二维反三角超混沌系统及其在图像加密上的应用
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摘要
为了进一步提高混沌系统的混沌特性,为图像加密算法提供更可靠的混沌系统,增强图像加密算法的安全性,提出了一种基于二维反三角超混沌系统的新型图像加密算法。首先,在一维三角混沌函数的基础上构建了一个二维反三角超混沌系统,通过分岔图和Lyapunov指数等仿真实验,验证了该系统具有更广的混沌区间和更强随机性的迭代序列,遍历性更加优秀;然后,基于此混沌系统,采用"置乱-扩散"策略,根据不同密钥生成的不同超混沌序列,对图像矩阵进行无重复置乱和循环移位扩散,循环三次得到密文,完成加密过程;最后,对图像加密方案进行了直方图分析、密钥空间分析、相邻像素相关性分析、明文敏感性分析和信息熵分析等性能测试。其中密文图像的相关指标参数像素变化率(NPCR)和统一平均变化强度(UACI)的测试值非常接近于它们的理想期望值,信息熵的测试结果约为7. 997,也非常接近于理想期望值8。实验结果表明,此图像加密系统具有更可靠的安全性,抵抗攻击能力强,在图像安全领域具有较好的应用前景。
In order to improve chaos complexity and provide more reliable chaotic system for image encryption, and enhance the security of image encryption algorithm, a new image encryption algorithm based on two-dimensional inversetrigonometric hyperchaotic system was proposed. Firstly, based on one-dimensional triangular function, a two-dimensional inverse-trigonometric hyperchaotic system was constructed. Compared with some two-dimensional chaotic systems, this system had wider chaotic range, more random iteration sequences and better ergodicity by simulation experiments about bifurcation diagram and Lyapunov exponent. Then based on the proposed chaotic system, the scrambling-diffusion strategy was designed and different keys were given, which were used to generate different hyperchaotic sequences. The image matrix was scrambled without repetition by hyperchaotic sequences, then the scrambled sequence were shifted and diffused. So the ciphertext was obtained by looping thrice. Finally, histogram analysis, key space analysis, correlation analysis of adjacent pixels, plaintext sensitivity analysis and information entropy analysis were carried out. The test values of Number of Pixels Change Rate( NPCR) and Unified Average Changing Intersity( UACI) of ciphertext images were very close to their ideal expected values.The test results of information entropy were about 7. 997, which was also very close to the expected value of 8. The experimental results show that the image encryption system has more reliable security, stronger ability to resist attacks, and had a good application prospect in the field of image security.
In order to improve chaos complexity and provide more reliable chaotic system for image encryption, and enhance the security of image encryption algorithm, a new image encryption algorithm based on two-dimensional inversetrigonometric hyperchaotic system was proposed. Firstly, based on one-dimensional triangular function, a two-dimensional inverse-trigonometric hyperchaotic system was constructed. Compared with some two-dimensional chaotic systems, this system had wider chaotic range, more random iteration sequences and better ergodicity by simulation experiments about bifurcation diagram and Lyapunov exponent. Then based on the proposed chaotic system, the scrambling-diffusion strategy was designed and different keys were given, which were used to generate different hyperchaotic sequences. The image matrix was scrambled without repetition by hyperchaotic sequences, then the scrambled sequence were shifted and diffused. So the ciphertext was obtained by looping thrice. Finally, histogram analysis, key space analysis, correlation analysis of adjacent pixels, plaintext sensitivity analysis and information entropy analysis were carried out. The test values of Number of Pixels Change Rate( NPCR) and Unified Average Changing Intersity( UACI) of ciphertext images were very close to their ideal expected values.The test results of information entropy were about 7. 997, which was also very close to the expected value of 8. The experimental results show that the image encryption system has more reliable security, stronger ability to resist attacks, and had a good application prospect in the field of image security.
引文
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[12]LI C, LIN D, LU J. Cryptanalyzing an image-scrambling encryption algorithm of pixel bits[J]. IEEE Multimedia, 2017, 24(3):64-71.
[13]CHEN J X, HUA F F, QIAN W, et al. Cryptanalysis and improvement in an image encryption scheme using combination of the1D chaotic map[J]. Nonlinear Dynamics, 2018, 93(4):2399-2413.
[14]ZHU H G, ZHANG X D, YU H, et al. A novel image encryption scheme using the composite discrete chaotic system[J]. Entropy,2016, 18(8):276-302.
[15]ZHU H G, ZHANG X D, YU H, et al. An image encryption algorithm based on compound homogeneous hyper-chaotic system[J].Nonlinear Dynamics, 2017, 89(1):61-79.
[16]谷帆,唐晨,苏永钢.基于离散余弦变换与二维Ushiki混沌的图像加密[J].光学技术,2017,43(4):319-328.(GU F, TANG C, SU Y G. Image encryption based on discrete cosine transform and Ushiki map[J]. Optical Technique, 2017, 43(4):319-328.)
