Cubature Kalman filter-based chaotic synchronization and image encryption

Abstract In this paper, a chaotic communication method based on the Cubature Kalman Filter (CKF) is presented. Using CKF, state estimation of a chaotic dynamical system and synchronization, in the presence of processing noise and measurement noise, are presented. The proposed method is then applied to a private secure communication setup, and an image encryption algorithm is introduced, where the original image is encoded by a chaotic state. Simulation results show that the original image is well masked in the cipher texts and is recovered successfully from the chaotic signals. Further, the cryptanalysis is conducted in detail through histogram, correlation of two adjacent pixels, differential analysis, information entropy, key and computational complexity analysis to demonstrate the high security, sensitivity and speed of the proposed encryption scheme.

[1]  Martin Hasler,et al.  Synchronization of chaotic systems and transmission of information , 1998 .

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

[3]  Michael Peter Kennedy,et al.  Digital communications using chaos , 2000, Signal Process..

[4]  Dominique Barchiesi,et al.  A new image encryption scheme based on a chaotic function , 2012, Signal Process. Image Commun..

[5]  Ana Cristina Dascalescu,et al.  A new hyperchaotic map and its application in an image encryption scheme , 2014, Signal Process. Image Commun..

[6]  Behrooz Khadem,et al.  A self-synchronized chaotic image encryption scheme , 2015, Signal Process. Image Commun..

[7]  Henk Nijmeijer,et al.  Synchronization through Filtering , 2000, Int. J. Bifurc. Chaos.

[8]  Xingyuan Wang,et al.  Image encryption using DNA complementary rule and chaotic maps , 2012, Appl. Soft Comput..

[9]  Safwan El Assad,et al.  A new chaos-based image encryption system , 2016, Signal Process. Image Commun..

[10]  Chi-Chuan Hwang,et al.  A linear continuous feedback control of Chua's circuit , 1997 .

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

[12]  Simo Särkkä,et al.  Bayesian Filtering and Smoothing , 2013, Institute of Mathematical Statistics textbooks.

[13]  S. Haykin,et al.  Cubature Kalman Filters , 2009, IEEE Transactions on Automatic Control.

[14]  Zhongmeng Zhao,et al.  Chaotic image encryption based on circular substitution box and key stream buffer , 2014, Signal Process. Image Commun..

[15]  M. Yaghoobi,et al.  A new image encryption method: parallel sub-image encryption with hyper chaos , 2011, Nonlinear Dynamics.

[16]  Jacques M. Bahi,et al.  Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Hua Wang,et al.  Image encryption based on synchronization of fractional chaotic systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[18]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

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

[20]  Magno T. M. Silva,et al.  Do chaos-based communication systems really transmit chaotic signals? , 2015, Signal Process..

[21]  Ljupco Kocarev,et al.  General approach for chaotic synchronization with applications to communication. , 1995, Physical review letters.

[22]  Ali Shokouhi Rostami,et al.  A private secure communication scheme using UKF-based chaos synchronization , 2015 .

[23]  Zhengzhi Han,et al.  Controlling and synchronizing chaotic Genesio system via nonlinear feedback control , 2003 .

[24]  E. Stear,et al.  The simultaneous on-line estimation of parameters and states in linear systems , 1976 .

[25]  Jing Li,et al.  A novel image encryption scheme based on a linear hyperbolic chaotic system of partial differential equations , 2013, Signal Process. Image Commun..

[26]  Kazufumi Ito,et al.  Gaussian filters for nonlinear filtering problems , 2000, IEEE Trans. Autom. Control..

[27]  S. Mascolo,et al.  Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal , 1997 .

[28]  Henk Nijmeijer,et al.  An observer looks at synchronization , 1997 .

[29]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[30]  Safya Belghith,et al.  A novel image encryption scheme based on substitution-permutation network and chaos , 2016, Signal Process..

[31]  Moez Feki,et al.  Observer-based chaotic synchronization in the presence of unknown inputs , 2003 .

[32]  Zhongmeng Zhao,et al.  Chaos-based image encryption with total shuffling and bidirectional diffusion , 2013, Nonlinear Dynamics.

[33]  F. M. Kakmeni,et al.  A new adaptive observer-based synchronization scheme for private communication , 2006 .

[34]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[35]  Ioannis M. Kyprianidis,et al.  Image encryption process based on chaotic synchronization phenomena , 2013, Signal Process..

[36]  Chen Gang,et al.  A new image encryption algorithm , 2004 .

[37]  Safya Belghith,et al.  Algebraic analysis of a RGB image encryption algorithm based on DNA encoding and chaotic map , 2014 .

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

[39]  Tzung-Her Chen,et al.  Cryptanalysis and improvement of two hyper-chaos-based image encryption schemes , 2015, Signal Process. Image Commun..

[40]  Yicong Zhou,et al.  2D Sine Logistic modulation map for image encryption , 2015, Inf. Sci..