Color image encryption using random transforms, phase retrieval, chaotic maps, and diffusion

Abstract The recent tremendous proliferation of color imaging applications has been accompanied by growing research in data encryption to secure color images against adversary attacks. While recent color image encryption techniques perform reasonably well, they still exhibit vulnerabilities and deficiencies in terms of statistical security measures due to image data redundancy and inherent weaknesses. This paper proposes two encryption algorithms that largely treat these deficiencies and boost the security strength through novel integration of the random fractional Fourier transforms, phase retrieval algorithms, as well as chaotic scrambling and diffusion. We show through detailed experiments and statistical analysis that the proposed enhancements significantly improve security measures and immunity to attacks.

[1]  Rafael C. González,et al.  Digital image processing using MATLAB , 2006 .

[2]  S. Mazloom,et al.  Color image encryption based on Coupled Nonlinear Chaotic Map , 2009 .

[3]  Edoardo Ardizzone,et al.  A tunable digital ishihara plate for pre-school aged children , 2016, EMBC.

[4]  Xin-Wen Wu,et al.  On the Security of Permutation-Only Image Encryption Schemes , 2016, IEEE Transactions on Information Forensics and Security.

[5]  Madhusudan Joshi,et al.  Color image encryption and decryption using fractional Fourier transform , 2007 .

[6]  Garrett M. Johnson,et al.  Color Imaging: Fundamentals and Applications , 2008 .

[7]  Lin Teng,et al.  A novel colour image encryption algorithm based on chaos , 2012, Signal Process..

[8]  Ping Liu,et al.  A novel hybrid color image encryption algorithm using two complex chaotic systems , 2016 .

[9]  Ayman Alfalou,et al.  Simultaneous compression and encryption of color video images , 2015 .

[10]  Isaac N. Bankman,et al.  Handbook of medical image processing and analysis , 2009 .

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

[12]  I. Shatheesh Sam,et al.  Chaos Based Image Encryption Scheme Based on Enhanced Logistic Map , 2011, ICDCIT.

[13]  Gaurav Sharma,et al.  Color imaging for multimedia , 1998, Proc. IEEE.

[14]  Elisabet Pérez-Cabré,et al.  Optical Data Encryption , 2011 .

[15]  John T. Sheridan,et al.  A review of optical image encryption techniques , 2014 .

[16]  S. Agaian,et al.  NPCR and UACI Randomness Tests for Image Encryption , 2011 .

[17]  Xing-Zhou Zhang,et al.  An image encryption scheme based on new spatiotemporal chaos , 2013 .

[18]  Mahmoud H. Annaby,et al.  Image encryption via discrete fractional Fourier-type transforms generated by random matrices , 2016, Signal Process. Image Commun..

[19]  Guanrong Chen,et al.  Chaos-Based Encryption for Digital Images and Videos , 2004 .

[20]  A Alfalou,et al.  Simultaneous compression and encryption of closely resembling images: application to video sequences and polarimetric images. , 2014, Optics express.

[21]  Dezhao Kong,et al.  Multiple-image encryption based on optical wavelet transform and multichannel fractional Fourier transform , 2014 .

[22]  Gonzalo Alvarez,et al.  Cryptanalysis of two chaotic encryption schemes based on circular bit shift and XOR operations , 2006, nlin/0611017.

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

[24]  X. Liao,et al.  Cryptanalysis and improvement on a block cryptosystem based on iteration a chaotic map , 2007 .

[25]  Chandra Shakher,et al.  Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys , 2010 .

[26]  Xingyuan Wang,et al.  Color image encryption using spatial bit-level permutation and high-dimension chaotic system , 2011 .

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

[28]  Fan Ge,et al.  A half-blind color image hiding and encryption method in fractional Fourier domains , 2008 .

[29]  Abdul Hanan Abdullah,et al.  Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence , 2014 .

[30]  Hsien-Che Lee,et al.  Introduction to Color Imaging Science , 2005 .

[31]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[32]  A. Alfalou,et al.  Recent Advances in Optical Image Processing , 2015 .

[33]  R. Devaney.  An Introduction to Chaotic Dynamical Systems , 1990 .

[34]  Yonina C. Eldar,et al.  On the 2D Phase Retrieval Problem , 2016, IEEE Transactions on Signal Processing.

[35]  Li Deng.  Transiems as dynamically defined, sub-phonemic units of speech: A computational model , 1996, Signal Process..

[36]  M. Omair Ahmad,et al.  Binary Discrete Cosine and Hartley Transforms , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[37]  Gerald Schaefer,et al.  Color Medical Image Analysis , 2012 .

[38]  Ting Liu,et al.  Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains , 2011 .

[39]  P. Halmos.  Finite-Dimensional Vector Spaces , 1960 .

[40]  John T. Sheridan,et al.  Image encryption and the fractional Fourier transform , 2003, SPIE OPTO-Ireland.

[41]  Ailing Tian,et al.  Single-channel color image encryption using phase retrieve algorithm in fractional Fourier domain , 2013 .

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

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

[44]  L. Sui,et al.  Single-channel color image encryption based on iterative fractional Fourier transform and chaos , 2013 .

[45]  Bahram Javidi,et al.  Roadmap on optical security , 2016 .

[46]  Sattar Mirzakuchaki,et al.  A fast color image encryption algorithm based on coupled two-dimensional piecewise chaotic map , 2012, Signal Process..

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

[48]  Dawei Wang,et al.  A novel lossless color image encryption scheme using 2 D DWT and 6 D hyperchaotic system , 2016 .

[49]  Paul Cull,et al.  Difference Equations: From Rabbits to Chaos , 2005 .

[50]  Di Xu.  Application of Color-Based Image Rendering in Art Education Based on Computer Drawing Board , 2015, 2015 7th International Conference on Information Technology in Medicine and Education (ITME).

[51]  M. N. Islam,et al.  Optical cryptographic system employing multiple reference-based joint transform correlation technique , 2011 .

[52]  Roberto Torroba,et al.  Three-dimensional joint transform correlator cryptosystem. , 2016, Optics letters.

[53]  John Skilling,et al.  Maximum entropy method in image processing , 1984 .

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

[55]  S. Pei,et al.  Improved discrete fractional Fourier transform. , 1997, Optics letters.

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

[57]  Hui Liu,et al.  Colour image encryption based on advanced encryption standard algorithm with two-dimensional chaotic map , 2013, IET Inf. Secur..

[58]  V. V. Fedorenko,et al.  Dynamics of One-Dimensional Maps , 1997 .

[59]  Zhengjun Liu,et al.  Color image encryption by using the rotation of color vector in Hartley transform domains , 2010 .

[60]  Cagatay Candan,et al.  The discrete fractional Fourier transform , 2000, IEEE Trans. Signal Process..

[61]  Leonard C. Maximon.  Differential and Difference Equations: A Comparison of Methods of Solution , 2016 .

[62]  Xingyuan Wang,et al.  A novel chaotic block image encryption algorithm based on dynamic random growth technique , 2015 .

[63]  Chenggen Quan,et al.  Optical color image encryption based on Arnold transform and interference method , 2009 .