混沌密码学在图像加密中的应用
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摘要
在信息时代,越来越多的信息在网络中传输。网络信息安全与保密问题显得愈发重要和突出,这也引起各国政府的高度重视。由于传统的加密方法并不能完全有效地用于数据量大的实时传输多媒体信息的加密,多媒体信息的隐藏和加密技术成为一个非常具有挑战性的课题。近几年来,混沌同步及其在保密通信中的应用引起了人们的广泛兴趣,混沌的特殊性质使得混沌密码技术成为信息科学与技术中的一个重要研究领域。混沌现象作为非线性动力系统中一种确定的类随机过程,广泛存在于客观世界中。由于混沌动力系统对初始条件的极端敏感性,而能产生大量的非周期、连续宽带频谱、似噪声且可再生的混沌信号,使它具有天然的隐蔽性,再加上混沌信号的长期不可预测性,高复杂性和易于实现,对该问题的研究,将具有十分重要的理论意义和实际应用价值,将混沌理论应用于密码学已成为目前国内外关注的学术热点和前沿课题。
本文主要研究混沌序列密码的设计与实现的有关问题,以及将混沌序列用于图像加解密的算法。论文系统的介绍了混沌保密通信技术的发展情况,对现代密码学的基本原理进行了阐述。着重讨论了混沌序列在密码学中的应用,提出了一种新的混沌映射,并对其初始条件为有限小数的非轨道进行了证明。在此基础上,提出了一种新的基于复合混沌的加密算法,并对其进行了详细描述。接下来通过实验对该算法进行计算机仿真,对其多方面性能(包括密钥空间,密钥敏感性以及统计特性)进行了分析计算。仿真实验表明该算法的加解密对外部密钥极端敏感,它有巨大的密钥空间,并且具有良好的统计特性。
论文最后对研究工作进行了概括总结,并对将来的研究方向做出了展望。
In this information age, with the technology of the communication and internet, more and more messages are transmitted in the internet. The security of messages became more and more important that make the encryption theory and technology to be a primary domain of the information science and technology. Many governments have attached great importance to thereveal of messages. Chaos widely exists in our natural world as a series of stochastic process in non-linear deterministic dynamical system. Because chaos is extremely sensitive to initial conditions of the chaotic system, and a large number of non-periodic, continuous broadband frequency spectrum, noise-like, yet deterministic and reproducible signals can be generated, it has natural concealment. What's more, chaotic signals can't be forecast for a long term, and it is extremely complicated, and easily realized, the application of chaos theory has been one of important issues and forefront project.
This work mainly includes the design and realization of the chaotic cryptography, especially the cryptography algorithms of images that used chaotic sequences. The author scientifically introduced the development of the chaotic security communication and the principle of modern cryptography. This work pays emphasis on the application of chaotic sequences in cryptography and the theoretical analysis of their performances and proposed a novel chaos map. We also proofed that the orbits of the map wre aperiodic if the initial conditionis a rational number. On this basis, the author proposed an image encryption algorithm. At first, the work described the algorithm's details, and then simulated the algorithm in the computer in order to analyze the performances(such as key spaces, sensitivity of the key and the statistical performances)of the algorithm. The results of the simulation showed that the algorithm based on mixed chaotic dynamic systems is greatly sensitive to the key and the algorithm has a large space of the key, a good encryption speed. Moreover, a better security performance of the statistical analysis is acquired.
The paper finally has carried on the summary to the researchwork, and has made the forecast to the future research direction.
