摘要
针对加密灰度图像安全级别低的问题,提出基于超混沌系统及其状态观测器实现函数投影同步的混沌时间序列,应用加取模像素扩散算法对灰度图像进行加密和解密.首先,利用超混沌系统的状态输出向量,构造其状态观测器系统,根据控制理论方法,给出超混沌系统及其状态观测器实现函数投影同步的充分条件;然后,基于函数投影同步的混沌时间序列,利用加取模像素扩散算法得到灰度图像的加密图像和解密图像.理论分析和数值仿真表明,构造的状态观测器系统是正确的,得出的函数投影同步的充分条件是有效的,密文图像分布与均匀分布没有显著差异.同时算法对密钥具有高度敏感性,有很强的抵御攻击的能力和精准的解密效果.
To solve the problem of low security level of encrypted gray image,based on chaotic time series from functional projective synchronization of the hyper-chaotic system and its state observer,the"add modulus pixel diffusion algorithm"was used to encrypt and decrypt gray image. The state observer of the hyper-chaotic system was constructed. First,the state observer of the hyper-chaotic system was conducted by using the state output vector of the hyper-chaotic system,and according to control theory method,the sufficient condition of function projective synchronization was given for the hyper-chaotic system and the state observer. Then, based on chaotic time series of functional projective synchronization,encrypted and decrypted images of gray image were obtained by using the"add modulus pixel diffusion algorithm ". Theoretical analysis and numerical simulation show the constructed state observer is correct,the sufficient condition of functional projection synchronization is effective,and there is no significant difference between the encrypted image distribution and the uniform distribution. At the same time,the algorithm is highly sensitive to the key,and has strong ability to resisting attack and has accurate decryption effect.
引文
[1] PECORA L M,CARROLL T L. Synchronization in chaotic system[J]. Physical Review Letters,1990,64(4):821-824.
[2] JUAN L,MATA M,RAFAEL M G,et al. A chaotic system in synchronization and secure communications[J].Commun Nonlinear Sci Numer Simulat,2012,17(4):1706-1713.
[3] LI Z G, XU D L. Stability criterion for projective synchronization in three-dimensional chaotic systems[J].Physical Review Letters,2001,282(3):175-179.
[4] LI G H. Generalized projective synchronization of two chaotic systems by using active control[J]. Chaos Solitons&Fractals,2006,30(1):77-82.
[5] LI C P,YAN J P. Generalized projective synchronization of chaos:the cascade synchronization approach[J].Chaos Solitons&Fractals,2006,30(1):140-146.
[6] LI G H. Modified projective synchronization of chaotic system[J]. Chaos Solitons&Fractals,2007,32(5):1786-1790.
[7] ZHANG R, YANG Y Q, XU Z Y, et al. Function projective synchronization in drive-response dynamical network[J]. Physics Letters A,2010,374(30):3025-3028.
[8]李德奎.激活控制不同维混沌系统的修正函数投影同步[J].延边大学学报,2017,43(2):137-143.LI D K. Active control modified function projective synchronization of different dimensional chaotic systems[J]. Journal of Yanbian university,2017,43(2):137-143.(in Chinese)
[9] HAMED T, SAEID S A, HAMIDREZA T. Chaos synchronization and parameter identification of a finance chaotic system with unknown parameters,a linear feedback controller[J]. Alexandria Engineering Journal,2018,57(3):1519-1524.
[10]李德奎,连玉平,张建刚.时变时滞耦合复杂网络的函数投影同步[J].北京工业大学学报,2015,41(2):207-214.LI D K,LIAN Y P,ZHANG J G. Function projective synchronization of complex networks with time-varying delay coupling[J]. Journal of Beijing University of Technology,2015,41(2):207-214.
[11]盛苏英,吴新华.一种混沌图像加密算法的研究与改进[J].微电子学与计算机,2010,27(10):61-64.SHENG S Y,WU X H. Study and improvement of a chaotic image encryption algorithm[J]. Microelectronics&Computer,2010,27(10):61-64.(in Chinese)
[12]程甲,赵怀勋,朱建杨.基于复合离散混沌系统的图像加密算法[J].计算机工程,2009,35(6):162-163.CHENG J,ZHAO H X,ZHU J Y. Image encryption algorithm based on composite discrete chaotic system[J].Computer Engineering,2009,35(6):162-163.(in Chinese)
[13] CHENG C J,FENG S T, WANG C K. An image encryption algorithm based on adapative synchronization between two different chaotic system[C]∥2010International Conference on Electronics and Information Enginerring. Tokyo:The International Association of Computer Science and Information Technology,2010:487-490.
[14]刘洪娟,朱志良,于海.统一混沌系统的混合同步在图像加密中的应用[J].小型微型计算机系统,2013,34(7):1680-1684.LIU H J, ZHU Z L, YU H. Application of hybrid synchronization of the unified chaotic system in image encryption[J]. Journal of Chinese Computer Systems,2013,34(7):1680-1684.(in Chinese)
[15]黄晗文,韩凤英,杨幸.基于改进的Liu混沌系统序列的图像加密算法[J].计算机工程与应用,2009,45(4):188-191.HUANG H W,HAN F Y,YANG X. Image encryption algorithm based on improved chaotic sequences of Liu system[J]. Computer Engineering and Applications,2009,45(4):188-191.(in Chinese)
[16]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.ZHU C X,SUN K H. Cryptanalysis and improvement of a class of hyperchaos based image encryption algorithms[J]. Acta Phys Sin,2012,61(12):1-12.
[17] GAO T G,CHEN Z Q. New image encryption algorithm based on hyper-chaos[J]. Physics Letters A,2008,372(4):394-400.
[18]易小琳,刘旭辉.基于时空混沌同步的同步密钥生成算法[J].北京工业大学学报,2013,39(5):696-699.YI X L,LIU X H. Synchronized key generation algorithm based on spatiotemporal chaos synchronization[J].Journal of Beijing University of Technology,2013,39(5):696-699.
[19]张学义,陈实如,王文武,等.利用状态观测器实现超混沌信号的高精度同步[J].哈尔滨工程大学学报,2001,22(4):29-34.ZHANG X Y,CHEN S R,WANG W W,et al. High accurate synchronization of super chaos signal using state observers[J]. Journal of Harbin Engineering University,2001,22(4):29-34.(in Chinese)
[20]李德奎.一个新超混沌Lorenz系统的Hopf分岔及电路实现[J].宁夏大学学报,2016,37(3):294-310.LI D K. Hopf bifurcation and circuit implementation of a new hyperchaotic Lorenz system[J]. Journal of Ningxia University,2016,37(3):294-310.(in Chinese)
[21]薛薇. SPSS统计分析方法及应用[M]. 3版.北京:电子工业出版社,2013:141-174.
