基于圆柱衍射与离散余弦变换的图像光学加密算法
|
摘要
目的为了实现多幅图像的同步加密,并增强加密系统的抗破译能力,提出一种基于圆柱衍射域的相位截断与离散余弦变换的多图像光学加密算法。方法首先引入压缩感知(CS,Compress Transform)方法,对输入明文实施压缩;基于离散余弦变换DCT(Discrete Cosine Transform)对压缩明文完成分解,获取相应的DCT系数,形成系数矩阵;构建迭代复数,将每个压缩明文对应的系数矩阵融合为一个复矩阵,通过DCT逆变换,形成一幅组合图像。联合Hilbert变换与波带片相位模型,构建调制掩码;引入圆柱衍射域的相位截断机制,联合调制掩码,对组合图像实施光学加密,获取密文与私钥。结果实验数据表明,相对于已有的多图像同步加密方法而言,所提算法具备更高的加密安全性,密文熵值以及相邻像素间的相关系数分别达到了7.998,0.0012,且具有强烈的密钥敏感性。结论所提加密算法可以抵御网络中外来攻击,在图像信息防伪领域具有一定的参考价值。
The paper aims to propose a multi-image synchronous encryption algorithm based on phase truncation in cylindrical diffraction domain and discrete cosine transform to realize the fast-synchronous encryption of multi-images and enhance the anti-cracking ability of the encryption system. Firstly, the compress transform(CS) was introduced to compress input plaintext. The compressed plaintext was decomposed based on discrete cosine transform(discrete cosine transform) to obtain the corresponding DCT coefficients. And these coefficients were combined into matrices. Iterative complex function was constructed to fuse the coefficient matrix corresponding to each compressed plaintext into a complex matrix. And a combined image was formed by reversible DCT method. The modulation mask was constructed by combining Hilbert transform with waveband plate phase model. Finally, the ciphertext and private key of combined images were obtained by introducing the phase truncation mechanism in cylindrical diffraction domain and modulation mask. The experimental data showed that compared with existing multi-image synchronous encryption, the proposed algorithm had higher encryption security. Its entropy of ciphertext and correlation coefficients between adjacent pixels were 7.998 and 0.0012, respectively. It also has stronger key sensitivity. This encryption algorithm can resist external attacks in the network, which has certain reference value in the field of anti-counterfeiting of image information.
The paper aims to propose a multi-image synchronous encryption algorithm based on phase truncation in cylindrical diffraction domain and discrete cosine transform to realize the fast-synchronous encryption of multi-images and enhance the anti-cracking ability of the encryption system. Firstly, the compress transform(CS) was introduced to compress input plaintext. The compressed plaintext was decomposed based on discrete cosine transform(discrete cosine transform) to obtain the corresponding DCT coefficients. And these coefficients were combined into matrices. Iterative complex function was constructed to fuse the coefficient matrix corresponding to each compressed plaintext into a complex matrix. And a combined image was formed by reversible DCT method. The modulation mask was constructed by combining Hilbert transform with waveband plate phase model. Finally, the ciphertext and private key of combined images were obtained by introducing the phase truncation mechanism in cylindrical diffraction domain and modulation mask. The experimental data showed that compared with existing multi-image synchronous encryption, the proposed algorithm had higher encryption security. Its entropy of ciphertext and correlation coefficients between adjacent pixels were 7.998 and 0.0012, respectively. It also has stronger key sensitivity. This encryption algorithm can resist external attacks in the network, which has certain reference value in the field of anti-counterfeiting of image information.
引文
[1]郭静博,王彦超,周丽宴.基于离散分数阶角变换与关联混沌映射的双图像加密算法[J].量子电子学报,2017,34(4):420-431.GUO Jing-bo,WANG Yan-chao,ZHOU Li-yan.Double Image Encryption Algorithm Based on Discrete Fractional Order Angle Transformation and Associated Chaotic Map[J].Quantum Electronic Journal,2017,34(4):420-431.