本文主要研究混沌序列密码的设计与实现的有关问题,以及将混沌序列用于图像加解密的算法。论文系统的介绍了混沌保密通信技术的发展情况,对现代密码学的基本原理进行了阐述。着重讨论了混沌序列在密码学中的应用,提出了一种新的混沌映射,并对其初始条件为有限小数的非轨道进行了证明。在此基础上,提出了一种新的基于复合混沌的加密算法,并对其进行了详细描述。接下来通过实验对该算法进行计算机仿真,对其多方面性能(包括密钥空间,密钥敏感性以及统计特性)进行了分析计算。仿真实验表明该算法的加解密对外部密钥极端敏感,它有巨大的密钥空间,并且具有良好的统计特性。
论文最后对研究工作进行了概括总结,并对将来的研究方向做出了展望。
In this information age, with the technology of the communication and internet, more and more messages are transmitted in the internet. The security of messages became more and more important that make the encryption theory and technology to be a primary domain of the information science and technology. Many governments have attached great importance to thereveal of messages. Chaos widely exists in our natural world as a series of stochastic process in non-linear deterministic dynamical system. Because chaos is extremely sensitive to initial conditions of the chaotic system, and a large number of non-periodic, continuous broadband frequency spectrum, noise-like, yet deterministic and reproducible signals can be generated, it has natural concealment. What's more, chaotic signals can't be forecast for a long term, and it is extremely complicated, and easily realized, the application of chaos theory has been one of important issues and forefront project.
This work mainly includes the design and realization of the chaotic cryptography, especially the cryptography algorithms of images that used chaotic sequences. The author scientifically introduced the development of the chaotic security communication and the principle of modern cryptography. This work pays emphasis on the application of chaotic sequences in cryptography and the theoretical analysis of their performances and proposed a novel chaos map. We also proofed that the orbits of the map wre aperiodic if the initial conditionis a rational number. On this basis, the author proposed an image encryption algorithm. At first, the work described the algorithm's details, and then simulated the algorithm in the computer in order to analyze the performances(such as key spaces, sensitivity of the key and the statistical performances)of the algorithm. The results of the simulation showed that the algorithm based on mixed chaotic dynamic systems is greatly sensitive to the key and the algorithm has a large space of the key, a good encryption speed. Moreover, a better security performance of the statistical analysis is acquired.
The paper finally has carried on the summary to the researchwork, and has made the forecast to the future research direction.
引文
1 Lorenz.E.N.Deterministic Nonperiodic Flow.Atmospheric Sciences.1963,20(2):130-141
2 Li.T.Y,York.J A.Period Three Implies Chaos.Amer Math Monthly.1975,82(10):985-992
3 Pecora.L.M,Carroll.T.L.Driving Systems with Chaotic Signals.Phys Rev A.1991,44(4):2374-2382
4 Parker.A.T,Short.K.M.Reconstructing the Key Stream from a Chaotic Encryption Scheme.IEEE Transactions on Circuits Systems.2001,48(5):624-630
