基于分数阶统一混沌系统的图像加密算法
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摘要
为了解决数字图像信息传输所面临的安全性问题,基于分数阶统一混沌系统,提出了一种新的图像加密算法。采用经典的置乱—扩散机制,整个加密策略分为图像像素位置置乱和像素值替代两个过程。在像素置乱的过程中,采用排序的方式分别对图像的行和列进行置乱。在像素值替代的过程中,通过与密钥序列进行异或运算来实现加密。而混沌系统则作为伪随机序列发生器,并作用于加密的各个阶段。安全性和时间复杂度分析表明:该算法具有高的安全性和低的时间复杂度,且能够抵御几种常见的攻击方式。
In order to solve the security problem during transmitting digital image information,a novel image encryption algorithm based on fractional order unified chaotic system is proposed. This algorithm utilizes the classical confusion and diffusion mechanism,and the whole encryption strategy can be divided into two stages:image pixel position permutation and pixel value substitution. In the first stage,each row and column of the image are respectively scrambled by the way of ranking. In the second stage,the pixel values of image are substituted by the XOR operation with key sequence. Besides,the chaotic system is used as pseudo-random sequence generator,and acts on the two stages. Security and time complexity analysis shows that the algorithm has high security and low time complexity,and can resist several common cryptogram attacks.
In order to solve the security problem during transmitting digital image information,a novel image encryption algorithm based on fractional order unified chaotic system is proposed. This algorithm utilizes the classical confusion and diffusion mechanism,and the whole encryption strategy can be divided into two stages:image pixel position permutation and pixel value substitution. In the first stage,each row and column of the image are respectively scrambled by the way of ranking. In the second stage,the pixel values of image are substituted by the XOR operation with key sequence. Besides,the chaotic system is used as pseudo-random sequence generator,and acts on the two stages. Security and time complexity analysis shows that the algorithm has high security and low time complexity,and can resist several common cryptogram attacks.
引文
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[12]刘叙含,申晓红,姚海洋,等.基于帐篷混沌映射观测矩阵的图像压缩感知[J].传感器与微系统,2014,33(9):26-31.
[13]Liu Wenhao,Sun Kehui,Zhu Congxu.A fast image encryption algorithm based on chaotic map[J].Optics and Lasers in Engineering,2016,84:26-36.
[14]Wu Xiangjun,Lu Yang.Generalized projective synchronization of the fractional-order Chen hyperchaotic system[J].Nonlinear Dynamics,2009,57(1-2):25-35.
[15]Kia Arman K,Naser F,Henry P L.A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter[J].Communications in Nonlinear Science&Numerical Simulation,2009,14(3):863-879.
[16]Wang Yaqing,Zhou Shangbo.Image encryption algorithm based on fractional-order Chen chaotic system[J].Journal of Computer Applications,2013,33(4):1043-1046.
[17]王力,吕秀宾.基于IBE加密算法的远程抄表系统的优化[J].无线电通信技术,2016,42(1):86-88.
[18]Zhao Jianfeng,Wang Shuying,Chang Yingxiang,et al.A novel image encryption scheme based on an improper fractional-order chaotic system[J].Nonlinear Dynamics,2015,80:1721-1729.
[19]贺少波,孙克辉,王会海.分数阶混沌系统的Adomian分解法求解及其复杂性分析[J].物理学报,2014,63(3):030502.
[20]LüJinhu,Chen Guanrong,Chen Daizhan,et al.Bridge the gap between the Lorenz system and Chen system[J].International Journal of Bifucation and Chaos,2002,12(12):2917-2976.
[2]艾星星,孙克辉,贺少波,等.简化Lorenz多涡卷混沌吸引子的设计与应用[J].物理学报,2014,63(12):120511.
[3]朱从旭,孙克辉.对一类超混沌图像加密算法的密码分析与改进[J].物理学报,2012,61(12):1-12.
[4]Hua Zhongyun,Zhou Yicong,Pun Chiman,et al.2D Sine Logistic modulation map for image encryption[J].Information Sciences,2014,297:80-94.
[5]Majid K.A novel image encryption scheme based on multiple chaotic S-boxes[J].Nonlinear Dynamics,2015,82:527-533.
[6]Wang Xingyuan,Wang Qian.A novel image encryption algorithm based on dynamic S-box constructed by chaos[J].Nonlinear Dynamics,2014,75:567-576.
[7]Zhang Wei,Yu Hai,Zhu Zhiliang.Color image encryption based on paired interpermuting planes[J].Optics Communications,2015,338:199-208.
[8]Ye Ruisong.A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism[J].Optics Communications,2011,284:5290-5298.
[9]Majid K.A novel image encryption scheme based on multiple chaotic S-boxes[J].Nonlinear Dynamics,2015,82:527-533.
[10]孙克辉.混沌保密通信原理与技术[M].北京:清华大学出版社,2015.
[11]李正周,丁浩,刘梅,等.实测海杂波光电图像混沌特性研究[J].传感器与微系统,2013,32(4):27-33.
[12]刘叙含,申晓红,姚海洋,等.基于帐篷混沌映射观测矩阵的图像压缩感知[J].传感器与微系统,2014,33(9):26-31.
[13]Liu Wenhao,Sun Kehui,Zhu Congxu.A fast image encryption algorithm based on chaotic map[J].Optics and Lasers in Engineering,2016,84:26-36.
[14]Wu Xiangjun,Lu Yang.Generalized projective synchronization of the fractional-order Chen hyperchaotic system[J].Nonlinear Dynamics,2009,57(1-2):25-35.
[15]Kia Arman K,Naser F,Henry P L.A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter[J].Communications in Nonlinear Science&Numerical Simulation,2009,14(3):863-879.
[16]Wang Yaqing,Zhou Shangbo.Image encryption algorithm based on fractional-order Chen chaotic system[J].Journal of Computer Applications,2013,33(4):1043-1046.
[17]王力,吕秀宾.基于IBE加密算法的远程抄表系统的优化[J].无线电通信技术,2016,42(1):86-88.
[18]Zhao Jianfeng,Wang Shuying,Chang Yingxiang,et al.A novel image encryption scheme based on an improper fractional-order chaotic system[J].Nonlinear Dynamics,2015,80:1721-1729.
[19]贺少波,孙克辉,王会海.分数阶混沌系统的Adomian分解法求解及其复杂性分析[J].物理学报,2014,63(3):030502.
[20]LüJinhu,Chen Guanrong,Chen Daizhan,et al.Bridge the gap between the Lorenz system and Chen system[J].International Journal of Bifucation and Chaos,2002,12(12):2917-2976.