Binary-tree encryption strategy for optical multiple-image encryption.

In traditional optical multiple-image encryption schemes, different images typically have almost the same encryption or decryption process. Provided that an attacker manages to correctly decrypt some image, the conventional attacks upon other images are much easier to be made. In this paper, a binary-tree encryption strategy for multiple images is proposed to resist the attacks in this case. The encryption schemes produced by this strategy can not only increase the security of multiple-image encryption, but also realize an authority management with high security among the users sharing a cipher image. For a simulation test, we devise a basic binary-tree encryption scheme, whose encryption nodes are based on an asymmetric double random phase encoding in the gyrator domain. The favorable simulation results about the tested scheme can testify to the feasibility of the strategy.

[1]  Daomu Zhao,et al.  Multiple-image encryption using phase retrieve algorithm and intermodulation in Fourier domain , 2012 .

[2]  John T. Sheridan,et al.  Optical image encryption by random shifting in fractional Fourier domains. , 2003, Optics letters.

[3]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[4]  In-Kwon Lee,et al.  Modified computational integral imaging-based double image encryption using fractional Fourier transform , 2015 .

[5]  Jingjuan Zhang,et al.  Double random-phase encoding in the Fresnel domain. , 2004, Optics letters.

[6]  José A. Rodrigo,et al.  Applications of gyrator transform for image processing , 2007 .

[7]  Qindong Sun,et al.  Double-image encryption using discrete fractional random transform and logistic maps , 2014 .

[8]  Hai Yu,et al.  Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains , 2015 .

[9]  Muhammad Rafiq Abuturab Securing color information using Arnold transform in gyrator transform domain , 2012 .

[10]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[11]  Zhengjun Liu,et al.  Image encryption scheme by using iterative random phase encoding in gyrator transform domains , 2011 .

[12]  Ting Liu,et al.  Double-image encryption based on the affine transform and the gyrator transform , 2010 .

[13]  Wang Xin,et al.  Multiple-image encryption scheme based on cascaded fractional Fourier transform. , 2013, Applied optics.

[14]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[15]  Zhengjun Liu,et al.  Double image encryption by using iterative random binary encoding in gyrator domains. , 2010, Optics express.

[16]  Junli Liang,et al.  Asymmetric multiple-image encryption based on coupled logistic maps in fractional Fourier transform domain , 2014 .

[17]  Zhengjun Liu,et al.  Image encryption algorithm by using fractional Fourier transform and pixel scrambling operation based on double random phase encoding , 2013 .

[18]  Naveen K Nishchal,et al.  Image encryption based on interference that uses fractional Fourier domain asymmetric keys. , 2012, Applied optics.

[19]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[20]  Xiang Peng,et al.  Asymmetric cryptosystem based on phase-truncated Fourier transforms. , 2010, Optics letters.

[21]  A. Alfalou,et al.  Simultaneous fusion, compression, and encryption of multiple images. , 2011, Optics express.

[22]  Daomu Zhao,et al.  Double images encryption method with resistance against the specific attack based on an asymmetric algorithm. , 2012, Optics express.

[23]  Yonina C. Eldar,et al.  Introduction to Compressed Sensing , 2022 .

[24]  Zhengjun Liu,et al.  Double image encryption based on iterative fractional Fourier transform , 2007 .

[25]  Xiaogang Wang,et al.  Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval , 2011 .

[26]  Junli Liang,et al.  Asymmetric double-image encryption based on cascaded discrete fractional random transform and logistic maps. , 2014, Optics express.

[27]  Ran Tao,et al.  Image encryption based on the multiple-parameter discrete fractional Fourier transform and chaos function , 2010 .

[28]  B Deepan,et al.  Multiple-image encryption by space multiplexing based on compressive sensing and the double-random phase-encoding technique. , 2014, Applied optics.

[29]  Zhiyong Xu,et al.  Digital image information encryption based on Compressive Sensing and double random-phase encoding technique , 2013 .

[30]  Muhammad Rafiq Abuturab Single-channel color information security system using LU decomposition in gyrator transform domains , 2014 .

[31]  Hai Yu,et al.  Gyrator transform based double random phase encoding with sparse representation for information authentication , 2015 .

[32]  Jiawang Yi,et al.  Optical compression and encryption system combining multiple measurement matrices with fractional Fourier transform. , 2015, Applied optics.

[33]  Jingjuan Zhang,et al.  Multiple-image encryption by wavelength multiplexing. , 2005, Optics letters.

[34]  Sui Liansheng,et al.  Multiple-image encryption based on phase mask multiplexing in fractional Fourier transform domain. , 2013, Optics letters.

[35]  Zhengjun Liu,et al.  A novel double-image encryption scheme based on cross-image pixel scrambling in gyrator domains. , 2014, Optics express.

[36]  Xiaoyan Zhao,et al.  Double-image encryption by using chaos-based local pixel scrambling technique and gyrator transform , 2013 .