5 Scott Hayes,Celso Crebogi,Edward Ott.Communication with Chaos.Phys Rev Lett.1993,70(20):3031-3034
6 盛昭翰,马军海.非线性动力系统分析引论.科学出版社,2001:191-196
7 陈关荣.控制非线性动力系统的混沌现象.控制理论与应用.1997,4(1):1-6
8 Andreas Abel,Wolfgang Schwarz.Chaos Communications—Principles,Schemes,and System Analysis.In:Proceeding of the IEEE.2002,90(5):691-710
9 Goce.Jakimoski,L.J.Kocarev.Chaos and Cryptography:Block Encryption Ciphers Based on Chaotic Maps.IEEE Transactions on Circuits Systems.2001,48(2):163-169
10 陈关荣,汪小帆.动力系统的混沌化—理论、方法与应用.上海交通大学出版社.2006:1-2
11 李力.基于混沌理论的密码算法研究和实现.中南大学硕士毕业论文.200:7-10
12 杨义先,林须端.编码密码学.人民邮电出版社,1992:52-56
13 Chen.G.Chaos:Control and Anticontrol.IEEE Circuits and Systems Society Newsletter.1998,9(1):1-5
14 郝鸣奇.混沌技术与序列密码结合的研究.哈尔滨工业大学硕士毕业论文.2005,14-17
15 赵耿,方锦清.现代信息安全与混沌保密通信应用研究的进展.物理学 进展.2003,23(2):212-255
16 吴祥兴,陈忠.混沌学导论.上海科学技术文献出版社,1996,57-66
17 邹恩,李祥飞,陈建国.混沌控制及其优化应用.国防科技大学出版社,2002:1180146
18 Coppersmith.D,Kawczys.H and Mansour.Y..The Shrinking Generator.Advances in Cryptology-Crypto'93.Springer-Verlag,1994:22-3 5
19 王光瑞,陈光旨.非线性常微分方程的混沌运动.广西科学技术出版社,1995:26-30
20 顾勤龙.混沌理论及其在信息安全和优化中的应用研究.浙江工业大学出版社,2003:85-88
21 范艺.一种混沌图像加密系统及混沌信号发生器研究.华南理工大学硕士毕业论文.2005:18-23
22 禹思敏,林清华,丘水生.四维系统中多涡卷混沌与超混沌吸引子的仿真研究.物理学报.2003,52(1):25-33
23 Shannon C.E.Communication Theory of Secrecy Systems.Bell System Technology Journal.1949,28(4):656-715
24 Namajunas.A,Tamasevicius.A.Simple RC Chaotic Oscillator.Electronics Lett.1996,32(11):945-946
25 Kolumban.G,Kennedy.M.P,Chua.L.O.The Role of Synchronization in Digital Communications Using Chaos-Part Ⅱ:Chaotic Modulation and Chaotic Synchronization.IEEE Transactions on Circuits Systems Part Ⅰ.1998,45(11):1129-1140
26 Tiegang Gao,Zengqiang Chen.A New Image Encryption Algorithm Based on Hyper-chaos.Physics Letters A.2008,372(4):394-400
27 易开祥,孙鑫,石教英.一种基于混沌序列的图像加密算法计算机辅助设计与图形学学报.2000,12(9):672-676
28 J.M.Amig,L.Kocarev.Theory and Practice of Chaotic Cryptography.Physics Letters A.2007,366(4):211-216
29 N.K.Pareek,Vinod Patidar.Cryptography Using Multiple One-dimensional Chaotic Maps.Communications in Non-linear Science and Numerical Simulation.2005,10(7):715-723
30 Chuan-Kuei Huang,Hsiau-Hsian Nien.Image Encryption with Chaotic Random Codes by Grey Relational Grade and Taguchi Method.Optic Communications.2007,280(2):300-310
31 Tao Xiang,Kwok-wo Wong.An Improved Chaotic Cryptosystem with External Key.Communications in Nonlinear Science and Numerical Simulation.2008,13(9):1879-1887
32 李雄军,彭建华,徐宁.基于二维超混沌序列的图像加密算法.中国图像图形学报.2003,8(10):1172-1176
33 Guanrong C,Yaobin M,Charles K.C.A Symmetric Image Encryption Scheme Based on 3D Chaotic Cat Maps.Chaos,Solitons & Fractals.2004,21(3):749-761
34 邹建成,李国富,齐东旭.广义Gray码及其在数字图像置乱中的应用.高校应用数学学报A辑.2002,17(3):363-370
35 XiaoJun Tong,MingGeng Cui.Image Encryption with Compound Chaotic Sequence Cipher Shifting Dynamically.Image vicion computing.2008,26(6):843-850
36 翁贻方,鞠磊.基于混沌的序列密码加密算法.计算机工程.2002,28(11):79-80
37 卢侃,孙建华,欧阳荣百等.混沌动力学.上海翻译出版公司,1990