[2]郭静博.基于物理随机位生成器与混沌像素交叉互换的图像加密算法[J].包装工程,2018,39(13):222-232.GUO Jing-bo.Image Encryption Algorithm Based on Physical Random Bit Generator and Chaotic Pixel Cross Interchange[J].Packaging Engineering,2018,39(13):222-232.
[3]张博,龙慧,江沸菠.基于相干叠加与模均等矢量分解的光学图像加密算法[J].电子与信息学报,201840(2):438-446.ZHANG Bo,LONG Hui,JIANG Fei-bo.Optical Image Encryption Algorithm Based on Coherent Superposition and Modulus Equal Vector Decomposition[J].Journal of Electronics and Information,2018,40(2):438-446.
[4]CHAI Xiu-li,ZHENG Xiao-yu,GAN Zhi-hua.An Image Encryption Algorithm Based on Chaotic System and Compressive Sensing[J].Signal Processing,2018,148(19):124-144.
[5]WANG Xing-yuan,ZHU Xiao-qiang,WU Xiang-jun.Image Encryption Algorithm Based on Multiple Mxed Hash Functions and Cyclic Shift[J].Optics and Lasers in Engineering,2018,107(8):370-379.
[6]GHEBLEH M,KANSO A,STEVANOVIC D.A Novel Image Encryption Algorithm Based on Piecewise Linear Chaotic Maps and Least Squares Approximation[J].Multimedia Tools and Applications,2018,77(6):7305-7326.
[7]张红梅,张智高,裴志利.基于迭代复数模型的多图像无损同步加密算法研究[J].科学技术与工程,2014,14(26):123-130.ZHANG Hong-mei,ZHANG Zhi-gao,PEI Zhi-li Study on Synchronous Lossless Encryption Algorithm for Multi-Image Based on Iteration Plural Model[J].Science Technology and Engineering,2014,14(26):123-130.
[8]PAN Shu-min,WEN Ru-hong,ZHOU Zhi-hong.Optical Multi-image Encryption Scheme Based on Discrete Cosine Transform and Nonlinear Fractional MellinTransform[J].Multimedia Tools and Applications,2017,76(2):2933-2953.
[9]CHEN Xu-dong,LIU Qi,WANG Jun.Asymmetric Encryption of Multi-image Based on Compressed Sensing and Feature Fusion with High Quality Image Reconstruction[J].Optics and Laser Technology,2018107(11):302-312.
[10]CHAI Xiu-li,GAN Zhi-hua,CHEN Yi-ran.A Visually Secure Image Encryption Scheme Based on Compressive Sensing[J].Signal Processing,2017,134(9):35-51.
[11]HUO Dong-ming,ZHOU Xin,ZHANG Luo-zhi.Multiple-Image Encryption Scheme Via Compressive Sensing and Orthogonal Encoding Based on Double Random Phase Encoding[J].Journal of Modern Optics,2018,65(18):2093-2102.
[12]WANG Jun,LI Xiao-wei,HU Yu-hen.Phase-retrieval Attack Free Cryptosystem Based on Cylindrical Asymmetric Diffraction and Double-Random Phase Encoding[J].Optics Communications,2018,410(29):468-474.
[13]JI Xiao-yong,BAI Sen,ZHU Gui-bin.Image Encryption and Compression Based on the Generalized Knight’s Tour,Discrete Cosine Transform and Chaotic Maps[J].Multimedia Tools and Applications,2017,76(10):12965-12979.
[14]MOHAMMED H A,GHAZALI S,TANZILA S.Detection of Copy-move Image Forgery Based on Discrete Cosine Transform[J].Neural Computing and Applications,2018,30(1):183-192.