[37]  Isha Mehra,et al.  Optical asymmetric watermarking using modified wavelet fusion and diffractive imaging , 2015 .

[38]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[39]  Wen-Nung Lie,et al.  Multiple-image encryption and multiplexing using a modified Gerchberg-Saxton algorithm and phase modulation in Fresnel-transform domain. , 2009, Optics letters.

[40]  Naveen K Nishchal,et al.  Known-plaintext attack-based optical cryptosystem using phase-truncated Fresnel transform. , 2013, Applied optics.

[41]  Aloka Sinha,et al.  Gyrator transform-based optical image encryption, using chaos , 2009 .

[42]  M. L. Calvo,et al.  Gyrator transform: properties and applications. , 2007, Optics express.

[43]  Ayman Alfalou,et al.  Double random phase encryption scheme to multiplex and simultaneous encode multiple images. , 2009, Applied optics.

[44]  Yuan Sheng,et al.  An improved method to enhance the security of double random-phase encoding in the Fresnel domain , 2012 .

[45]  Isha Mehra,et al.  Wavelet-based image fusion for securing multiple images through asymmetric keys , 2015 .

[46]  Muhammad Rafiq Abuturab,et al.  Fully phase multiple information encoding based on superposition of two beams and Fresnel-transform domain , 2015 .

[47]  Ayman Alfalou,et al.  Using the RMS time-frequency structure for multiple-image optical compression and encryption , 2010 .

[48]  Muhammad Rafiq Abuturab,et al.  Generalized Arnold map-based optical multiple color-image encoding in gyrator transform domain , 2015 .

[49]  Li-Hua Gong,et al.  Novel optical image encryption scheme based on fractional Mellin transform , 2011 .

[50]  Jingjuan Zhang,et al.  Position multiplexing for multiple-image encryption , 2006 .

[51]  Feng Zhang,et al.  Asymmetric multiple-image encryption based on the cascaded fractional Fourier transform , 2015 .

[52]  B Javidi,et al.  Encrypted optical memory system using three-dimensional keys in the Fresnel domain. , 1999, Optics letters.

[53]  Di Wang,et al.  Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform , 2015 .

[54]  Wei Liu,et al.  Multiple-image encryption based on optical asymmetric key cryptosystem , 2015 .

[55]  Li-Hua Gong,et al.  Novel single-channel color image encryption algorithm based on chaos and fractional Fourier transform , 2011 .

[56]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[57]  Sheng Yuan,et al.  An improved optical identity authentication system with significant output images , 2012 .

[58]  B Javidi,et al.  Optical image encryption based on input plane and Fourier plane random encoding. , 1995, Optics letters.

[59]  Di Xiao,et al.  Double optical image encryption using discrete Chirikov standard map and chaos-based fractional random transform , 2013 .

[60]  Xiaoping Du,et al.  Color image encryption based on the affine transform and gyrator transform , 2013 .

[61]  José A Rodrigo,et al.  Experimental implementation of the gyrator transform. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[62]  G. Unnikrishnan,et al.  Optical encryption by double-random phase encoding in the fractional Fourier domain. , 2000, Optics letters.

[63]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[64]  Jinpeng Ma,et al.  Fast algorithm of discrete gyrator transform based on convolution operation , 2011 .

[65]  E. Candès The restricted isometry property and its implications for compressed sensing , 2008 .

[66]  Yan Zhang,et al.  Multiple-image encryption based on computational ghost imaging , 2016 .

[67]  Zhihong Zhou,et al.  Double-image encryption scheme combining DWT-based compressive sensing with discrete fractional random transform , 2015 .

[68]  Ran Tao,et al.  Double image encryption based on random phase encoding in the fractional Fourier domain. , 2007, Optics express.

[69]  Xiaogang Wang,et al.  Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain , 2011 .

[70]  Li-Hua Gong,et al.  Novel image compression–encryption hybrid algorithm based on key-controlled measurement matrix in compressive sensing , 2014 .

[71]  Xiaogang Wang,et al.  Fully phase multiple-image encryption based on superposition principle and the digital holographic technique , 2012 .

[72]  Chandra Shakher,et al.  Logarithms-based RGB image encryption in the fractional Fourier domain : A non-linear approach , 2009 .

[73]  Juan Liu,et al.  Multiple-image encryption based on position multiplexing of Fresnel phase , 2013 .

[74]  Zhengjun Liu,et al.  Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains , 2013 .

[75]  Ayman Alfalou,et al.  Optical image compression and encryption methods , 2009 .

[76]  Christian Jutten,et al.  A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed $\ell ^{0}$ Norm , 2008, IEEE Transactions on Signal Processing.

[77]  Ching-Mu Chen,et al.  Optical multiple-image encryption based on phase encoding algorithm in the Fresnel transform domain , 2012 .

[78]  Kehar Singh,et al.  Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane , 2015 .