38 Fridrich J.Symmetric Ciphers Based on Two-Dimensional Chaotic Maps.Int.J.Bifurcation and Chaos.1998,8(6):1259-1284
39 丁玖,周爱辉.确定性系统的统计性质.清华大学出版社,2006
40 K W Wong.A Fast Chaotic Cryptographic Cheme with Cynamic Look-up Table.Phys Lett A.2002,298(4):238-242
41 Roland Schmitz.Use of Chaotic Dynamical Systems in Cryptography.The Franklin Institute.2001,328(6):429-441
42 方洪,崔国华.信息安全导论.华中科技大学出版社,2005
43 Hua C,Yang B,Ouyang G.A New Chaotic Secure Communication Scheme.Phys Lett A.2005,342(5):395-308
44 李昌刚,韩正之,张浩然.一种基于指数性混沌序列的灰度图像加密算法.计算机工程与应用.2002,26(3):16-17
45 Dongxu Q,Zou Q,Cheng J.A New Class of Scrambling Transformationg and Its Application in the Image Information Covering.Chinese in Science (Series E).2000,43(3):304-312
46 肖要强,王玲.基于超混沌的活动图像的加密新方法.计算机工程与应 用.2004,40(35):53-54
47 Shujun L,Xuanqin M,Yuanglong C.Improving Security of Chaotic Encryption Approach.Physics Letters A.2001,290(3-4):127-133
48 郝文化.MATLAB图形图像处理应用教程.中国水利水电出版社,2004:28-43
49 R.A.Rueppel.Linear Complexity and Random Sequences.Advances in Cryptology-EURO CRYPT.1986,219(5):167-188
50 Kocarev.L,Halle.K.S,Eckert.K,et al.Experimental Demonstration of Decure Communications ViaChaotic Synchronization.Int.J.Bifurc.Chaos.1992,2(3):709-713
51 Kocarev L,Jakimoski G..Logistic Map as a Block Encryption Algorithm.Phys Lett A,2001,289(4):199-206
2 Li.T.Y,York.J A.Period Three Implies Chaos.Amer Math Monthly.1975,82(10):985-992
3 Pecora.L.M,Carroll.T.L.Driving Systems with Chaotic Signals.Phys Rev A.1991,44(4):2374-2382
4 Parker.A.T,Short.K.M.Reconstructing the Key Stream from a Chaotic Encryption Scheme.IEEE Transactions on Circuits Systems.2001,48(5):624-630
5 Scott Hayes,Celso Crebogi,Edward Ott.Communication with Chaos.Phys Rev Lett.1993,70(20):3031-3034
6 盛昭翰,马军海.非线性动力系统分析引论.科学出版社,2001:191-196
7 陈关荣.控制非线性动力系统的混沌现象.控制理论与应用.1997,4(1):1-6
8 Andreas Abel,Wolfgang Schwarz.Chaos Communications—Principles,Schemes,and System Analysis.In:Proceeding of the IEEE.2002,90(5):691-710
9 Goce.Jakimoski,L.J.Kocarev.Chaos and Cryptography:Block Encryption Ciphers Based on Chaotic Maps.IEEE Transactions on Circuits Systems.2001,48(2):163-169
10 陈关荣,汪小帆.动力系统的混沌化—理论、方法与应用.上海交通大学出版社.2006:1-2
11 李力.基于混沌理论的密码算法研究和实现.中南大学硕士毕业论文.200:7-10
12 杨义先,林须端.编码密码学.人民邮电出版社,1992:52-56
13 Chen.G.Chaos:Control and Anticontrol.IEEE Circuits and Systems Society Newsletter.1998,9(1):1-5
14 郝鸣奇.混沌技术与序列密码结合的研究.哈尔滨工业大学硕士毕业论文.2005,14-17
15 赵耿,方锦清.现代信息安全与混沌保密通信应用研究的进展.物理学 进展.2003,23(2):212-255
16 吴祥兴,陈忠.混沌学导论.上海科学技术文献出版社,1996,57-66
17 邹恩,李祥飞,陈建国.混沌控制及其优化应用.国防科技大学出版社,2002:1180146
18 Coppersmith.D,Kawczys.H and Mansour.Y..The Shrinking Generator.Advances in Cryptology-Crypto'93.Springer-Verlag,1994:22-3 5
19 王光瑞,陈光旨.非线性常微分方程的混沌运动.广西科学技术出版社,1995:26-30
20 顾勤龙.混沌理论及其在信息安全和优化中的应用研究.浙江工业大学出版社,2003:85-88
21 范艺.一种混沌图像加密系统及混沌信号发生器研究.华南理工大学硕士毕业论文.2005:18-23
22 禹思敏,林清华,丘水生.四维系统中多涡卷混沌与超混沌吸引子的仿真研究.物理学报.2003,52(1):25-33
23 Shannon C.E.Communication Theory of Secrecy Systems.Bell System Technology Journal.1949,28(4):656-715
