基于混沌Gyrator变换与矩阵分解的光学图像加密算法
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摘要
为了解决当前光学图像加密技术没有考虑明文自身特性,使其抗明文攻击能力较低,且易增加密钥的分配与管理难度的问题,设计了基于混沌Gyrator变换与矩阵分解的非对称彩色图像加密算法。首先,从彩色图像中分别获取其R、G、B分量;设计二维耦合混沌系统,生成3个随机相位掩码,分别对R、G、B分量进行调制;基于卷积操作,将调制后的R、G、B分量融合为一幅灰度图像;利用混沌系统输出的随机序列来计算Gyrator机制的旋转角度,对灰度图像完成Gyrator变换,获取Gyrator频谱;根据相位-幅度截断机制,对Gyrator图像完成截断操作,形成幅度与相位信息;再引入一种矩阵分解机制,将相位截断图像分解为酉矩阵与三角矩阵,利用旋转角度不同的Gyrator变换分别处理酉矩阵与三角矩阵,完成图像加密。在图像加密过程中,利用其幅度截断图像信息来生成R、G、B分量的解密密钥,使得加密与解密密钥是截然不同的,只需利用私钥即可解密图像。测试数据表明,与较为主流的光学加密方案相比,所提技术具备更高的安全性,可有效抗击明文攻击。
In order to enhance the ability to resist plain attack and better the management in current optical image encryption technology.An asymmetric color image encryption algorithm based on chaotic Gyrator transform and matrix decomposition was designed in this paper.Firstly,the R,G and B components were obtained from the color image. A two-dimensional coupled chaotic system was designed to generate three random phase masks for modulating R,G and B components respectively. And the modulated R,G and B components were fused into a grayscale image. Then the rotation angle of the Gyrator mechanism was calculated by the random sequence,and the Gyrator transform was used to process the grayscale image for obtaining the Gyrator spectrum. The Gyrator spectrum was processed based on the phase-amplitude truncation mechanism to output two coded images. Finally,the phase truncated image was decomposed into a unitary matrix and a triangular matrix based on matrix decomposition mechanism,and image encryption was completed by using the Gyrator transform of different rotation angles to process the unitary matrix and triangulation matrix. In the process of image encryption,the decryption key of R,G and B components were generated by using its amplitude-truncate image information which make its encryption and decryption key completely different,and the image can be decrypted by only using the private key. The experimental results show that the proposed algorithm has higher security level compared with the current optical image encryption technology.
In order to enhance the ability to resist plain attack and better the management in current optical image encryption technology.An asymmetric color image encryption algorithm based on chaotic Gyrator transform and matrix decomposition was designed in this paper.Firstly,the R,G and B components were obtained from the color image. A two-dimensional coupled chaotic system was designed to generate three random phase masks for modulating R,G and B components respectively. And the modulated R,G and B components were fused into a grayscale image. Then the rotation angle of the Gyrator mechanism was calculated by the random sequence,and the Gyrator transform was used to process the grayscale image for obtaining the Gyrator spectrum. The Gyrator spectrum was processed based on the phase-amplitude truncation mechanism to output two coded images. Finally,the phase truncated image was decomposed into a unitary matrix and a triangular matrix based on matrix decomposition mechanism,and image encryption was completed by using the Gyrator transform of different rotation angles to process the unitary matrix and triangulation matrix. In the process of image encryption,the decryption key of R,G and B components were generated by using its amplitude-truncate image information which make its encryption and decryption key completely different,and the image can be decrypted by only using the private key. The experimental results show that the proposed algorithm has higher security level compared with the current optical image encryption technology.
引文
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[14] WANG X G,ZHAO D M. Multiple-image encryptionbased on nonlinear amplitude-truncation and phase-truncation in Fourier domain[J]. OpticsCommunications,2012,284(1):148-152.
[15]王晓红,孙业强.基于QR码和Schur分解的感兴趣区域水印算法[J].光电子·激光,2017,28(4):419-425.WANG X H,SUN Y Q. Region of interest watermarkingalgorithm based on QR code and schur decomposition[J].Photoelectron Laser,2017,28(4):419-425.
[16] TONG X J,CUI M G. Image encryption scheme based on3D baker with dynamical compound chaotic sequencecipher generator[J]. Signal Processing,2009,89(4):480-491.
[17]王涛涛,张超.基于Diophantus模型与动态S盒的图像加密算法[J].计算机工程与设计,2017,38(10):2678-2685.WANG T T,ZHANG CH. Image encryption algorithmbased on diophantus model and dynamic S box[J].Computer Engineering and Design, 2017, 38(10):2678-2685.
[18]张春艳,李京兵,王双双.基于离散小波变换和感知哈希的加密医学图像检索算法[J].计算机应用,2018,38(2):539-544,572.ZHANG CH Y, LI J B, WANG SH SH. Encryptedmedical image retrieval algorithm based on discretewavelet transform and perceptual hash[J]. Journal ofComputer Applications,2018,38(2):539-544,572.
[19]程云龙.基于忆阻超混沌系统的医学图像加密算法的设计与实现[D].开封:河南大学,2016:28-46.CHENG Y L. Design and implementation of medicalimage encryption algorithm based on memristor hyper-chaos system[D]. Kaifeng:Henan University,2016:28-46.