[17]于万波,赵斌.曲面迭代混沌特性研究[J].物理学报,2014,63(12):35-45.(YU W B, ZHAO B. A new chaotic attractor graphics drawing method based on the curved iteration[J]. Acta Physica Sinica, 2014, 63(12):35-45.)
[18]方鹏飞,吴成茂,王保平.反馈移位寄存器和三角混沌相结合的加密算法[J].小型微型计算机系统,2014,35(3):630-635.(FANG P F, WU C M, WANG B P. Linear feedback shift register and triangular chaotic system encryption algorithm combining[J].Journal of Chinese Computer Systems, 2014, 35(3):630-635.)
[19]刘会师,余重秀,尹霄丽,等.切比雪夫光混沌发生器的优化[J].物理学报,2009,58(4):2231-2234.(LIU H S, YU C X,YIN X L, et al. An optimization scheme for generating of Cheby-shev optical chaotic sequence[J]. Acta Physica Sinica, 2009,58(4):2231-2234.)
[20]甘建超,肖先赐.混沌的可加性[J].物理学报,2003,52(5):1085-1090.(GAN J C, XIAO X C. Characteristic of addition of chaos[J]. Acta Physica Sinica, 2003, 52(5):1085-1090.)
[21]于津江,曹鹤飞,许海波,等.复合混沌系统的非线性动力学行为分析[J].物理学报,2006,55(1):29-34.(YU J J, CAO H F,XU H B, et al. Nonlinear dynamic behaviors of complex chaotic systems[J]. Acta Physica Sinica, 2006, 55(1):29-34.)
[22]ZHU H G, ZHANG X D, YU H, et al. An image encryption algorithm based on compound homogeneous hyper-chaotic system[J].Nonlinear Dynamics, 2017, 89(1):61-79.
[23]HUA Z Y, ZHOU Y C. Image encryption using 2D Logistic adjusted Sine map[J]. Information Sciences, 2016, 339(C):237-253.
[24]NOROUZI B, SEYEDZADEH S M, MIRZAK-UCHAKI S, et al.A novel image encryption based on row-column, masking and main diffusion processes with hyper chaos[J]. Multimedia Tools and Applications, 2013, 74(3):781-811.
[25]徐扬,黄迎久,李海荣.一个切换Lorenz混沌系统在图像加密中的应用[J].包装工程,2018,39(5):179-184.(XU Y, HUANG Y J, LI H R. Application of a switched Lorenz chaotic system in image encryption[J]. Packaging Engineering, 2018, 39(5):179-184.)
[26]ZHOU, Y C, BAO L, CHEN C L P. A new 1D chaotic system for image encryption[J]. Signal Processing, 2014, 97(7):172-182.
[27]王静,蒋国平.一种超混沌图像加密算法的安全性分析及其改进[J].物理学报,2011,60(6):83-93.(WANG J, JIANG G P.Cryptanalysis of a hyperchaotic image encryption algorithm and its improved version[J]. Acta Phsica Sinica, 2011,60(6):83-93.)
[28]林青,王延江,王珺.基于超混沌系统的图像加密算法[J].中国科学(技术科学),2016,46(9):910-918.(LIN Q, WANG Y J,WANG J. The image encryption scheme with optional dynamic state variables based on hyperchaotic system[J]. Scientia Sinica Technologica, 2016, 46(9):910-918.)
[2]MATTEWS R. On the derivation of aChaotic Encryption Algorithm[J]. Cryptologia, 1989, 8(8):29-42.
[3]FRIDRICH J. Symmetric ciphers based on two-dimensional chaotic maps[J]. International Journal of Bifurcation and Chaos, 1998, 8(6):1259-1284.
[4]TANG G, WANG S, LU H, et al. Chaos-based cryptograph incorporated with S-box algebraic operation[J]. Physics Letters A, 2003,318(4):388-398.
[5]CHEN G R, MAO Y, CHUI C K. A symmetric image encryption scheme based on 3D chaotic Cat maps[J]. Chaos Solitons and Fractals, 2004, 21(3):749-761.
[6]MAO Y, CHEN G R, LIAN S. A novel fast image encryption scheme based on 3D chaotic Baker maps[J]. International Journal of Bifurcation and Chaos, 2004, 14(10):3613-3624.
[7]ZHANG Y. Plaintext related image encryption scheme using chaotic map[J]. Telkomnika, 2014, 12(1):635-643.
[8]ZHANG Y, XIA J, CAI P, et al. Plaintext related two-level secret key image encryption scheme[J]. Telkomnika, 2012, 10(6):1254-1262.
[9]ZHANG Y. A chaotic system based image encryption algorithm using plaintext-related confusion[J]. Telkomnika, 2014, 12(11):7952-7962.
