A new color image encryption scheme based on chaos synchronization of time-delay Lorenz system

Abstract

In this paper, a new image encryption scheme is presented based on time-delay chaos synchronization. Compared with existing methods, a new method is proposed and a lot of coupled items can be taken as zero items to simplify the whole system. A simple linear controller is introduced to realize time-delay chaos synchronization and image encryption. The positions of the image pixels are firstly shuffled and then be hidden in the carrier image. The address codes of the chaotic sequences are adopted to avoid the disturbances induced by the initial value and computer accuracy error. Simulation results for color image are provided to illustrate the effectiveness of the proposed method. It can be seen clearly that the system can converge quickly and the image can be encrypted rapidly.

Keywords

Delay chaotic system / Chaos synchronization / Linear controller / Color image encryption / Address code

References

[1] Zhou YC, Cao WJ, Chen CLP. Image encryption using binary bitplane. Signal Process, 2014, 100(7): 197-207.

[2] Kocarev L, Parlitz U. General approach for chaotic synchronization with applications to communication. Phys Rev Lett, 1995, 74(25): 5028-5031.

[3] Zhou YC, Bao L, Chen CLP. A new 1D chaotic system for image encryption. Signal Process, 2014, 97(7): 172-182.

[4] Patidar V, Pareek NK, Sud KK. A new substitution-diffusion based image cipher using chaotic standard and logistic maps. Commun Nonlinear Sci Numer Simul, 2009, 14(7): 3056-3075.

[5] Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys Rev Lett, 1990, 64(8): 821-824.

[6] Wang H, Han ZZ, Zhang W, et al. Synchronization of unified chaotic systems with uncertain parameters based on the CLF. Nonlinear Anal Real World Appl, 2009, 10(5): 715-722.

[7] Ahn CK, Shi P, Basin MV. Two-dimensional dissipative control and filtering for Roesser model. IEEE Trans Autom Control, 2015, 60(7): 1745-1759.

[8] Banerjee S. Synchronization of time-delayed systems with chaotic modulation and cryptography, chaos. Solitons Fractals, 2009, 42: 745-750.

[9] Guan ZH, Huang FJ, Guan WJ. Chaos-based image encryption algorithm. Phys Lett A, 2005, 346: 153-157.

[10] Wang H, Wu JP, Sheng XS, et al. A new stability result for nonlinear cascade time-delay system and its application in chaos control. Nonlinear Dyn, 2015, 80(1–2): 221-226.

[11] Burton T. Stability and periodic solutions of ordinary and functional differential equations, 1985, Orlando: Academic.

[12] Ahn CK. T-S fuzzy H _∞ synchronization for chaotic systems via delayed output feedback control. Nonlinear Dyn, 2010, 59(4): 535-543.

[13] Ahn CK, Jung ST, Kang SK, et al. Adaptive H _∞ synchronization for uncertain chaotic systems with external disturbance. Commun Nonlinear Sci Numer Simul, 2010, 15(8): 2168-2177.

[14] Ahn CK. l ₂–l _∞ elimination of overflow oscillations in 2-D digital filters described by Roesser model with external interference. IEEE Trans Circuits Syst II, 2013, 60(6): 361-365.

[15] Ahn CK. l ₂–l _∞ suppression of limit cycles in interfered two-dimensional digital filters: a Fornasini-Marchesini model case. IEEE Trans Circuits Syst II, 2014, 61(8): 614-618.

Funding

National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809(51375293)

Science and Technology Commission of Shanghai Municipality Project(16511108600)