基于分阶Fourier频谱分解与混合随机掩码的光学加密算法
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摘要
为了解决当前光学加密方法主要是借助普通相位掩码来调制初始图像,导致输出密文的安全性不理想的问题,通过融合Fresnel波带、Hilbert相位与混沌掩码,设计了分阶Fourier频谱分解与混合随机掩码的光学图像加密算法。首先,根据SHA-256哈希方法,形成一个256位的外部密钥,并将其分割为32个子密钥;引入二维Ushiki映射,利用子密钥来计算其初始条件,通过迭代来输出一组随机序列,从而构建一个混沌相位掩码;随后,引入Fresnel波带振幅与Hilbert相位函数,将二者与混沌相位掩码融合,形成一个混合掩码,兼顾其随机性与光轴校准精度;基于分阶Fourier变换,联合混合掩码,对初始明文完成光学调制,获取Fourier频谱;最后,通过等模分解方法来分割Fourier频谱,输出密文与私钥。测试数据表明:较已有的光学加密方案而言,所研究加密技术具备更理想的抗干扰能力与安全性,在噪声、剪切等攻击下,具有更为理想的解密质量。
In order to solve the defect as low security of output cipher induced by using the ordinary phase mask to modulate the initial image in current optical image encryption methods,the optical image encryption algorithm based on fractional Fourier spectral decomposition and mixed random mask was designed by fusing Fresnel band,Hilbert phase and chaotic mask. Firstly,the 256 bit external key was formed according to the SHA-256 hash method and divided it into 32 sub-keys. The initial conditions of two-dimensional Ushiki map were computed by these subkeys,which was used to iterate the Ushiki map for obtaining a group of random sequences to construct the chaotic phase mask. Then,the Fresnel band amplitude and Hilbert phase function were introduced to fuse the chaotic phase mask for forming a hybrid mask,which took into account the randomness of the mask and the calibration accuracy of the optical axis. The optical modulation of the original plaintext was completed based on fractional Fourier transform and hybrid mask to obtain Fourier spectrum. Finally,the Fourier spectrum was segmented by the equal modulus decomposition method to output the ciphertext and the private key. Test data show that the proposed encryption scheme has better anti-disturbance ability and higher security,which has better quality of decryption under noise,shearing and other attacks compared with current optical encryption scheme.
In order to solve the defect as low security of output cipher induced by using the ordinary phase mask to modulate the initial image in current optical image encryption methods,the optical image encryption algorithm based on fractional Fourier spectral decomposition and mixed random mask was designed by fusing Fresnel band,Hilbert phase and chaotic mask. Firstly,the 256 bit external key was formed according to the SHA-256 hash method and divided it into 32 sub-keys. The initial conditions of two-dimensional Ushiki map were computed by these subkeys,which was used to iterate the Ushiki map for obtaining a group of random sequences to construct the chaotic phase mask. Then,the Fresnel band amplitude and Hilbert phase function were introduced to fuse the chaotic phase mask for forming a hybrid mask,which took into account the randomness of the mask and the calibration accuracy of the optical axis. The optical modulation of the original plaintext was completed based on fractional Fourier transform and hybrid mask to obtain Fourier spectrum. Finally,the Fourier spectrum was segmented by the equal modulus decomposition method to output the ciphertext and the private key. Test data show that the proposed encryption scheme has better anti-disturbance ability and higher security,which has better quality of decryption under noise,shearing and other attacks compared with current optical encryption scheme.
