×

Real-time image encryption using a low-complexity discrete 3D dual chaotic cipher. (English) Zbl 1441.94010

Summary: In this paper, an algorithm is proposed for real-time image encryption. This scheme employs a dual chaotic generator based on a three-dimensional discrete Lorenz attractor. Encryption is achieved using non-autonomous modulation where the image data are injected into the dynamics of a master chaotic generator. The second generator is used to permute the dynamics of the master generator using the same approach. Since the image data can be regarded as a random source, the resulting permutations of the generator dynamics greatly increase the security of the encrypted signal. In addition, a technique is proposed to mitigate the error propagation due to the finite precision arithmetic of digital hardware. In particular, truncation and rounding errors are eliminated by employing an integer representation of the image data which can easily be implemented. The simple hardware architecture of the algorithm makes it suitable for secure real-time applications.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
94A60 Cryptography
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Álvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurcat. Chaos 16, 2129-2151 (2006) · Zbl 1192.94088 · doi:10.1142/S0218127406015970
[2] Carroll, T., Pecora, L.: Synchronizing chaotic circuits. IEEE Trans. Circuits Syst. I 38, 453-456 (1991) · Zbl 1058.37538
[3] Masuda, N., Aihara, K.: Dynamical characteristics of discretized chaotic permutations. Int. J. Bifurcat. Chaos 12, 2087-2103 (2002) · Zbl 1043.37515 · doi:10.1142/S0218127402005686
[4] Li, S., Chen, G., Mou, X.: On the dynamical degradation of digital piecewise linear chaotic maps. Int. J. Bifurcat. Chaos 15, 119-151 (2005) · Zbl 1069.94505 · doi:10.1142/S0218127405012053
[5] Socek, D., Li, S., Magliveras, S., Furht, B.: Enhanced 1-D chaotic key-based algorithm for image encryption. In: Proceedings of the International Conference Security and Privacy for Emerging Areas in Communication Networks, pp. 406-407 (2005)
[6] Gao, H., Zhang, Y., Liang, S., Li, D.: A new chaotic algorithm for image encryption. Chaos Solitons Fractals 29, 393-399 (2006) · Zbl 1096.94006 · doi:10.1016/j.chaos.2005.08.110
[7] Pareek, N., Patidar, V., Sud, K.: Image encryption using chaotic logistic map. Image Vis. Comput. 24, 926-934 (2006) · doi:10.1016/j.imavis.2006.02.021
[8] Li, C., Li, S., Asim, M., Nunez, J., Alvarez, G., Chen, G.: On the security defects of an image encryption scheme. Image Vis. Comput. 27, 1371-1381 (2009) · doi:10.1016/j.imavis.2008.12.008
[9] Li, C., Li, S., Alvarez, G., Chen, G., Lo, K.: Cryptanalysis of a chaotic block cipher with external key and its improved version. Chaos Solitons Fractals 37, 299-307 (2008) · Zbl 1136.94320 · doi:10.1016/j.chaos.2006.08.025
[10] Arroyo, D., Rhouma, R., Alvarez, G., Li, S., Fernandez, V.: On the security of a new image encryption scheme based on chaotic map lattices. Chaos Interdiscip. J. Nonlinear Sci. 18, 033112 (2008) · doi:10.1063/1.2959102
[11] Kocarev, L., Parlitz, U.: General approach for chaotic synchronization with applications to communications. Phys. Rev. Lett. 74, 5028-5031 (1995) · doi:10.1103/PhysRevLett.74.5028
[12] Sobhy, M., Shehata, A.: Secure computer communication using chaotic algorithms. Int. J. Bifurcat. Chaos 10, 2831-2839 (2000) · Zbl 0972.68808 · doi:10.1142/S021812740000181X
[13] Lorenz, E., Edward, N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141 (1963) · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[14] Cartwright, J., Piro, O.: The dynamics of Runge-Kutta methods. Int. J. Bifurcat. Chaos 2, 427-449 (1992) · Zbl 0876.65061 · doi:10.1142/S0218127492000641
[15] Butcher, J.: A history of Runge-Kutta methods. Appl. Numer. Math. 20, 247-260 (1996) · Zbl 0858.65073 · doi:10.1016/0168-9274(95)00108-5
[16] Zeng, X., Eykholt, R., Pielke, R.: Estimating the Lyapunov exponent spectrum from short time series of low precision. Phys. Rev. Lett. 66, 3229-3232 (1991) · doi:10.1103/PhysRevLett.66.3229
[17] Christiansen, F., Rugh, H.: Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization. Nonlinearity 10, 1063 (1997) · Zbl 0910.34055 · doi:10.1088/0951-7715/10/5/004
[18] Brown, R., Bryant, P.: Computing the Lyapunov spectrum of a dynamical system from an observed time series. Phys. Rev. A 43, 2787-2806 (1991) · doi:10.1103/PhysRevA.43.2787