[10]ZHANG Y. The image encryption algorithm with plaintext-related shuffling[J]. IETE Technical Review, 2015, 33(3):310-322.
[11]刘乐鹏,张雪锋.基于混沌和位运算的图像加密算法[J].计算机应用,2013,33(4):1070-1073.(LIU L P, ZHANG X F. Image encryption algorithm based on chaos and bit operations[J].Journal of Computer Applications, 2013, 33(4):1070-1073.)
[12]LI C, LIN D, LU J. Cryptanalyzing an image-scrambling encryption algorithm of pixel bits[J]. IEEE Multimedia, 2017, 24(3):64-71.
[13]CHEN J X, HUA F F, QIAN W, et al. Cryptanalysis and improvement in an image encryption scheme using combination of the1D chaotic map[J]. Nonlinear Dynamics, 2018, 93(4):2399-2413.
[14]ZHU H G, ZHANG X D, YU H, et al. A novel image encryption scheme using the composite discrete chaotic system[J]. Entropy,2016, 18(8):276-302.
[15]ZHU H G, ZHANG X D, YU H, et al. An image encryption algorithm based on compound homogeneous hyper-chaotic system[J].Nonlinear Dynamics, 2017, 89(1):61-79.
[16]谷帆,唐晨,苏永钢.基于离散余弦变换与二维Ushiki混沌的图像加密[J].光学技术,2017,43(4):319-328.(GU F, TANG C, SU Y G. Image encryption based on discrete cosine transform and Ushiki map[J]. Optical Technique, 2017, 43(4):319-328.)
[17]于万波,赵斌.曲面迭代混沌特性研究[J].物理学报,2014,63(12):35-45.(YU W B, ZHAO B. A new chaotic attractor graphics drawing method based on the curved iteration[J]. Acta Physica Sinica, 2014, 63(12):35-45.)
[18]方鹏飞,吴成茂,王保平.反馈移位寄存器和三角混沌相结合的加密算法[J].小型微型计算机系统,2014,35(3):630-635.(FANG P F, WU C M, WANG B P. Linear feedback shift register and triangular chaotic system encryption algorithm combining[J].Journal of Chinese Computer Systems, 2014, 35(3):630-635.)
[19]刘会师,余重秀,尹霄丽,等.切比雪夫光混沌发生器的优化[J].物理学报,2009,58(4):2231-2234.(LIU H S, YU C X,YIN X L, et al. An optimization scheme for generating of Cheby-shev optical chaotic sequence[J]. Acta Physica Sinica, 2009,58(4):2231-2234.)
[20]甘建超,肖先赐.混沌的可加性[J].物理学报,2003,52(5):1085-1090.(GAN J C, XIAO X C. Characteristic of addition of chaos[J]. Acta Physica Sinica, 2003, 52(5):1085-1090.)
[21]于津江,曹鹤飞,许海波,等.复合混沌系统的非线性动力学行为分析[J].物理学报,2006,55(1):29-34.(YU J J, CAO H F,XU H B, et al. Nonlinear dynamic behaviors of complex chaotic systems[J]. Acta Physica Sinica, 2006, 55(1):29-34.)
[22]ZHU H G, ZHANG X D, YU H, et al. An image encryption algorithm based on compound homogeneous hyper-chaotic system[J].Nonlinear Dynamics, 2017, 89(1):61-79.
[23]HUA Z Y, ZHOU Y C. Image encryption using 2D Logistic adjusted Sine map[J]. Information Sciences, 2016, 339(C):237-253.
[24]NOROUZI B, SEYEDZADEH S M, MIRZAK-UCHAKI S, et al.A novel image encryption based on row-column, masking and main diffusion processes with hyper chaos[J]. Multimedia Tools and Applications, 2013, 74(3):781-811.
[25]徐扬,黄迎久,李海荣.一个切换Lorenz混沌系统在图像加密中的应用[J].包装工程,2018,39(5):179-184.(XU Y, HUANG Y J, LI H R. Application of a switched Lorenz chaotic system in image encryption[J]. Packaging Engineering, 2018, 39(5):179-184.)
[26]ZHOU, Y C, BAO L, CHEN C L P. A new 1D chaotic system for image encryption[J]. Signal Processing, 2014, 97(7):172-182.
[27]王静,蒋国平.一种超混沌图像加密算法的安全性分析及其改进[J].物理学报,2011,60(6):83-93.(WANG J, JIANG G P.Cryptanalysis of a hyperchaotic image encryption algorithm and its improved version[J]. Acta Phsica Sinica, 2011,60(6):83-93.)
[28]林青,王延江,王珺.基于超混沌系统的图像加密算法[J].中国科学(技术科学),2016,46(9):910-918.(LIN Q, WANG Y J,WANG J. The image encryption scheme with optional dynamic state variables based on hyperchaotic system[J]. Scientia Sinica Technologica, 2016, 46(9):910-918.)