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提出了一种新的能产生多翼混沌吸引子的四维混沌系统, 该系统在不同的参数条件下能产生混沌、超混沌吸引子. 然后对此混沌系统的一些基本的动力学特性进行了理论分析和数值仿真, 如平衡点、Poincaré映射、耗散性、功率谱、Lyapunov指数谱、分岔图等. 同时设计了一个模拟振荡电路实现四翼超混沌吸引子, 硬件电路模拟实验结果与数值仿真结果相一致. 最后将此四维多翼超混沌系统用于物理混沌加密和高级加密标准加密级联的混合图像加密算法, 这种利用物理混沌不可预测性的混合加密系统, 不存在确定的明文密文映射关系, 且密文统计特性也比其他加密系统要好.In this paper, a novel four-dimensional chaotic system for generating multi-wing chaotic attractors is proposed, and chaotic and hyper-chaotic attractors are generated in different parameters. Besides, basic dynamical properties of the chaotic system, such as equilibrium point Poincaré mapping, dissipativity, power spectrum, Lyapunov exponent spectrum, bifurcation diagram are studied numerically and theoretically. An analog oscillator circuit is designed for implementing the four-wing hyper-chaotic attractors, and the hardware circuit experimental results are shown to be in good agreement with the numerical simulation results. Finally, the four-wing hyper-chaotic system is used for hybrid image encryption of physical chaos encryption and advanced encryption standard encryption algorithm. Because physical chaos is adopted in this system, there does not exist a definitive relationship between plaintexts and ciphertexts. And the statistical characteristics of ciphertexts should be better than those of any other encryption system.
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Keywords:
- four-dimensional chaotic system /
- advanced encryption standard /
- physical chaos /
- hybrid encryption system
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[14] Ashraf A Z, Abdulnasser A R 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3721
[15] Jin J X, Qiu S S 2010 Acta Phys. Sin. 59 792 (in Chinese) [晋建秀, 丘水生 2010 59 792]
[16] Lin Y, Wang C H, Xu H 2012 Acta Phys. Sin. 61 240503 (in Chinese) [林愿, 王春华, 徐浩 2012 61 240503]
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[1] Weiss J N, Garfinkel A, Spano M L 1994 J. Clin. Invest. 93 1355
[2] Elwakil A S, Kennedy M P 1999 Microelectronics J. 30 739
[3] Suzuki T, Saito T 1994 IEEE Trans. Circuits Syst. I 41 876
[4] Gao T, Chen Z 2008 Phys. Lett. A 372 394
[5] Chen G, Mao Y, Chui C K 2004 Chaos Soliton. Fract. 21 749
[6] Pareek N K, Patidar V, Sud K K 2006 Image. Vision Comput. 24 926
[7] Miranda R, Stone E 1993 Phys. Lett. A 178 105
[8] Grassi G 2008 Chin. Phys. B 17 3247
[9] Zhou X, Wang C H, Guo X R 2012 Acta Phys. Sin. 61 200506 (in Chinese) [周欣, 王春华, 郭小蓉 2012 61 200506]
[10] Qi G, van Wyk M A, van Wyk B J, Chen G R 2009 Chaos Soliton. Fract. 40 2544
[11] Guan Z H, Huang F J, Guan W J 2005 Phys. Lett. A 346 153
[12] Zhang L H, Liao X F, Wang X B 2005 Chaos Soliton. Fract. 24 759
[13] Wong K, Kwor B, Law W 2008 Phys. Lett. A 372 2645
[14] Ashraf A Z, Abdulnasser A R 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3721
[15] Jin J X, Qiu S S 2010 Acta Phys. Sin. 59 792 (in Chinese) [晋建秀, 丘水生 2010 59 792]
[16] Lin Y, Wang C H, Xu H 2012 Acta Phys. Sin. 61 240503 (in Chinese) [林愿, 王春华, 徐浩 2012 61 240503]
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