A Chaotic Cryptosystem for Images Based on Henon and Arnold Cat Map

The rapid evolution of imaging and communication technologies has transformed images into a widespread data type. Different types of data, such as personal medical information, official correspondence, or governmental and military documents, are saved and transmitted in the form of images over public networks. Hence, a fast and secure cryptosystem is needed for high-resolution images. In this paper, a novel encryption scheme is presented for securing images based on Arnold cat and Henon chaotic maps. The scheme uses Arnold cat map for bit- and pixel-level permutations on plain and secret images, while Henon map creates secret images and specific parameters for the permutations. Both the encryption and decryption processes are explained, formulated, and graphically presented. The results of security analysis of five different images demonstrate the strength of the proposed cryptosystem against statistical, brute force and differential attacks. The evaluated running time for both encryption and decryption processes guarantee that the cryptosystem can work effectively in real-time applications.

[1]  Michael Ganley,et al.  Encryption algorithms , 1992 .

[2]  Hai Yu,et al.  A fast chaos-based image encryption scheme with a dynamic state variables selection mechanism , 2015, Commun. Nonlinear Sci. Numer. Simul..

[3]  Paul M. Chau,et al.  Image encryption for secure Internet multimedia applications , 2000, 2000 Digest of Technical Papers. International Conference on Consumer Electronics. Nineteenth in the Series (Cat. No.00CH37102).

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

[5]  Xuanqin Mou,et al.  Pseudo-random Bit Generator Based on Couple Chaotic Systems and Its Applications in Stream-Cipher Cryptography , 2001, INDOCRYPT.

[6]  Yixian Yang,et al.  An improved chaotic cryptosystem based on circular bit shift and XOR operations , 2012 .

[7]  Xing-yuan Wang,et al.  A new compound mode of confusion and diffusion for block encryption of image based on chaos , 2010 .

[8]  Zhang Xing,et al.  Chaotic Image Encryption Based on Running-Key Related to Plaintext , 2014, TheScientificWorldJournal.

[9]  Jan Nordin,et al.  A Survey on Principal Aspects of Secure Image Transmission , 2012 .

[10]  Kwok-Wo Wong,et al.  Breaking a novel colour image encryption algorithm based on chaos , 2012, Nonlinear Dynamics.

[11]  Zhiliang Zhu,et al.  A Novel Image Encryption Algorithm Based on Improved 3D Chaotic Cat Map , 2008, 2008 The 9th International Conference for Young Computer Scientists.

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

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

[14]  Xing-yuan Wang,et al.  A chaotic image encryption algorithm based on perceptron model , 2010 .

[15]  Wei Zhou,et al.  A Chaos-based Image Encryption Scheme Using 3D Skew Tent Map and Coupled Map Lattice , 2012 .

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

[17]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[18]  Tao Xie,et al.  Breaking a novel image encryption scheme based on improved hyperchaotic sequences , 2012, Nonlinear Dynamics.

[19]  Hassan N. Noura,et al.  An image encryption scheme based on irregularly decimated chaotic maps , 2014, Signal Process. Image Commun..

[20]  Paul M. Chau,et al.  Implementation of the IDEA algorithm for image encryption , 2000, SPIE Optics + Photonics.

[21]  M. Hénon,et al.  A two-dimensional mapping with a strange attractor , 1976 .

[22]  Celso Grebogi,et al.  Cryptography with chaos at the physical level. , 2004 .

[23]  Y. Mu,et al.  Optical Image Encryption Based on Chaotic Baker Map and Double Random Phase Encoding , 2013, Journal of Lightwave Technology.

[24]  Z. Guan,et al.  Chaos-based image encryption algorithm ✩ , 2005 .

[25]  Di Xiao,et al.  Analysis and improvement of a chaos-based image encryption algorithm , 2009 .

[26]  Peng Xu,et al.  Research of Image Encryption Algorithm Based on Chaotic Magic Square , 2012 .

[27]  S. Li,et al.  Cryptographic requirements for chaotic secure communications , 2003, nlin/0311039.

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

[29]  Xiao Liu,et al.  A novel chaos-based bit-level permutation scheme for digital image encryption , 2011 .

[30]  E. Lorenz,et al.  Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set off a Tornado in Texas? , 2013 .

[31]  B. Subramanyan,et al.  Image Encryption Based on AES Key Expansion , 2011, 2011 Second International Conference on Emerging Applications of Information Technology.

[32]  Somaya Al-Máadeed,et al.  A New Chaos-Based Image-Encryption and Compression Algorithm , 2012, J. Electr. Comput. Eng..

[33]  S. Li,et al.  Cryptanalyzing a nonlinear chaotic algorithm (NCA) for image encryption , 2009 .

[34]  Qiang Zhang,et al.  A Novel Image Encryption Algorithm Based on DNA Subsequence Operation , 2012, TheScientificWorldJournal.

[35]  Wei Zhang,et al.  A chaos-based symmetric image encryption scheme using a bit-level permutation , 2011, Inf. Sci..

[36]  Sergio Cerutti,et al.  Nonlinear Analysis of Experimental Time Series , 2011 .

[37]  Yu Zhang,et al.  Breaking a chaotic image encryption algorithm based on perceptron model , 2011, Nonlinear Dynamics.

[38]  Ting Cao,et al.  A Chaos-Based Image Encryption Scheme with Confusion- Diffusion Architecture , 2011, CSIE 2011.

[39]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[40]  Wei Zhou,et al.  An Image Encryption Scheme Based on 2D Tent Map and Coupled Map Lattice , 2011 .

[41]  S. Li,et al.  Breaking an encryption scheme based on chaotic baker map , 2004, Physics Letters.

[42]  Kwok-Wo Wong,et al.  Image Encryption Using Chaotic Maps , 2009, Intelligent Computing Based on Chaos.

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

[44]  Xin Zhang,et al.  A new chaotic algorithm for image encryption , 2006 .

[45]  X. Liao,et al.  A novel block cryptosystem based on iterating a chaotic map , 2006 .

[46]  Samrat L. Sabat,et al.  A fast chaotic block cipher for image encryption , 2014, Commun. Nonlinear Sci. Numer. Simul..