24 Namajunas.A,Tamasevicius.A.Simple RC Chaotic Oscillator.Electronics Lett.1996,32(11):945-946
25 Kolumban.G,Kennedy.M.P,Chua.L.O.The Role of Synchronization in Digital Communications Using Chaos-Part Ⅱ:Chaotic Modulation and Chaotic Synchronization.IEEE Transactions on Circuits Systems Part Ⅰ.1998,45(11):1129-1140
26 Tiegang Gao,Zengqiang Chen.A New Image Encryption Algorithm Based on Hyper-chaos.Physics Letters A.2008,372(4):394-400
27 易开祥,孙鑫,石教英.一种基于混沌序列的图像加密算法计算机辅助设计与图形学学报.2000,12(9):672-676
28 J.M.Amig,L.Kocarev.Theory and Practice of Chaotic Cryptography.Physics Letters A.2007,366(4):211-216
29 N.K.Pareek,Vinod Patidar.Cryptography Using Multiple One-dimensional Chaotic Maps.Communications in Non-linear Science and Numerical Simulation.2005,10(7):715-723
30 Chuan-Kuei Huang,Hsiau-Hsian Nien.Image Encryption with Chaotic Random Codes by Grey Relational Grade and Taguchi Method.Optic Communications.2007,280(2):300-310
31 Tao Xiang,Kwok-wo Wong.An Improved Chaotic Cryptosystem with External Key.Communications in Nonlinear Science and Numerical Simulation.2008,13(9):1879-1887
32 李雄军,彭建华,徐宁.基于二维超混沌序列的图像加密算法.中国图像图形学报.2003,8(10):1172-1176
33 Guanrong C,Yaobin M,Charles K.C.A Symmetric Image Encryption Scheme Based on 3D Chaotic Cat Maps.Chaos,Solitons & Fractals.2004,21(3):749-761
34 邹建成,李国富,齐东旭.广义Gray码及其在数字图像置乱中的应用.高校应用数学学报A辑.2002,17(3):363-370
35 XiaoJun Tong,MingGeng Cui.Image Encryption with Compound Chaotic Sequence Cipher Shifting Dynamically.Image vicion computing.2008,26(6):843-850
36 翁贻方,鞠磊.基于混沌的序列密码加密算法.计算机工程.2002,28(11):79-80
37 卢侃,孙建华,欧阳荣百等.混沌动力学.上海翻译出版公司,1990
38 Fridrich J.Symmetric Ciphers Based on Two-Dimensional Chaotic Maps.Int.J.Bifurcation and Chaos.1998,8(6):1259-1284
39 丁玖,周爱辉.确定性系统的统计性质.清华大学出版社,2006
40 K W Wong.A Fast Chaotic Cryptographic Cheme with Cynamic Look-up Table.Phys Lett A.2002,298(4):238-242
41 Roland Schmitz.Use of Chaotic Dynamical Systems in Cryptography.The Franklin Institute.2001,328(6):429-441
42 方洪,崔国华.信息安全导论.华中科技大学出版社,2005
43 Hua C,Yang B,Ouyang G.A New Chaotic Secure Communication Scheme.Phys Lett A.2005,342(5):395-308
44 李昌刚,韩正之,张浩然.一种基于指数性混沌序列的灰度图像加密算法.计算机工程与应用.2002,26(3):16-17
45 Dongxu Q,Zou Q,Cheng J.A New Class of Scrambling Transformationg and Its Application in the Image Information Covering.Chinese in Science (Series E).2000,43(3):304-312
46 肖要强,王玲.基于超混沌的活动图像的加密新方法.计算机工程与应 用.2004,40(35):53-54
47 Shujun L,Xuanqin M,Yuanglong C.Improving Security of Chaotic Encryption Approach.Physics Letters A.2001,290(3-4):127-133
48 郝文化.MATLAB图形图像处理应用教程.中国水利水电出版社,2004:28-43
49 R.A.Rueppel.Linear Complexity and Random Sequences.Advances in Cryptology-EURO CRYPT.1986,219(5):167-188
50 Kocarev.L,Halle.K.S,Eckert.K,et al.Experimental Demonstration of Decure Communications ViaChaotic Synchronization.Int.J.Bifurc.Chaos.1992,2(3):709-713
51 Kocarev L,Jakimoski G..Logistic Map as a Block Encryption Algorithm.Phys Lett A,2001,289(4):199-206