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Lorenz system is one of the most typical chaotic system models, and it has been well studied and widely applied. In order to obtain more complex structure and dynamic behavior of chaotic attractor for Lorenz system, improving the Lorenz system has become one of the important tasks in chaotic dynamical system. Therefore, an improved Lorenz system with complex dynamic behavior is proposed and used to protect image information security. Based on the existing various improvement Lorenz systems, firstly, a new Lorenz chaotic system is constructed by increasing the control parameters and modifying nonlinear expression in the existing Lorenz chaotic system; secondly, the mathematical properties of dissipation, symmetry, and stability in the proposed Lorenz system, which are similar to those in the existing Lorenz system, Bao system, Tee system and Y system, are investigated by modern differential dynamical system, and the experimental results of Lyapunov index and random sequence correlation of five different Lorenz systems show that the proposed Lorenz system has a more complex structure and chaotic dynamic behavior; finally, the discrete pseudo random sequences generated by five different Lorenz chaotic systems are used for scrambling the pixel position and diffusing the pixel value to protect image information security. The analyses of correlation and statistic histogram entropy of adjacent pixels, anti-differential attack and key sensitivity of the encrypted image, indicate that the improved Lorenz system proposed in this paper has much better potential advantages than other existing improved Lorenz system in image encryption application.
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Keywords:
- Lorenz system /
- Lyapunov index /
- image encryption /
- correlation analysis
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[2] Pareek N K,Patidar V,Sud K K 2006 Image Vision Comput. 24 9
[3] Rhouma R, Belghith S 2008 Phys. Lett. A 372 38
[4] Singh N, Sinha A 2009 Opt. Commun. 282 6
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[10] Panchev S, Spassova T, Vitanov N K 2007 Chaos, Soliton. Fract. 33 5
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[24] Li C G, Chen G R 2005 Chaos, Soliton. Fract. 5 23
[25] Liu Y J 2010 Ph. D. Dissertation (Guangzhou: South China University of Teehnology) (in Chinese) [ 刘永建 2010 博士学位论文(广州: 华南理工大学)]
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[31] Chen X J, Li Z, Bai B M, Pan W, Chen Q H 2011 J. Electron. Inform. Technol. 33 5 (in Chinese) [陈小军, 李赞, 白宝明, 潘玮, 陈清华 2011 电子与信息学报 33 5]
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[36] Wang X Y, Xie Y X 2011 Chin. Phys. B 20 8
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 113
[2] Pareek N K,Patidar V,Sud K K 2006 Image Vision Comput. 24 9
[3] Rhouma R, Belghith S 2008 Phys. Lett. A 372 38
[4] Singh N, Sinha A 2009 Opt. Commun. 282 6
[5] Cui L, Ou Q L, Zhang H Q 2010 Commun. Technol. 5 43 (in Chinese) [崔力, 欧青立, 张红强 2010 通信技术 5 43]
[6] Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[7] L J H, Chen G R 2002 Int. J. Bifur. Chaos 12 659
[8] Qi G Y, Chen G R, Du S Z 2005 Physica A 352 295
[9] Elwakil A S, Özoğuz S, Kennedy P M 2002 IEEE Trans. Circ. Syst. 49 4
[10] Panchev S, Spassova T, Vitanov N K 2007 Chaos, Soliton. Fract. 33 5
[11] Wang Z, Mao P W 2008 J. Dyn. Contr. 6 16 (in Chinese) [王震, 毛鹏伟 2008 动力学与控制学报 6 16]
[12] Zhang Z Z, Shan Z P, Liu Y M 2013 Appl. Math. Mech. 34 12 (in Chinese) [张转周, 陕振沛, 刘衍民 2013 应用数学和力学 34 12]
[13] Huang G Q, Zhou Y Z 2013 J. Inform. Comput. Sci. 10 4763
[14] El-Sayed A M A, Salman S M 2013 Electon. J. Math. Anal. Appl. 1 2
[15] Tee L S, Salleh Z 2013 J. Math. 2013 820946
[16] Li C B, Wang H K, Huang X M 2009 Microcomput. Inform. 25 8 (in Chinese) [李春彪, 王翰康, 黄新民 2009 微计算机信息 25 8]
[17] Pan S Q, Liu Y J, Zhu C X 2013 Comput. Engin. Appl. 49 7 (in Chinese) [庞寿全, 刘永建, 朱从旭 2013 计算机工程与应用 49 7]
[18] Celikovsky S, Chen G 2002 Int. J. Bifur. Chaos 12 8
[19] Sun K H, Sprott J C 2009 Int. J. Bifur. Chaos 19 4
[20] Bao B C 2013 An Introduction to Chaotic Circuits (Beijing: Science Press) p41 (in Chinese) [包伯成 2013 混沌电路导论(北京:科学出版社) 第41页]
[21] Bao B C, Liu Z, Xu J P 2009 J. Systems Eng. Electron. 20 6
[22] Yuan D 2009 J. Anyang Teach. Coll. 2 26 (in Chinese) [袁地 2009 安阳师范学院学报 2 26]
[23] Luo X W, Wang C H, Wan Zhao 2014 Nonlinear Anal. Model. Control 19 2
[24] Li C G, Chen G R 2005 Chaos, Soliton. Fract. 5 23
[25] Liu Y J 2010 Ph. D. Dissertation (Guangzhou: South China University of Teehnology) (in Chinese) [ 刘永建 2010 博士学位论文(广州: 华南理工大学)]
[26] Grassberger P, Procaccia I 1983 Physica D 9 189
[27] Ramasubramanian K, Sriram M S 2000 Physica D 139 72
[28] Han M, Wei R 2010 Syst. Eng. Electron. 32 11 (in Chinese) [韩敏, 魏茹 2010 系统工程与电子技术 32 11]
[29] Guo J B, Xu X Z, Shi Q H, Hu T H 2013 Acta Phys. Sin. 62 110508 (in Chinese) [郭静波, 徐新智, 史启航, 胡铁华 2013 物理学报 62 110508]
[30] Wang Y X, Weng Y F, Zheng D L 2006 J. Beijing Technol. Bus. Univ. (Nat. Sci. Ed.) 24 2 (in Chinese) [王云雄, 翁贻方, 郑德玲 2006 北京工商大学学报(自然科学版) 24 2 ]
[31] Chen X J, Li Z, Bai B M, Pan W, Chen Q H 2011 J. Electron. Inform. Technol. 33 5 (in Chinese) [陈小军, 李赞, 白宝明, 潘玮, 陈清华 2011 电子与信息学报 33 5]
[32] Cao G H, Hu K 2013 J. Beijing Univ. Aeron. Astron. 39 1 (in Chinese) [曹光辉, 胡凯 2013 北京航空航天大学学报 39 1]
[33] Zhu C X, Sun K H 2012 Acta Phys. Sin. 61 120503 (in Chinese) [朱从旭, 孙克辉 2012 物理学报 61 120503]
[34] Li H N, Guo C F 2012 J. Data Acquisi. Process. 27 1 (in Chinese) [李慧娜, 郭超峰 2012 数据采集与处理 27 1]
[35] Wang J, Jiang G P 2011 Acta Phys. Sin. 60 060503 (in Chinese) [王静, 蒋国平 2011 物理学报 60 060503]
[36] Wang X Y, Xie Y X 2011 Chin. Phys. B 20 8
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