[15]李建军,梁利利,张福泉.基于混合相位掩码与Gyrator小波变换的光学图像加密算法[J].光学技术,2018,44(6):717-726.LI Jian-jun,LIANG Li-li,ZHANG Fu-quan.Optical Image Encryption Based on Hybrid Phase Mask and Gyrator Wavelet Transform[J].Optical Technology2018,44(6):717-726.
[16]ZHAO Meng-dan,GAO Xu-zhen,PAN Yue.Image Encryption Based on Fractal-structured Phase Mask in Fractional Fourier Transform Domain[J].Journal of Optics,2018,20(4):45703-45711.
[17]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 Ning,LI Ai-jun.Optical Image Encryption Algorithm Based on Circular Harmonic Component Expansion and Gyrator Transform Domain Phase Retrieval[J].Journal of Electronic Measurement and Instrument,2017,31(6):876-884.
[18]徐嵩松,蒲斌.基于8方向折叠与自更新置乱的图像加密算法[J].西南大学学报(自然科学版),2018,40(4):139-150.XU Song-song,PU Bin.Image Encryption Based on Eight Directions Folding and Self-Updating Scrambling[J].Journal of Southwest University(Natural Science Edition),2018,40(4):139-150.
[19]YOUHYUN K,JAEHUM S,INKYU M.Interference-Based Multiple-Image Encryption Using Binary Phase Masks[J].Optics&Lasers in Engineering,2018,107(8):281-287.
[20]ZHANG Luo-zhi,ZHOU Yuan-yuan,HUO Dongming.Multiple-Image Encryption Based on Double Random Phase Encoding and Compressive Sensing by Using a Measurement Array Preprocessed with Orthogonal-basis Matrices[J].Optics Communications,2016,361(15):6-12.
[21]耿卫江.结构相似度索引耦合最优稀疏表示的大规模损坏图像动态修复[J].科学技术与工程,2013,14(25):107-114.GENG Wei-jiang.Study on the Large-scale Damage Image Inpainting Mechanism Based on Structural Similarity Index Coupled Optimal Sparse Representations[J].Science and Technology and Engineering,2013,14(25):107-114.
[2]郭静博.基于物理随机位生成器与混沌像素交叉互换的图像加密算法[J].包装工程,2018,39(13):222-232.GUO Jing-bo.Image Encryption Algorithm Based on Physical Random Bit Generator and Chaotic Pixel Cross Interchange[J].Packaging Engineering,2018,39(13):222-232.
[3]张博,龙慧,江沸菠.基于相干叠加与模均等矢量分解的光学图像加密算法[J].电子与信息学报,201840(2):438-446.ZHANG Bo,LONG Hui,JIANG Fei-bo.Optical Image Encryption Algorithm Based on Coherent Superposition and Modulus Equal Vector Decomposition[J].Journal of Electronics and Information,2018,40(2):438-446.
[4]CHAI Xiu-li,ZHENG Xiao-yu,GAN Zhi-hua.An Image Encryption Algorithm Based on Chaotic System and Compressive Sensing[J].Signal Processing,2018,148(19):124-144.
[5]WANG Xing-yuan,ZHU Xiao-qiang,WU Xiang-jun.Image Encryption Algorithm Based on Multiple Mxed Hash Functions and Cyclic Shift[J].Optics and Lasers in Engineering,2018,107(8):370-379.
[6]GHEBLEH M,KANSO A,STEVANOVIC D.A Novel Image Encryption Algorithm Based on Piecewise Linear Chaotic Maps and Least Squares Approximation[J].Multimedia Tools and Applications,2018,77(6):7305-7326.
[7]张红梅,张智高,裴志利.基于迭代复数模型的多图像无损同步加密算法研究[J].科学技术与工程,2014,14(26):123-130.ZHANG Hong-mei,ZHANG Zhi-gao,PEI Zhi-li Study on Synchronous Lossless Encryption Algorithm for Multi-Image Based on Iteration Plural Model[J].Science Technology and Engineering,2014,14(26):123-130.
