第1期 臧鸿雁等：基于离散混沌系统广义同步定理的数字图像加密方案 101. [10]Celikovsky S,Chen G R.Secure synchronization of a class of nization and applications.J Univ Sci Technol Beijing.2000.7 chaotic systems from a nonlinear observe approach.IEEE Trans (3):225 Autom Control.2005.50(1):76 [14]Min L,Zhang X,Yang M.Secure communication by general- [11]Yang S S.Duan C K.Generalized synchronization in chaotic ized chaotic synchronization.JUniv Sci Technol Beijing.2003. system.Chaos Solitons Fractals.1998.9:1703 10(2):75 [12]Brown R.Kocarev L.A unifying definition of synchronization [15]Min L,Chen G.Zhang X.et al.Approach to generalized syn- for dynamical systems.Chaos,2002.10:344 chronization with application to chaos-based secure communica- [13]Zhang X.Min L.Theory for constructing generalized synchro tion.Commun Theory Phys,2004.41:632 An image encryption scheme based on generalized synchronization theorem for dis- crete chaos system ZANG Hongyan,MIN Lequan,WU Chunxue,ZHAO Geng2) 1)Applied Science School.University of Science and Technology Beijing,Beijing 100083.China 2)Department of Computer Science.Beijing Electronic Science and Technology Institute.Beijing 100070.China ABSTRACT A constructive theorem of generalized synchronization for discrete chaos systems is established. Based on the theorem,a generalized chaotic synchronization discrete system was constructed.Combining this system with the Henon chaotic mapping designs a digital image encryption scheme,which can successfully en- crypt and decrypt gray-scale images without any lost.The scheme is sensitive to perturbations of the parameters and initial conditions of the chaos system Any perturbations which are larger than 105will make correspond- ing decryptions become impossible.The key space of the scheme is as large as 1076.The analysis of key space and key parameter sensitivity shows that the scheme has sound security.Numerical simulations reveal that the scheme is effective in network communication. KEY WORDS image encryption;generalized synchronization;Henon mapping;network secure communication［10］ Celikovsky S‚Chen G R．Secure synchronization of a class of chaotic systems from a nonlinear observe approach．IEEE Trans Autom Control‚2005‚50（1）：76 ［11］ Yang S S‚Duan C K．Generalized synchronization in chaotic system．Chaos Solitons Fractals‚1998‚9：1703 ［12］ Brown R‚Kocarev L．A unifying definition of synchronization for dynamical systems．Chaos‚2002‚10：344 ［13］ Zhang X‚Min L．Theory for constructing generalized synchro￾nization and applications．J Univ Sci Technol Beijing‚2000‚7 （3）：225 ［14］ Min L‚Zhang X‚Yang M．Secure communication by general￾ized chaotic synchronization．J Univ Sci Technol Beijing‚2003‚ 10（2）：75 ［15］ Min L‚Chen G‚Zhang X‚et al．Approach to generalized syn￾chronization with application to chaos-based secure communica￾tion．Commun Theory Phys‚2004‚41：632 An image encryption scheme based on generalized synchronization theorem for dis￾crete chaos system ZA NG Hongyan 1）‚MIN Lequan 1）‚W U Chunxue 1）‚ZHAO Geng 2） 1） Applied Science School‚University of Science and Technology Beijing‚Beijing100083‚China 2） Department of Computer Science‚Beijing Electronic Science and Technology Institute‚Beijing100070‚China ABSTRACT A constructive theorem of generalized synchronization for discrete chaos systems is established． Based on the theorem‚a generalized chaotic synchronization discrete system was constructed．Combining this system with the Henon chaotic mapping designs a digital image encryption scheme‚which can successfully en￾crypt and decrypt gray-scale images without any lost．The scheme is sensitive to perturbations of the parameters and initial conditions of the chaos system．Any perturbations which are larger than10－15will make correspond￾ing decryptions become impossible．The key space of the scheme is as large as1076．The analysis of key space and key parameter sensitivity shows that the scheme has sound security．Numerical simulations reveal that the scheme is effective in network communication． KEY WORDS image encryption；generalized synchronization；Henon mapping；network secure communication 第1期 臧鸿雁等： 基于离散混沌系统广义同步定理的数字图像加密方案 ·101·