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To analyze the complexity of chaotic pseudo-random sequences accurately, spectral entropy (SE) algorithm is used to analyze chaotic pseudo-random sequences generated by Logistic map, Gaussian map or TD-ERCS system. The SE algorithm has few parameters, and has high robustness with the sequence length N (the only parameter) and the pseudo-random binary number K. Using sliding window method, the evolution features are analyzed, and complexity of discrete chaotic systems with different initial conditions and system parameters are calculated. The results show that SE algorithm is effective for analyzing the complexity of the chaotic pseudo-random sequences, and TD-ERCS is a high complexity system with wide parameter range, and has the best complex performance among the three chaotic systems. The complexity of the same chaotic system with different initial values fluctuates within a small range. It provides a theoretical and experimental basis for the applications of chaotic sequences in the field of information security.
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Keywords:
- structure complexity /
- spectral entropy /
- Logistic map /
- Gaussian map
[1] Zhou Q, Hu Y, Liao X F 2009 Acta Phys. Sin. 58 4477 (in Chinese) [周庆, 胡月, 廖晓峰 2009 物理学报 58 4477]
[2] Li J B, Zeng Y C, Chen S B, Chen J S 2011 Acta Phys. Sin. 60 060508 (in Chinese) [李家标, 曾以成, 陈仕必, 陈家胜 2011 物理学报 60 060508]
[3] Li Z, Cai J P, Chang Y L 2009 IEEE Trans. Commun. 57 812
[4] Li Z, Cai J P, Lu X F, Si J B 2009 Communications, 2009. ICC 09. IEEE International Conference on (6) p1-5
[5] Kolmogorov A N 1965 Prob. Inform. Trans. 35 1546
[6] Shannon C E 1948 Bell System Technical Journal 27 397
[7] Liu N S 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 761
[8] Lempel A, Ziv J 1976 IEEE Trans. IT-22 75
[9] Sun K H, Tan G Q, Sheng L Y 2008 Acta Phys. Sin. 57 3359 (in Chinese) [孙克辉, 谈国强, 盛利元 2008 物理学报 57 3359]
[10] Chen X J, Li Z, Bai B M 2011 J. Electron. Inform. Technol. 33 1198 (in Chinese) [陈小军, 李赞, 白宝明 2011 电子与信息学报 33 1198]
[11] Pincus S M 1995 Chaos 5 110
[12] Chen W T, Wang Z, Xie H, Yu W X 2007 IEEE Trans. Neural Sys. Rehabilit. Eng. 15 266
[13] Sun K H, He S B, Sheng L Y 2011 Acta Phys. Sin. 60 020505 (in Chinese) [孙克辉, 贺少波, 盛利元 2011物理学报 60 020505]
[14] Luo S J, Qiu S S, Chen X 2010 J. South China Univ. Technol. 38 18 (in Chinese) [罗松江, 丘水生, 陈旭 2010华南理工大学学报 38 18]
[15] Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese) [肖方红, 阎桂荣, 韩宇航 2004物理学报 53 2877]
[16] Larrondo H A, González C M, Martin M T 2005 Physica A 356 133
[17] Rajeev K A, Subba R J, Ramakrishna R 2002 Chaos, Solitons and Fractals 14 633
[18] Abdulnasir Y, Mehmet A, Mustafa P 2009 Exp. Syst. Appl. 36 7390
[19] Phillip P A, Chiu F L, Nick S J 2009 Phys. Rev. E 79 011915
[20] Malihe S, Serajeddin K, Reza B 2009 Artif. Intell. Med. 47 263
[21] Vinod P 2006 Electron. J. Theor. Phys. 3 29
[22] Sheng L Y, Wen J, Cao L L, Xiao Y Y 2007 Acta Phys. Sin. 56 78 (in Chinese) [盛利元, 闻姜, 曹莉凌, 肖燕予 2007 物理学报 56 78]
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[1] Zhou Q, Hu Y, Liao X F 2009 Acta Phys. Sin. 58 4477 (in Chinese) [周庆, 胡月, 廖晓峰 2009 物理学报 58 4477]
[2] Li J B, Zeng Y C, Chen S B, Chen J S 2011 Acta Phys. Sin. 60 060508 (in Chinese) [李家标, 曾以成, 陈仕必, 陈家胜 2011 物理学报 60 060508]
[3] Li Z, Cai J P, Chang Y L 2009 IEEE Trans. Commun. 57 812
[4] Li Z, Cai J P, Lu X F, Si J B 2009 Communications, 2009. ICC 09. IEEE International Conference on (6) p1-5
[5] Kolmogorov A N 1965 Prob. Inform. Trans. 35 1546
[6] Shannon C E 1948 Bell System Technical Journal 27 397
[7] Liu N S 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 761
[8] Lempel A, Ziv J 1976 IEEE Trans. IT-22 75
[9] Sun K H, Tan G Q, Sheng L Y 2008 Acta Phys. Sin. 57 3359 (in Chinese) [孙克辉, 谈国强, 盛利元 2008 物理学报 57 3359]
[10] Chen X J, Li Z, Bai B M 2011 J. Electron. Inform. Technol. 33 1198 (in Chinese) [陈小军, 李赞, 白宝明 2011 电子与信息学报 33 1198]
[11] Pincus S M 1995 Chaos 5 110
[12] Chen W T, Wang Z, Xie H, Yu W X 2007 IEEE Trans. Neural Sys. Rehabilit. Eng. 15 266
[13] Sun K H, He S B, Sheng L Y 2011 Acta Phys. Sin. 60 020505 (in Chinese) [孙克辉, 贺少波, 盛利元 2011物理学报 60 020505]
[14] Luo S J, Qiu S S, Chen X 2010 J. South China Univ. Technol. 38 18 (in Chinese) [罗松江, 丘水生, 陈旭 2010华南理工大学学报 38 18]
[15] Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese) [肖方红, 阎桂荣, 韩宇航 2004物理学报 53 2877]
[16] Larrondo H A, González C M, Martin M T 2005 Physica A 356 133
[17] Rajeev K A, Subba R J, Ramakrishna R 2002 Chaos, Solitons and Fractals 14 633
[18] Abdulnasir Y, Mehmet A, Mustafa P 2009 Exp. Syst. Appl. 36 7390
[19] Phillip P A, Chiu F L, Nick S J 2009 Phys. Rev. E 79 011915
[20] Malihe S, Serajeddin K, Reza B 2009 Artif. Intell. Med. 47 263
[21] Vinod P 2006 Electron. J. Theor. Phys. 3 29
[22] Sheng L Y, Wen J, Cao L L, Xiao Y Y 2007 Acta Phys. Sin. 56 78 (in Chinese) [盛利元, 闻姜, 曹莉凌, 肖燕予 2007 物理学报 56 78]
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