Simulation of algorithm for generating the encryption key information based on dynamical systems

Григорій Васильович Косован, Микола Ярославович Кушнір, Леонід Францович Політанський

Abstract


The modern state of telecommunications requires the development of new digital communication systems. The paper presents and investigates the scheme of digital transmission of information with the usage of chaotic masking. Recovery signal is based on diagnostication of the chaotic regime of synchronous response of the slave system to the synchrosignal of the driving system in their unidirection coupled communication. Chua’s circuit has been selected as chaos generator. The essence of the proposed changes to the classical scheme of transmission with the usage of chaotic masking is the introduction of additional generator of harmonic, chaotic or noise oscillations which initially modulates digital information signal, and then additionally is added in adder to the carrying signal. The research has shown that the hiding increases with decrease of the amplitude of harmonic signal, and increase of its frequency to a value that does not exceed the practical width of the spectrum of carrying signal. The power of the signal of desynchronization at low frequency of informational signal increases almost linearly with increasing amplitude at frequencies close to the limited frequency spectrum of a chaotic signal, the power of the desynchronization signal practically does not depend on the amplitude. The results can be used for the construction of communication systems which use a chaotic signal as a carrying one.

The suitability of the proposed scheme for digital data exchange has been demonstrated and the conditions of reestablishment of the information in the receiver have been determined


Keywords


chaotic masking; digital signal; harmonic signal; Chua’s circuit

References


Pecora, L. M. Synchronization in chaotic systems [Текст] / L.M. Pecora, T.L. Carroll // Phys. Rev. Lett. - 1990. - Vol. 64. - № 8. - P. 821-824.

Птицын, Н.В. Приложение теории детерминированного хаоса в криптографии [Текст] / Птицын Н.В. – М.: Изд. МГТУ им Н.Э Баумана, 2002. – 80 с.

Strogatz, S. H. Nonlinear systems and chaos. Perseus Publishing [Текст] / Strogatz Steven H. – 1994.

Ali-Pacha, A. Chaotic behaviour for the secrete key of cryptographic system [Текст] / Ali-Pacha A, N. Hadj-Said, B. Belmekki, Belgoraf A. // Chaos, Solitons & Fractals 2005;23:1549–52.

Schneier, B. Applied cryptography – protocols, algorithms and source code in C [Текст] / Bruce Schneier // second ed. New York: John Wiley & Sons, Inc.; 1996.

González, O. A. Cryptosystem Using a Lorenz Chaotic Oscillator [Текст] / O.A. González, G. Han, J.P. de Gyvez, and Edgar CMOS // Proceedings of the IEEE International Symposium on Circuits and Systems. ISCAS '99. Vol. 5. - PP 442-445.

Шахтарин, Б.И. Генераторы хаотических колебаний [Текст] / Б.И. Шахтарин, П.И. Кобылкина, Ю.А. Сидоркина, А.В. Кондратьэв, С.В. Митин – Галилеос АРВ. – Москва. - 2007 – 247 с.

Ali-Pacha, А. Lorenz’s attractor applied to the stream cipher (Ali-Pacha generator) [Текст] / Adda Ali-Pacha, Naima Hadj-Said, A. M’Hamed, A. Belgoraf // Chaos Solitons and Fractals 33 (2007) 1762–1766

Kocarev, L. Logistic map as a block encryption algorithm [Текст] / L. Kocarev, G. Jakimoski // Physics Letters A, 289 (4-5) 2001 – PP 199–206.

Vaidya, P. G. and Angadi, S. Decoding chaotic cryptography without access to the superkey [Текст] / P.G. Vaidya and S. Angadi // Chaos, Solitons and Fractals, 17:379-386, 2003.

Solak, E. Cryptanalysis of observer based discrete-time chaotic encryption schemes [Текст] / E. Solak // International Journal of Bifurcation and Chaos, 15(2):653-658, 2005.

Pecora, L.M. & Carroll, T. L. (1990). Synchronization in chaotic systems. Phys. Rev. Lett. Vol. 64. - № 8, 821-824.

Pticyn, N. V. (2002). Prilozhenie teorii determinirovannogo haosa v kriptografii. Izd. MGTU im N.Je Baumana, 80.

Strogatz, S. H. (1994). Nonlinear systems and chaos. Perseus Publishing. 1994.

Ali-Pacha A, Hadj-Said, N., Belmekki, B., Belgoraf, A. (2005). Chaotic behaviour for the secrete key of cryptographic system. Chaos, Solitons & Fractals, 23:1549–52.

Schneier, B. (1996). Applied cryptography – protocols, algorithms and source code in C. New York: John Wiley & Sons, Inc. 1028.

González, O. A., Han, G., de Gyvez, J. P., and Edgar CMOS (1999). Cryptosystem Using a Lorenz Chaotic Oscillator. Proceedings of the IEEE International Symposium on Circuits and Systems. ISCAS '99. Vol. 5. 442-445.

Shahtarin, B. I., Kobylkina, P. I., Sidorkina, Ju. A., Kondrat'jev, A. V., Mitin, S. V. (2007). Generatory haoticheskih kolebanij. Galileos ARV. – Moskva, 247.

Ali-Pacha, А., Naima Hadj-Said, M’Hamed, A., Belgoraf, A. (2007). Lorenz’s attractor applied to the stream cipher (Ali-Pacha generator). Chaos, Solitons and Fractals 33, 1762–1766.

Kocarev, L., Jakimoski, G. (2001). Logistic map as a block encryption algorithm. Physics Letters A, 289 (4-5), 199–206.

Vaidya, P. G., and Angadi, S. (2003). Decoding chaotic cryptography without access to the superkey. Chaos, Solitons and Fractals 17, 379-386.

Solak, E. (2005). Cryptanalysis of observer based discrete-time chaotic encryption schemes. International Journal of Bifurcation and Chaos 15(2), 653-658.


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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061