[8]PAN Shu-min,WEN Ru-hong,ZHOU Zhi-hong.Optical Multi-image Encryption Scheme Based on Discrete Cosine Transform and Nonlinear Fractional MellinTransform[J].Multimedia Tools and Applications,2017,76(2):2933-2953.
[9]CHEN Xu-dong,LIU Qi,WANG Jun.Asymmetric Encryption of Multi-image Based on Compressed Sensing and Feature Fusion with High Quality Image Reconstruction[J].Optics and Laser Technology,2018107(11):302-312.
[10]CHAI Xiu-li,GAN Zhi-hua,CHEN Yi-ran.A Visually Secure Image Encryption Scheme Based on Compressive Sensing[J].Signal Processing,2017,134(9):35-51.
[11]HUO Dong-ming,ZHOU Xin,ZHANG Luo-zhi.Multiple-Image Encryption Scheme Via Compressive Sensing and Orthogonal Encoding Based on Double Random Phase Encoding[J].Journal of Modern Optics,2018,65(18):2093-2102.
[12]WANG Jun,LI Xiao-wei,HU Yu-hen.Phase-retrieval Attack Free Cryptosystem Based on Cylindrical Asymmetric Diffraction and Double-Random Phase Encoding[J].Optics Communications,2018,410(29):468-474.
[13]JI Xiao-yong,BAI Sen,ZHU Gui-bin.Image Encryption and Compression Based on the Generalized Knight’s Tour,Discrete Cosine Transform and Chaotic Maps[J].Multimedia Tools and Applications,2017,76(10):12965-12979.
[14]MOHAMMED H A,GHAZALI S,TANZILA S.Detection of Copy-move Image Forgery Based on Discrete Cosine Transform[J].Neural Computing and Applications,2018,30(1):183-192.
[15]李建军,梁利利,张福泉.基于混合相位掩码与Gyrator小波变换的光学图像加密算法[J].光学技术,2018,44(6):717-726.LI Jian-jun,LIANG Li-li,ZHANG Fu-quan.Optical Image Encryption Based on Hybrid Phase Mask and Gyrator Wavelet Transform[J].Optical Technology2018,44(6):717-726.
[16]ZHAO Meng-dan,GAO Xu-zhen,PAN Yue.Image Encryption Based on Fractal-structured Phase Mask in Fractional Fourier Transform Domain[J].Journal of Optics,2018,20(4):45703-45711.
[17]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 Ning,LI Ai-jun.Optical Image Encryption Algorithm Based on Circular Harmonic Component Expansion and Gyrator Transform Domain Phase Retrieval[J].Journal of Electronic Measurement and Instrument,2017,31(6):876-884.
[18]徐嵩松,蒲斌.基于8方向折叠与自更新置乱的图像加密算法[J].西南大学学报(自然科学版),2018,40(4):139-150.XU Song-song,PU Bin.Image Encryption Based on Eight Directions Folding and Self-Updating Scrambling[J].Journal of Southwest University(Natural Science Edition),2018,40(4):139-150.
[19]YOUHYUN K,JAEHUM S,INKYU M.Interference-Based Multiple-Image Encryption Using Binary Phase Masks[J].Optics&Lasers in Engineering,2018,107(8):281-287.
[20]ZHANG Luo-zhi,ZHOU Yuan-yuan,HUO Dongming.Multiple-Image Encryption Based on Double Random Phase Encoding and Compressive Sensing by Using a Measurement Array Preprocessed with Orthogonal-basis Matrices[J].Optics Communications,2016,361(15):6-12.
[21]耿卫江.结构相似度索引耦合最优稀疏表示的大规模损坏图像动态修复[J].科学技术与工程,2013,14(25):107-114.GENG Wei-jiang.Study on the Large-scale Damage Image Inpainting Mechanism Based on Structural Similarity Index Coupled Optimal Sparse Representations[J].Science and Technology and Engineering,2013,14(25):107-114.