Statistical Analysis of Imaging Encryption Using Chaos

In this work, we propose a comparative statistical analysis of some image encrypting methods using discrete chaotic systems (Logistic Map, Henon Map, Chen System and Trigonometric Chaotic Map). For each one of the methods we considered a process of permutation, followed by a diffusion process. In the statistical analysis we develop histograms of the encrypted and plane image. For the correlation we evaluate the behavior of two adjacent pixels on horizontal, vertical and diagonal directions. We also analyzed the performance of these algorithms to the most commons cryptographic attacks. Key-Words: Chaos, image encryption, statistical analysis.

[1]  Zhi-Hong Guan,et al.  Adaptive synchronization for Chen chaotic system with fully unknown parameters , 2004 .

[2]  D. López-Mancilla,et al.  Communicating via robust synchronization of chaotic lasers , 2009 .

[3]  Ennio Gambi,et al.  A new chaotic algorithm for video encryption , 2002, IEEE Trans. Consumer Electron..

[4]  Amir Akhavan,et al.  Chaotic Cryptographic Scheme Based on Composition Maps , 2006, Int. J. Bifurc. Chaos.

[5]  Guanrong Chen,et al.  Breaking a chaos-based secure communication scheme designed by an improved modulation method , 2004, nlin/0411007.

[6]  L. Kocarev Chaos-based cryptography: a brief overview , 2001 .

[7]  C. Chui,et al.  A symmetric image encryption scheme based on 3D chaotic cat maps , 2004 .

[8]  Stephen Lynch,et al.  Dynamical Systems with Applications using MATLAB 2nd Edition , 2014 .

[9]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[10]  Wolfgang A. Halang,et al.  Analog Chaos-based Secure Communications and Cryptanalysis: A Brief Survey , 2007, ArXiv.

[11]  M. Hénon Numerical study of quadratic area-preserving mappings , 1969 .

[12]  M.E.E. Abashar,et al.  On the chaotic behaviour of forced fluidized bed catalytic reactors , 1995 .

[13]  Gonzalo Álvarez,et al.  Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems , 2003, Int. J. Bifurc. Chaos.

[14]  E. E. García-Guerrero,et al.  Synchronization of Chua’s circuits with multi-scroll attractors: Application to communication , 2009 .

[15]  M. A. Jafarizadeh,et al.  Hierarchy of Chaotic Maps with an Invariant Measure and their Compositions , 2002 .

[16]  M. A. Jafarizadeh,et al.  Hierarchy of Chaotic Maps with an Invariant Measure , 2001 .

[17]  R. M. López-Gutiérrez,et al.  Synchronization of multi-scroll chaos generators: application to private communication , 2008 .

[18]  V I Ponomarenko,et al.  Extracting information masked by the chaotic signal of a time-delay system. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  H. Serrano-Guerrero,et al.  Experimental realization of binary signals transmission using chaos , 2002, IEEE 2002 International Conference on Communications, Circuits and Systems and West Sino Expositions.

[20]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[21]  H.M. Elkamchouchi,et al.  Measuring encryption quality for bitmap images encrypted with rijndael and KAMKAR block ciphers , 2005, Proceedings of the Twenty-Second National Radio Science Conference, 2005. NRSC 2005..

[22]  Robert M. May,et al.  Stability and Complexity in Model Ecosystems , 2019, IEEE Transactions on Systems, Man, and Cybernetics.