Deterministic chaotic finite-state automata

Chaotic dynamics have been widely applied in various domains such as cryptography, watermarking and optimization algorithms. Enhancing chaotic complexity of simple one-dimensional (1D) chaotic maps has been a popular topic of research in recent years. However, most of the proposed methods have low complexity and are not suitable for practical applications. To overcome these issues, this paper introduces a novel approach known as deterministic chaotic finite-state automata (DCFSA). Existing 1D chaotic maps are associated with deterministic finite automata states. Then, a transition rule dynamically selects which 1D chaotic map to compute. DCFSA allows the creation of a large number of possible chaotic configurations with enhanced nonlinearity while retaining the computational complexity comparable to a 1D map. Theoretical and performance analyses show that DCFSA provides a larger chaotic parameter range, higher nonlinearity and chaotic complexity, as well as longer cycle length as compared to its underlying 1D chaotic maps. Moreover, performance comparison against other existing chaotification methods demonstrates DCFSA’s superiority.

[1]  Huiling Chen,et al.  Predicting Intentions of Students for Master Programs Using a Chaos-Induced Sine Cosine-Based Fuzzy K-Nearest Neighbor Classifier , 2019, IEEE Access.

[2]  Pagavathigounder Balasubramaniam,et al.  T–S fuzzy predictive control for fractional order dynamical systems and its applications , 2016 .

[3]  Alan V. Oppenheim,et al.  Synchronization of Lorenz-based chaotic circuits with applications to communications , 1993 .

[4]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[5]  Guo-Ping Jiang,et al.  System Design and Performance Analysis of Orthogonal Multi-Level Differential Chaos Shift Keying Modulation Scheme , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  David Arroyo,et al.  Cryptanalysis of a one round chaos-based Substitution Permutation Network , 2012, Signal Process..

[7]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[8]  Yicong Zhou,et al.  Dynamic Parameter-Control Chaotic System , 2016, IEEE Transactions on Cybernetics.

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

[10]  Azman Samsudin,et al.  A Chaos-Based Authenticated Cipher with Associated Data , 2017, Secur. Commun. Networks.

[11]  Guanrong Chen,et al.  Design and FPGA-Based Realization of a Chaotic Secure Video Communication System , 2018, IEEE Transactions on Circuits and Systems for Video Technology.

[12]  Raphael C.-W. Phan,et al.  SPRING: a novel parallel chaos-based image encryption scheme , 2018 .

[13]  P. Balasubramaniam,et al.  Fast projective synchronization of fractional order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (DOB) , 2015 .

[14]  Lingfeng Liu,et al.  A new simple one-dimensional chaotic map and its application for image encryption , 2018, Multimedia Tools and Applications.

[15]  Pagavathigounder Balasubramaniam,et al.  Synchronization of a novel fractional order stretch-twist-fold (STF) flow chaotic system and its application to a new authenticated encryption scheme (AES) , 2014, Nonlinear Dynamics.

[16]  Hegui Zhu,et al.  Analyzing Devaney Chaos of a Sine-Cosine Compound Function System , 2018, Int. J. Bifurc. Chaos.

[17]  Fatih Özkaynak,et al.  Brief review on application of nonlinear dynamics in image encryption , 2018, Nonlinear Dynamics.

[18]  Pagavathigounder Balasubramaniam,et al.  Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography , 2013, Nonlinear Dynamics.

[19]  Jun Lin,et al.  A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map , 2017, Int. J. Bifurc. Chaos.

[20]  Hong-Bo Xie,et al.  Complexity analysis of the biomedical signal using fuzzy entropy measurement , 2011, Appl. Soft Comput..

[21]  Qixiang Mei,et al.  An efficient pixel-level chaotic image encryption algorithm , 2018, Nonlinear Dynamics.

[22]  N. K. Pareek,et al.  Modified substitution-diffusion image cipher using chaotic standard and logistic maps , 2010 .

[23]  Pagavathigounder Balasubramaniam,et al.  Detecting chaos in a system of four disk dynamos and its control , 2016 .