[19] Wolf, A., Swift, J., Swinney, H., Vastano, J.: Determining Lyapunov exponents from a time series. Phys. D Nonlinear Phenom. 16, 285-317 (1985) · Zbl 0585.58037 · doi:10.1016/0167-2789(85)90011-9
[20] Dedieu, H., Kennedy, M.P., Hasler, M.: Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuits. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 40, 634-642 (1993) · doi:10.1109/82.246164
[21] Haroun, M.F., Gulliver, T.A.: A new 3D chaotic cipher for encrypting two data streams simultaneously. Nonlinear Dyn. 81, 1053-1066 (2015) · Zbl 1417.37129
[22] Schneier, B.: Applied Cryptography: Protocols, Algorithms, and Source Code in C, 2nd edn. Wiley, New York (1996) · Zbl 0853.94001
[23] Yang, T., Yang, L., Yang, C.: Cryptanalyzing chaotic secure communications using return maps. Phys. Lett. A 245, 495-510 (1998) · doi:10.1016/S0375-9601(98)00425-3
[24] Wu, X., Hu, H., Zhang, B.: Analyzing and improving a chaotic encryption method. Chaos Solitons Fractals 22, 367-373 (2004) · Zbl 1061.94051 · doi:10.1016/j.chaos.2004.02.009
[25] Li, S., Álvarez, G., Chen, G.: Breaking a chaos-based secure communication scheme designed by an improved modulation method. Chaos Solitons Fractals 25, 109-120 (2005) · Zbl 1075.94527 · doi:10.1016/j.chaos.2004.09.077
[26] Orue, A., Álvarez, G., Pastor, G., Romera, M., Montoya, F., Li, S.: A new parameter determination method for some double-scroll chaotic systems and its applications to chaotic cryptanalysis. Commun. Nonlinear Sci. Numer. Simul. 15, 3471-3483 (2010) · Zbl 1222.94037 · doi:10.1016/j.cnsns.2009.12.017
[27] Orue, A., Fernandez, V., Álvarez, G., Pastor, G., Romera, M., Li, S., Montoya, F.: Determination of the parameters for a Lorenz system and application to break the security of two-channel chaotic cryptosystems. Phys. Lett. A 372, 5588-5592 (2008) · Zbl 1223.94017 · doi:10.1016/j.physleta.2008.06.066
[28] Liu, H., Wang, X.: Color image encryption based on one-time keys and robust chaotic maps. Comput. Math. Appl. 59, 3320-3327 (2010) · Zbl 1198.94109 · doi:10.1016/j.camwa.2010.03.017
[29] Fouda, J.S., Effa, J., Sabat, S., Ali, M.: A fast chaotic block cipher for image encryption. Commun. Nonlinear Sci. Numer. Simul. 19, 578-588 (2014) · Zbl 1470.94073 · doi:10.1016/j.cnsns.2013.07.016
[30] Zhou, Y., Bao, L., Chen, C.L.: A new 1D chaotic system for image encryption. Signal Process. 97, 172-182 (2014) · doi:10.1016/j.sigpro.2013.10.034
[31] Abd El-Latif A., Niu, X.: A hybrid chaotic system and cyclic elliptic curve for image encryption. Int. J. Electron. Commun. 67, 136-143 (2013) · Zbl 0876.65061
[32] Patidar, V., Pareek, N., Purohit, G., Sud, K.: A robust and secure chaotic standard map based pseudorandom permutation-substitution scheme for image encryption. Opt. Commun. 284, 4331-4339 (2011) · doi:10.1016/j.optcom.2011.05.028
[33] Sayedzadeh, S., Mirzakuchaki, S.: A fast color image encryption algorithm based on coupled two dimensional piecewise chaotic map. Signal Process. 92, 1202-1215 (2012) · doi:10.1016/j.sigpro.2011.11.004
[34] Huang, X., Ye, G.: An efficient self-adaptive model for chaotic image encryption algorithm. Commun. Nonlinear Sci. Numer. Simul. 19, 4094-4104 (2014) · Zbl 1470.94088 · doi:10.1016/j.cnsns.2014.04.012
[35] Ghebleh, M., Kanso, A., Noura, H.: An image encryption scheme based on irregularly decimated chaotic maps. Signal Process. Image Commun. 29, 618-627 (2014) · doi:10.1016/j.image.2013.09.009
[36] Chen, G., Mao, Y., Chui, C.: A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Solitons Fractals 21, 749-761 (2004) · Zbl 1049.94009 · doi:10.1016/j.chaos.2003.12.022
[37] Kanso, A., Ghebleh, M.: A novel image encryption algorithm based on a 3D chaotic map. Commun. Nonlinear Sci. Numer. Simul. 17, 2943-2959 (2012) · Zbl 1335.94058
[38] Zhang, L., Hu, X., Liu, Y., Wong, K.: A chaotic image encryption scheme owning temp-value feedback. Commun. Nonlinear Sci. Numer. Simul. 19, 3653-3659 (2014) · Zbl 1470.94100 · doi:10.1016/j.cnsns.2014.03.016
[39] Zhang, X., Mao, Y., Zhao, Z.: An efficient chaotic image encryption based on alternate circular S-boxes. Nonlinear Dyn. 78, 359-369 (2014)
[40] Norouzi, B., Mirzakuchaki, S., Seyedzadeh, S., Mosavi, M.: A simple, sensitive and secure image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Multimed. Tools Appl. 71, 1469-1497 (2014) · doi:10.1007/s11042-012-1292-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.