[20]梁涤青,陈志刚,邓小鸿.基于超混沌映射的医学图像小波域加密算法[J].天津大学学报(自然科学与工程技术版),2016,49(12):1255-1261.LIANG D Q,CHEN ZH G,DENG X H. Wavelet domainencryption algorithm for medical images based onhyperchaotic mapping[J]. Journal of Tianjin University(Natural Science and Engineering Technology),2016,49(12):1255-1261.
[2]李奇,李丹.基于像素随机映射与引力扩散的图像加密算法[J].计算机工程与设计,2017,38(8):2104-2110.LI Q,LI D. Image encryption algorithm based on pixelrandom map and gravitational diffusion[J]. ComputerEngineering and Design,2017,38(8):2104-2110.
[3] OSAMA S,FARAGALLAH A A. Optical color imagecryptosystem using chaotic baker mapping based-doublerandom phase encoding[J]. Optical and QuantumElectronics,2017,49(3):1003-1012.
[4] CHEN H,TANOUGAST C,LIU Z G. Optical imageasymmetric cryptosystem using fingerprint based oniterative fraction Fourier transform[J]. Optical andQuantum Electronics,2017,49(4):802-903.
[5]张国平,黄淼,马丽.基于MGSA融合波分复用的光学彩色图像加密[J].激光杂志,2015,36(7):63-57.ZHANG G B,HUANG M,MA L. Optical color imageencryption based on MGSA fusion the FDM[J]. LaserJournal,2015,36(7):63-57.
[6] CHEN H,TANOUGAST C,LIU Z G,et al. Asymmetricoptical cryptosystem for color image based on equalmodulus decomposition in gyrator transform domains[J].Optics and Lasers in Engineering,2017,93(8):1-8.
[7] MUHAMMAD R A. An asymmetric single-channel colorimage encryption based on hartley transform and gyratortransforms[J]. Optics&Lasers in Engineering,2016,69(8):49-57.
[8]肖宁,李爱军.基于圆谐分量展开与Gyrator变换域相位检索的光学图像加密算法[J].电子测量与仪器学报,2017,31(6):876-884.XIAO N,LI AI J. Optical image encryption algorithmbased on circular harmonic component expansion andphase retrieval in gyrator transform domain[J]. Journal ofElectronic Measurement and Instrumentation, 2017,31(6):876-884.
[9] SUN J L,LIAO X F,CHEN X,et al. Privacy-aware imageencryption based on logistic map and data hiding[J].International Journal of Bifurcation and Chaos,2017,27(5):1750073-1750082.
[10] LEE C C,MANDANGAN A,DAUD M A. On theefficiency of the image encryption and decryption by usinglogistic-sine chaotic system and logistic-tent chaoticsystem[J]. AIP Conference Proceedings,2017,18(1):1-7.
[11] GIULIANO G L,PEDRO J M. Lyapunov exponent forLipschitz maps[J]. Nonlinear Dynamics,2018,92(3):1217-1224.
[12] CHAI X L,CHEN Y R,BROYDE L. A novel chaos-based image encryption algorithm using DNA sequenceoperations[J]. Optics and Lasers in Engineering,2017,88(19):197-213.
[13] ISHA M,SUDHEESH K R,NAVEEN K. Cryptanalysis of animage encryption scheme based on joint transform correlatorwith amplitude-and phase-truncation approach[J]. Opticsand Lasers in Engineering,2014,52(9):167-173.
[14] WANG X G,ZHAO D M. Multiple-image encryptionbased on nonlinear amplitude-truncation and phase-truncation in Fourier domain[J]. OpticsCommunications,2012,284(1):148-152.
[15]王晓红,孙业强.基于QR码和Schur分解的感兴趣区域水印算法[J].光电子·激光,2017,28(4):419-425.WANG X H,SUN Y Q. Region of interest watermarkingalgorithm based on QR code and schur decomposition[J].Photoelectron Laser,2017,28(4):419-425.
[16] TONG X J,CUI M G. Image encryption scheme based on3D baker with dynamical compound chaotic sequencecipher generator[J]. Signal Processing,2009,89(4):480-491.
[17]王涛涛,张超.基于Diophantus模型与动态S盒的图像加密算法[J].计算机工程与设计,2017,38(10):2678-2685.WANG T T,ZHANG CH. Image encryption algorithmbased on diophantus model and dynamic S box[J].Computer Engineering and Design, 2017, 38(10):2678-2685.
[18]张春艳,李京兵,王双双.基于离散小波变换和感知哈希的加密医学图像检索算法[J].计算机应用,2018,38(2):539-544,572.ZHANG CH Y, LI J B, WANG SH SH. Encryptedmedical image retrieval algorithm based on discretewavelet transform and perceptual hash[J]. Journal ofComputer Applications,2018,38(2):539-544,572.
[19]程云龙.基于忆阻超混沌系统的医学图像加密算法的设计与实现[D].开封:河南大学,2016:28-46.CHENG Y L. Design and implementation of medicalimage encryption algorithm based on memristor hyper-chaos system[D]. Kaifeng:Henan University,2016:28-46.
[20]梁涤青,陈志刚,邓小鸿.基于超混沌映射的医学图像小波域加密算法[J].天津大学学报(自然科学与工程技术版),2016,49(12):1255-1261.LIANG D Q,CHEN ZH G,DENG X H. Wavelet domainencryption algorithm for medical images based onhyperchaotic mapping[J]. Journal of Tianjin University(Natural Science and Engineering Technology),2016,49(12):1255-1261.
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