引文
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8 Wang Y,Quan C.Asymmetric optical image encryption based on an improved amplitude-phase retrieval algorithm[J].Optics and Lasers in Engineering,2016,78(10):8-16
9 Muhammad R A.An asymmetric single-channel color image encryption based on Hartley transform and Gyrator transforms[J].Optics and Lasers in Engineering,2016,69(8):49-57
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11杨宏宇,王在明.基于SHA-256和DNA序列的彩色二维码混沌加密方法[J].大连理工大学学报,2017,57(6):629-637Yang Hongyu,Wang Zaiming.Chaotic encryption method of color two-dimensional code based on SHA-256 and DNA sequences[J].Journal of Dalian University of Technology,2017,57(6):629-637
12洪英汉,熊建斌.基于相位截断菲涅耳变换的彩色图像加密系统[J].现代电子技术,2016,39(2):73-77Hong Yinghan,Xiong Jianbin.Color image encryption system based on phase truncated fresnel transform[J].Modern Electronic Technology,2016,39(2):73-77
13 Morales Y,Diaz L,Torres C.Radial Hilbert transform in terms of the Fourier transform applied to image encryption[J].Journal of Physics:Conference Series,2015,582(1):12063-12072
14谢国波,姜先值.二维离散分阶Fourier变换的双混沌图像加密算法[J].计算机工程与应用,2018,54(3):40-45Xie Guobo,Jiang Xianzhi.Two chaotic image encryption algorithm based on two dimensional discrete fractional Fourier transform[J].Computer Engineering and Application,2018,54(3):40-45
15 Cai J J,Shen X J.Modified optical asymmetric image cryptosystem based on coherent superposition and equal modulus decomposition[J].Optics and Laser Technology,2016,359(15):26-30
16田玉萍.混沌神经元耦合置乱神经元的图像加密算法研究[J].包装工程,2014,35(15):105-112Tian Yuping.Image encryption algorithm based on chaotic neurons coupled with scrambling neurons[J].Packaging Engineering,2014,35(15):105-112
17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):222-232Guo Jingbo.Image encryption algorithm based on physical random bit generator and chaotic pixel cross swaps[J].Packaging Engineering,2018,39(13):222-232
2石坤泉,魏文国.基于快速响应分解与颜色空间转换的光学彩色图像无损加密算法[J].光学技术,2018,44(5):576-585Shi Kunquan,Wei Wenguo.Optical color image lossless encryption algorithm based on fast response decomposition and color space conversion[J].Optical Technology,2018,44(5):576-585
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,2018,40(2):438-446Zhang Bo,Long Hui,Jiang Feibo.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康万杰.基于Gyrator频谱分解与混沌螺旋相位掩码的多图像光学加密算法[J].电子测量与仪器学报,2018,32(5):116-125Kang Wanjie.Multi-image optical encryption algorithm based on Gyrator spectrum decomposition and chaotic spiral phase mask[J].Journal of Electronic Measurement and Instrument,2018,32(5):116-125
5 Zhang Y,Tang Y J.A plaintext-related image encryption algorithm based on chaos[J].Multimedia Tools and Applications,2017,77(6):6647-6669
6 Liu J Y,Yang D D,Zhou H B.A digital image encryption algorithm based on bit-planes and an improved logistic map[J].Multimedia Tools and Applications,2018,77(8):10217-10233
7 Li Y P,Wang C H,Chen H.A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation[J].Optics and Lasers in Engineering,2017,2017,90(8):238-246
8 Wang Y,Quan C.Asymmetric optical image encryption based on an improved amplitude-phase retrieval algorithm[J].Optics and Lasers in Engineering,2016,78(10):8-16
9 Muhammad R A.An asymmetric single-channel color image encryption based on Hartley transform and Gyrator transforms[J].Optics and Lasers in Engineering,2016,69(8):49-57
10 Gao Y,Liu B.Study on the dynamical behaviors of a two-dimensional discrete system[J].Nonlinear Anal,2009,70(12):4209-4216
11杨宏宇,王在明.基于SHA-256和DNA序列的彩色二维码混沌加密方法[J].大连理工大学学报,2017,57(6):629-637Yang Hongyu,Wang Zaiming.Chaotic encryption method of color two-dimensional code based on SHA-256 and DNA sequences[J].Journal of Dalian University of Technology,2017,57(6):629-637
12洪英汉,熊建斌.基于相位截断菲涅耳变换的彩色图像加密系统[J].现代电子技术,2016,39(2):73-77Hong Yinghan,Xiong Jianbin.Color image encryption system based on phase truncated fresnel transform[J].Modern Electronic Technology,2016,39(2):73-77
13 Morales Y,Diaz L,Torres C.Radial Hilbert transform in terms of the Fourier transform applied to image encryption[J].Journal of Physics:Conference Series,2015,582(1):12063-12072
14谢国波,姜先值.二维离散分阶Fourier变换的双混沌图像加密算法[J].计算机工程与应用,2018,54(3):40-45Xie Guobo,Jiang Xianzhi.Two chaotic image encryption algorithm based on two dimensional discrete fractional Fourier transform[J].Computer Engineering and Application,2018,54(3):40-45
15 Cai J J,Shen X J.Modified optical asymmetric image cryptosystem based on coherent superposition and equal modulus decomposition[J].Optics and Laser Technology,2016,359(15):26-30
16田玉萍.混沌神经元耦合置乱神经元的图像加密算法研究[J].包装工程,2014,35(15):105-112Tian Yuping.Image encryption algorithm based on chaotic neurons coupled with scrambling neurons[J].Packaging Engineering,2014,35(15):105-112
17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):222-232Guo Jingbo.Image encryption algorithm based on physical random bit generator and chaotic pixel cross swaps[J].Packaging Engineering,2018,39(13):222-232