Abstract
In this study, a novel delayed coupled chaotic model to reduce the dynamical degradation of digital chaotic maps is firstly proposed. In this model, we introduce the delayed state variables in digital maps and use the state variable of one map to vary the control parameter of the other map. Numerical experimental results demonstrate that the delayed coupled system can effectively reduce the dynamical degradation of digital chaotic maps, and retain the phase space structure of the original system. Furthermore, we propose a simple image encryption algorithm based on the coupled model as a simple application. Numerical experiments show that our algorithm has high security level and can resist various attacks, which is competitive with some other chaotic image encryption algorithms.
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References
Amin M, Faragallah OS (2010) A chaotic block cipher algorithm for image cryptosystems. Commun Nonlinear Sci Numer Simulat 15:3484–3479
Bandt C, Pompe B (2002) Permutation entropy: a natural complexity measure for time series. Phys Rev Lett 88(17):174102
Dascalescu AC, Boriga R, Racuciu C (2012) A new pseudorandom bit generator using compounded chaotic tent maps. 2012 9th International Conference on Communications (COMM), Bucuresti, 339–342
Deng YS, Hu HP, Xiong NX, Xiong W, Liu LF (2015) A general hybrid model for chaos robust synchronization and degradation reduction. Inform Sci 305:146–164
Dogan S (2016) A new data hiding method based on chaos embedded genetic algorithm for color image. Artif Intell Rev 46(1):129–143
Francois M, Grosges T, Barchiesi D, Erra R (2012) A new image encryption scheme based on a chaotic function. Image Commun 27:249–259
Hu H, Xu Y, Zhu Z (2008) A method of improving the properties of digital chaotic system. Chaos, Solitons Fractals 38:439
Hua ZY, Zhou YC, Pun CM, Philip Chen CL (2015) 2D sine logistic modulation map for image encryption. Inf Sci 297:80–94
Jawad LM, Sulong G (2015) Chaotic map-embedded blowfish algorithm for security enhancement of colour image encryption. Nonlinear Dynam 81(4):2079–2093
Kalouptsidis N (1996) Signal processing systems, in Telecommunications and signal processing series. New York: Wiley
Kocarev L, Szczepanski J, Amigo JM, Tomovski I (2006) Discrete chaos—part I: theory. IEEE Trans Circuit Syst I 53:1300–1309
Li S, Mou X, Cai Y (2001) Improving security of a chaotic encryption approach. Phys Lett A 290:127–133
Li CY, Chen YH, Chang TY, Deng LY, To K (2012) Period extension and randomness enhancement using high-throughput reseeding-mixing PRNG. IEEE Trans Very Large Scale Integrat Syst 20(2):385–389
Liu LF, Miao SX (2017) Delay-introducing method to improve the dynamical degradation of a digital chaotic map. Inf Sci 396:1–13
Liu LF, Miao SX (2017) An image encryption algorithm based on baker map with varying parameter. Multimed Toolds Appl 76:16511–16527
Liu SB, Sun J, Xu ZQ, Liu JS (2009) Digital chaotic sequence generator based on coupled chaotic systems. Chin Phys B 18:5219–5227
Liu L. F., Hu H. P. and Deng Y. S., An analog-digital mixed method for solving the dynamical degradation of digital chaotic systems, IMA J Math Control Inf, 2015, 32(4), 703–715.
Nagaraj N, Shastry MC, Vaidya PG (2008) Increasing average period lengths by switching of robust chaos maps in finite precision. Eur Phys J Spec Topics 165(1):73–83
Persohn KJ, Povinelli RJ (2012) Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation. Chaos, Solitons Fractals 45:238–245
Pincus SM (1991) Approximate entropy as a measure of system complexity. Proc Nat Acad Sci 88:2297–2301
Sun F, Lu Z, Liu S (2010) A new cryptosystem based on spatial chaotic system. Opt Commun 283:2066–2073
Talarposhti KM, Jamei MK (2016) A secure image encryption method based on dynamic harmony search (DHS) combined with chaotic map. Opt Lasers Eng 81:21–34
Tong XJ, Wang Z, Zhang M, Liu Y, Xu H, Ma J (2015) An image encryption algorithm based on the perturbed high-dimensional chaotic map. Nonlinear Dynam 80:1493–1508
Vaferi E, Nadooshan RS (2015) A new encryption algorithm for color images based on total chaotic shuffling scheme. Optik 126(20):2474–2480
Wang XY, Guo K (2014) A new image alternate encryption algorithm based on chaotic map. Nonlinear Dynam 76(4):1943–1950
Wang Y, Wong K, Liao X, Xiang T, Chen G (2009) A chaos-based image encryption algorithm with variable control parameters. Chaos Soliton Fract 41(4):1773–1783
Wang XM, Zhang WF, Zhang JS (2013) Secure chaotic system with application to chaotic ciphers. Inf Sci 221:555–570
Wang W, Tan H, Pang Y, Li Z (2016) A novel encryption algorithm based on DWT and multichaos mapping. J Sens 5:2646205
Wang W, Si M, Pang Y, Ran P (2017) An encryption algorithm based on combined chaos in body area networks. Comput Electric Eng 65:282–291
Zhang M, Tong XJ (2014) A new chaotic map based image encryption schemes for several image formats. J Syst Softw 98:140–154
Zhou Q, Liao X (2012) Collision-based flexible image encryption algorithm. J Syst Softw 85:400–407
Zhou Y, Hua Z, Pun C, Chen CLP (2015) Cascade chaotic systems with applications. IEEE Trans Cybernet 45(9):2001–2012
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This work is supported by the National Natural Science Foundation of China (61601215, 61862042).
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Tang, J., Yu, Z. & Liu, L. A delay coupling method to reduce the dynamical degradation of digital chaotic maps and its application for image encryption. Multimed Tools Appl 78, 24765–24788 (2019). https://doi.org/10.1007/s11042-019-7602-8
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DOI: https://doi.org/10.1007/s11042-019-7602-8