Novel Image Encryption based on Quantum Walks

Quantum computation has achieved a tremendous success during the last decades. In this paper, we investigate the potential application of a famous quantum computation model, i.e., quantum walks (QW) in image encryption. It is found that QW can serve as an excellent key generator thanks to its inherent nonlinear chaotic dynamic behavior. Furthermore, we construct a novel QW-based image encryption algorithm. Simulations and performance comparisons show that the proposal is secure enough for image encryption and outperforms prior works. It also opens the door towards introducing quantum computation into image encryption and promotes the convergence between quantum computation and image processing.

[1]  Josef Scharinger Fast encryption of image data using chaotic Kolmogorov flows , 1998, J. Electronic Imaging.

[2]  Frédéric Magniez,et al.  Quantum Algorithm for the Triangle Problem , 2003 .

[3]  Kwok-Wo Wong,et al.  A Fast Image Encryption Scheme based on Chaotic Standard Map , 2006, ArXiv.

[4]  Schack,et al.  Chaos for Liouville probability densities. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  C. Caves,et al.  Hypersensitivity to perturbations in the quantum baker's map. , 1993, Physical review letters.

[6]  S. Mallat A wavelet tour of signal processing , 1998 .

[7]  Amir Akhavan,et al.  Pseudo random number generator based on quantum chaotic map , 2014, Commun. Nonlinear Sci. Numer. Simul..

[8]  Katsuhiko Shirai,et al.  A clustering experiment of the spectra and the spectral changes of speech to extract phonemic features , 1986 .

[9]  Der-Chyuan Lou,et al.  A steganographic scheme for secure communications based on the chaos and euler Theorem , 2004, IEEE Transactions on Multimedia.

[10]  Henry Ker-Chang Chang,et al.  A linear quadtree compression scheme for image encryption , 1997, Signal Process. Image Commun..

[11]  Pierre L'Ecuyer,et al.  TestU01: A C library for empirical testing of random number generators , 2006, TOMS.

[12]  Zengqiang Chen,et al.  A new image encryption algorithm based on hyper-chaos , 2008 .

[13]  Junwei Zhou,et al.  A block chaotic image encryption scheme based on self-adaptive modelling , 2014, Appl. Soft Comput..

[14]  Ofer Biham,et al.  One-dimensional quantum walk with unitary noise , 2003 .

[15]  C L Webber,et al.  Dynamical assessment of physiological systems and states using recurrence plot strategies. , 1994, Journal of applied physiology.

[16]  Arturo Carnicer,et al.  Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys. , 2005, Optics letters.

[17]  J. Kurths,et al.  Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Hua Zhang,et al.  Novel image encryption/decryption based on quantum Fourier transform and double phase encoding , 2013, Quantum Inf. Process..

[19]  Ricardo López-Ruiz,et al.  A Statistical Measure of Complexity , 1995, ArXiv.

[20]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[21]  J. Zbilut,et al.  Embeddings and delays as derived from quantification of recurrence plots , 1992 .

[22]  Zhengjun Liu,et al.  Color image encryption by using Arnold and discrete fractional random transforms in IHS space , 2010 .

[23]  Robert A. J. Matthews,et al.  On the Derivation of a "Chaotic" Encryption Algorithm , 1989, Cryptologia.

[24]  Rhouma Rhouma,et al.  Cryptanalysis of a new image encryption algorithm based on hyper-chaos , 2008 .

[25]  Shujun Li,et al.  Breaking a modified substitution-diffusion image cipher based on chaotic standard and logistic maps , 2009, ArXiv.

[26]  Nikolaos G. Bourbakis,et al.  Picture data encryption using scan patterns , 1992, Pattern Recognit..

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

[28]  Mohammad Eshghi,et al.  Chaotic image encryption system using phase-magnitude transformation and pixel substitution , 2011, Telecommunication Systems.

[29]  Chuan Zhou,et al.  A Color Image Encryption Algorithm Based on Magic Cube Transformation and Modular Arithmetic Operation , 2005, PCM.

[30]  Rafael Benítez,et al.  A wavelet-based tool for studying non-periodicity , 2010, Comput. Math. Appl..

[31]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[32]  A. Akhavan,et al.  An image encryption scheme based on quantum logistic map , 2012 .

[33]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[34]  Julia Kempe,et al.  Quantum random walks: An introductory overview , 2003, quant-ph/0303081.

[35]  Salvador Elías Venegas-Andraca,et al.  Quantum walks: a comprehensive review , 2012, Quantum Information Processing.

[36]  Chin-Chen Chang,et al.  A new encryption algorithm for image cryptosystems , 2001, J. Syst. Softw..

[37]  M. A. O. Ignacio,et al.  How to cite this article , 2016 .

[38]  Li Li,et al.  A new approach to chaotic image encryption based on quantum chaotic system, exploiting color spaces , 2013, Signal Process..

[39]  Xiang Peng,et al.  Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys , 2009 .

[40]  Frédéric Magniez,et al.  Quantum algorithms for the triangle problem , 2005, SODA '05.

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

[42]  Qiang Li,et al.  A hybrid classical-quantum clustering algorithm based on quantum walks , 2011, Quantum Inf. Process..

[43]  Osvaldo A. Rosso,et al.  Intensive statistical complexity measure of pseudorandom number generators , 2005 .

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

[45]  S. Mallat VI – Wavelet zoom , 1999 .

[46]  Cristel Chandre,et al.  Time–frequency analysis of chaotic systems , 2002, nlin/0209015.

[47]  Schack,et al.  Hypersensitivity to perturbation in the quantum kicked top. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[48]  O A Rosso,et al.  Distinguishing noise from chaos. , 2007, Physical review letters.

[49]  Yu-Guang Yang,et al.  Quantum cryptographic algorithm for color images using quantum Fourier transform and double random-phase encoding , 2014, Inf. Sci..

[50]  R. Ben A wavelet-based tool for studying non-periodicity , 2010 .

[51]  Ph Blanchard,et al.  Quantum random walks and piecewise deterministic evolutions. , 2004, Physical review letters.

[52]  Vinod Patidar,et al.  A new substitution–diffusion based image cipher using chaotic standard and logistic maps , 2009 .

[53]  Congxu Zhu,et al.  A novel image encryption scheme based on improved hyperchaotic sequences , 2012 .

[54]  Peng Zhang,et al.  Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain. , 2006, Optics letters.

[55]  Andris Ambainis,et al.  Quantum walk algorithm for element distinctness , 2003, 45th Annual IEEE Symposium on Foundations of Computer Science.

[56]  Osvaldo A. Rosso,et al.  Statistical complexity and disequilibrium , 2003 .

[57]  Osvaldo A. Rosso,et al.  Intensive entropic non-triviality measure , 2004 .

[58]  Xiaobo Li,et al.  Partial encryption of compressed images and videos , 2000, IEEE Trans. Signal Process..

[59]  Rolf Landauer,et al.  A simple measure of complexity , 1988, Nature.

[60]  H. J. Kimble,et al.  The quantum internet , 2008, Nature.

[61]  Xiaoling Huang,et al.  An efficient self-adaptive model for chaotic image encryption algorithm , 2014, Commun. Nonlinear Sci. Numer. Simul..