[24]  Azman Samsudin,et al.  A new hybrid digital chaotic system with applications in image encryption , 2019, Signal Process..

[25]  Yicong Zhou,et al.  Cascade Chaotic System With Applications , 2015, IEEE Transactions on Cybernetics.

[26]  Mark Reynolds,et al.  Toward Occlusion Handling in Visual Tracking via Probabilistic Finite State Machines , 2020, IEEE Transactions on Cybernetics.

[27]  Jianhua Lin,et al.  Divergence measures based on the Shannon entropy , 1991, IEEE Trans. Inf. Theory.

[28]  Yicong Zhou,et al.  Image encryption using a new parametric switching chaotic system , 2013, Signal Process..

[29]  Lingfeng Liu,et al.  Feedback control of digital chaotic systems with application to pseudorandom number generator , 2015 .

[30]  Mario Sportelli,et al.  A Mathematical Approach to Harrod's Open Economy Dynamics , 2011 .

[31]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[32]  Tariq Shah,et al.  A novel scheme for image encryption using substitution box and chaotic system , 2017 .

[33]  Reva Freedman,et al.  An intelligent tutoring system that generates a natural language dialogue using dynamic multi-level planning , 2006, Artif. Intell. Medicine.

[34]  Kaijun Tan,et al.  A chaos-based keyed hash function based on fixed point representation , 2018, Cluster Computing.

[35]  Ramachandran Amutha,et al.  A fast double-keyed authenticated image encryption scheme using an improved chaotic map and a butterfly-like structure , 2018, Nonlinear Dynamics.

[36]  M. Zarebnia,et al.  A combination chaotic system and application in color image encryption , 2017, ArXiv.

[37]  Sos S. Agaian,et al.  Local Shannon entropy measure with statistical tests for image randomness , 2013, Inf. Sci..

[38]  Thomas Johansson,et al.  A New Version of the Stream Cipher SNOW , 2002, Selected Areas in Cryptography.

[39]  D. Smirnov,et al.  Estimation of parameters in one-dimensional maps from noisy chaotic time series [rapid communication] , 2005 .

[40]  Lingfeng Liu,et al.  Delay-introducing method to improve the dynamical degradation of a digital chaotic map , 2017, Inf. Sci..

[41]  Giuseppe Orlando,et al.  Recurrence Quantification Analysis of Business Cycles , 2018, Nonlinearities in Economics.

[42]  Roger A. Sayle,et al.  Lingos, Finite State Machines, and Fast Similarity Searching , 2006, J. Chem. Inf. Model..

[43]  Azman Samsudin,et al.  Enhancing unimodal digital chaotic maps through hybridisation , 2019, Nonlinear Dynamics.

[44]  Min Lei,et al.  Fault Detection for Vibration Signals on Rolling Bearings Based on the Symplectic Entropy Method , 2017, Entropy.

[45]  Yicong Zhou,et al.  Discrete Wheel-Switching Chaotic System and Applications , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[46]  Nilanjan Sarkar,et al.  Symplectic Entropy as a Novel Measure for Complex Systems , 2016, Entropy.

[47]  Azman Samsudin,et al.  An image encryption scheme based on hybridizing digital chaos and finite state machine , 2019, Signal Process..

[48]  Yue Chen,et al.  A novel chaos-based fragile watermarking for image tampering detection and self-recovery , 2013, Signal Process. Image Commun..

[49]  Martin Hell,et al.  The Grain Family of Stream Ciphers , 2008, The eSTREAM Finalists.

[50]  Sankalap Arora,et al.  Chaotic grey wolf optimization algorithm for constrained optimization problems , 2018, J. Comput. Des. Eng..

[51]  Qun Ding,et al.  Analysing the dynamics of digital chaotic maps via a new period search algorithm , 2019 .

[52]  Yicong Zhou,et al.  One-Dimensional Nonlinear Model for Producing Chaos , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[53]  P. Balasubramaniam,et al.  Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system , 2015 .

[54]  Amir Akhavan,et al.  Parallel chaotic hash function based on the shuffle-exchange network , 2015 .