo No. RGS/013/2012, Subprograma 1. A.N.P. acknowledges CONACYT (Mexico) for the financial support through project No. 100429.

References

1. [1]	Pecora, L.M. and Carroll, T.L. (1990), Synchronization in chaotic systems,Physical Review Letters, 64, 821-824.

2. [2]	Boccaletti, S., Kurths, J., Osipov, G., Valladares, D.L., and Zhou, C.S. (2002), The synchronization of chaotic systems, Physics Reports, 366, 1-101.

3. [3]	Argyris, A., Syvridis, D., Larger, L., Annovazzi-Lodi, V., Colet, P., Fischer, I., Garcia-Ojalvo, J., Mirasso, C.R., Pesquera, L., and Shore, K.A., (2005), Chaos-based communications at high bit rates using commercial fibre-optic links, Nature, 438, 343-346.

4. [4]	Uchida, A., Rogister, F., Garcia-Ojalvo, J., and Roy, R. (2005), Synchronization and communication with chaotic laser systems, Progress in Optics, 48, 203-341.

5. [5]	Pisarchik, A.N. and Ruiz-Oliveras, F.R. (2010), Optical chaotic communication using generalized and complete synchronization, IEEE The Journal of Quantum Electronics 46 (3), 299a-299f.

6. [6]	Zanin, M. and Pisarchik, A.N. (2011), Boolean networks for cryptography and secure communication, Nonlinear Science Letters B: Chaos, Fractal and Synchronization, 1 (1), 25-32.

7. [7]	Alvarez, G. and Li, S. (2006), Some basic cryptographic requirements for chaos-based cryptosystems, International Journal of Bifurcation and Chaos, 16 (8), 2129-2151.

8. [8]	Kocarev, L. and Parlitz, U. (1995), General approach for chaotic synchronization with applications to communication, Physical Review Letters, 74, 5028-5031.

9. [9]	He, R. and Vaidya, P.G. (1998), Implementation of chaotic cryptography with chaotic synchronization, Physical Review Letters, 57, 1532-1535.

10. [10]	Annovazzi-Lodi, V., Donati, S., and Scire, A. (1997), Synchronization of chaotic lasers by optical feedback for cryptographic applications, IEEE The Journal of Quantum Electronics, 33 (9), 1449-1454.

11. [11]	Yu, W. and Cao, J. (1998), Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification, Physica A, 375 (2), 467-482.

12. [12]	Hegazi, A.S., Agiza, H.N., and El-Dessoky,M.M. (2001), Adaptive synchronization for Rössler and Chua's circuit systems, International Journal of Bifurcation and Chaos, 12 (7), 1579-1597.

13. [13]	Huang, D. (2004), Synchronization-based estimation of all parameters of chaotic systems from time series, Physical Review E, 69, 067201.

14. [14]	Marji, H.F., Asgharian, R., and Pariz, N. (2009), Adaptive control of chaotic Rössler system via synchronization, Trends in Applied Sciences Research, 4 (2), 98-106.

15. [15]	Parlitz, U., Junge, L., and Kocarev, L. (1996), Synchronization-based parameter estimation from time series, Physical Review E, 54, 6253-6259.

16. [16]	Konnur, R. (2003), Synchronization-based approach for estimating all model parameters of chaotic systems, Physical Review E, 67, 027204.

17. [17]	Pisarchik, A.N., Jaimes-Reátegui, R., and García-Lopez, J.H. (2008), Synchronization of coupled bistable chaotic systems: experimental study, Philosophical Transactions of the Royal Society A, 366, 459-473.

18. [18]	Pisarchik, A.N., Jaimes-Reátegui, R., Villalobos-Salazar, J.R., García-López, J.H., and Boccaletti, S. (2006), Synchronization of chaotic systems with coexisting attractors, Physical Review Letters 96, 244102.

19. [19]	Pisarchik, A.N., Jaimes-Reátegui, R., Sevilla-Escoboza, R., and Boccaletti, S. (2009), Experimental approach to the study of complex network synchronization using a single oscillator, Physical Review E, 79, 055202.

20. [20]	Cruz-Hernández, C. (2004), Synchronization of time-delay Chua's oscillator with application to secure communication, Nonlinear Dynamics and Systems Theory, 4, 1-13.

21. [21]	Cruz-Hernández, C., López-Mancilla, D., García-Gradilla, V., Serrano-Guerrero, H., and Núñez-Pérez, R. (2005), Experimental realization of binary signals transmission using chaos, Journal of Circuits, Systems and Computers, 14 (3), 453-468.

22. [22]	Chua, L.O., Itoh, M., Kocarev, L., and Eckert, K. (1993), Chaos synchronization in Chua's circuit, Journal of Circuits, Systems and Computers, 3 (1), 93-108.

23. [23]	García-López, J.H., Jaimes-Reátegui, R., Pisarchik, A.N., Murguía-Hernandez, A., Medina-Gutiérrez, C., Valdivia-Hernadez, R., and Villafana-Rauda, E. (2005), Novel communication scheme based on chaotic Rössler circuits, Journal of Physics: Conference Series, 23, 276-284.

24. [24]	Garcia-López, J.H., Jaimes-Reátegui, R., Chiu-Zarate, R., López-Mancilla, D., Ramirez-Jimenez, R., and Pisarchik, A.N. (2008), Secure computer communication based on chaotic Rössler oscillators, The Open Electrical and Electronic Engineering Journal, 2, 41-44.

25. [25]	Cuomo, K.M., Oppenheim, A.V., and Strogatz, S.H. (1993), Synchronization of Lorenz-based chaotic circuits, with applications to communications, IEEE Transactions on Circuits and Systems II, 40 (10), 626-633.

26. [26]	Wu, C.W. and Chua, L.O. (1993), A simple way to synchronize chaotic systems with applications to secure communication systems, International Journal of Bifurcation and Chaos, 3 (6), 1619-1627.

27. [27]	Hamming, R.W. (1950), Error detecting and error correcting codes, The Bell System Technical Journal, 29 (2), 147-160.

28. [28]

    López-Gutiérrez, R.M., Rodríguez-Orozco, E., Cruz-Hernández, C., Inzunza-González, E., Posadas-Castillo, C., García Guerrero, E.E., and Cardoza-Avendaño, L. (2009), Secret communications using synchronized sixth-order Chua's circuits, World Academy of Science, Engineering and Technology, 54, 608-613.

29. [29]	Stinson, D.R. (1995), Cryptography: Theory and Practice, Charman & Hall/CRC Press, Boca Raton.

30. [30]	Menezes, A., van Oorschot, P., and Vanstone, S. (1997), Handbook of Applied Cryptography, CRC Press, Boca Raton.

31. [31]	Stamp, M. (2006), Information Security - Principles and Practice, Wiley, Interscience.

32. [32]	Jiménez-Rodríguez, M., Jaimes-Reátegui, R., and Pisarchik, A.N. (2012), Secure communication based on chaotic cipher and chaos synchronization, Discontinuity, Nonlinearity, and Complexity, 1 (1), 57-68.