Real-time implementation of a chaos based cryptosystem on low-cost hardware

To overcome the worse statistical proprieties of digital chaotic maps, this paper proposes a modified version of the Henon chaotic map using a cosine function. What is new in this proposal is that the cosine function replaces only the nonlinear part of the chaotic map which increases the chaotic proprieties compared to other proposals. On the other hand, adding a constant with a high value ( $$F > 10^4$$ ) to the new control parameter eliminates the small zones of stability that cannot be observed easily. The improved Henon map has been evaluated in terms of randomness quality using a set of mathematical tools, in which good results have been obtained. The improved map is used to design a cryptosystem; we have proposed an efficient method for the aim of ensuring the diffusion property by feeding back the encrypted message to the modified map. So, a very small change on the plaintext leads to a different chaotic state. The proposed encryption scheme has been evaluated in terms of security, in which some known cryptographic attacks have been performed on it. The results showed that the proposed encryption scheme meets the nowadays security requirements. The proposed encryption scheme is evaluated in real-time using low-cost ARM (Cortex-M3 32-bit RISC core) under two different scenarios, emitter, and receiver, which are connected wirelessly. A comparison with some existing solutions showed that our proposal provides a good ratio between randomness, implementation cost, and performance.

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

[2]  Lingfeng Liu,et al.  Reducing the Dynamical Degradation of Digital Chaotic Maps with Time-Delay Linear Feedback and Parameter Perturbation , 2020 .

[3]  Esteban Tlelo-Cuautle,et al.  FPGA-based Chaotic Cryptosystem by Using Voice Recognition as Access Key , 2018, Electronics.

[4]  Pawel Dabal,et al.  A chaos-based pseudo-random bit generator implemented in FPGA device , 2011, 14th IEEE International Symposium on Design and Diagnostics of Electronic Circuits and Systems.

[5]  Yide Ma,et al.  A Novel 1D Hybrid Chaotic Map-Based Image Compression and Encryption Using Compressed Sensing and Fibonacci-Lucas Transform , 2016 .

[6]  E. Inzunza-González,et al.  Implementing a chaotic cryptosystem in a 64-bit embedded system by using multiple-precision arithmetic , 2019, Nonlinear Dynamics.

[7]  Alexander Marshak,et al.  Approximate Entropy and Sample Entropy: A Comprehensive Tutorial , 2019, Entropy.

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

[9]  Lahcene Merah,et al.  A pseudo random number generator based on the chaotic system of Chua's circuit, and its real time FPGA implementation , 2013 .

[10]  J. Nevima Visegrad Four Countries - Case Study of Econo- metric Panel Data Model for Regional Competi- tiveness Evaluation , 2012 .

[11]  Slawomir T. Fryska,et al.  Computer dynamics and shadowing of chaotic orbits , 1992 .

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

[13]  Abbas Dandache,et al.  A new auto-switched chaotic system and its FPGA implementation , 2013, Commun. Nonlinear Sci. Numer. Simul..

[14]  Pawel Dabal,et al.  FPGA-based cryptosystem with combined stream-block cipher and digital chaos generator , 2010, ICSES 2010 International Conference on Signals and Electronic Circuits.

[15]  Yolanda Vidal,et al.  An Experimental Realization of a Chaos-Based Secure Communication Using Arduino Microcontrollers , 2015, TheScientificWorldJournal.

[16]  Lahcene Merah,et al.  Real-time cryptosystem based on synchronized chaotic systems , 2015 .

[17]  Elaine B. Barker,et al.  A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2000 .

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

[19]  Dewi Utami,et al.  FPGA Implementation of Digital Chaotic Cryptography , 2002, EurAsia-ICT.

[20]  Lahcene Merah,et al.  New and Efficient Method for Extending Cycle Length of Digital Chaotic Systems , 2018, Iranian Journal of Science and Technology, Transactions of Electrical Engineering.

[21]  M. Stanciu,et al.  Atmel AVR microcontroller implementation of a new enciphering algorithm based on a chaotic Generalized Hénon Map , 2012, 2012 9th International Conference on Communications (COMM).

[22]  Enrico Macii,et al.  Designing low-power circuits: practical recipes , 2001 .

[23]  Xiao-Jun Tong,et al.  Design of an image encryption scheme based on a multiple chaotic map , 2013, Commun. Nonlinear Sci. Numer. Simul..

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

[25]  Ismail Koyuncu,et al.  The design and realization of a new high speed FPGA-based chaotic true random number generator , 2017, Comput. Electr. Eng..

[26]  M. Rosenstein,et al.  A practical method for calculating largest Lyapunov exponents from small data sets , 1993 .

[27]  Christos K. Volos,et al.  Chaotic Random Bit Generator Realized with a Microcontroller , 2013 .

[28]  Eli Biham,et al.  Differential cryptanalysis of DES-like cryptosystems , 1990, Journal of Cryptology.

[29]  Huaguang Zhang,et al.  Controlling Chaos: Suppression, Synchronization and Chaotification , 2009 .

[30]  Esteban Tlelo-Cuautle,et al.  Randomness improvement of chaotic maps for image encryption in a wireless communication scheme using PIC-microcontroller via Zigbee channels , 2020 .

[31]  Guanrong Chen,et al.  A cascading method for constructing new discrete chaotic systems with better randomness. , 2019, Chaos.

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

[33]  Lingfeng Liu,et al.  Counteracting the dynamical degradation of digital chaos via hybrid control , 2014, Commun. Nonlinear Sci. Numer. Simul..

[34]  Yicong Zhou,et al.  Sine Chaotification Model for Enhancing Chaos and Its Hardware Implementation , 2019, IEEE Transactions on Industrial Electronics.

[35]  Azman Samsudin,et al.  Digital Cosine Chaotic Map for Cryptographic Applications , 2019, IEEE Access.

[36]  Guanrong Chen,et al.  On the Dynamical Degradation of Digital Piecewise Linear Chaotic Maps , 2005, Int. J. Bifurc. Chaos.

[37]  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.

[38]  J. Cernák Digital generators of chaos , 1996 .

[39]  Nicolas Sklavos On the Hardware Implementation Cost of Crypto-Processors Architectures , 2010, Inf. Secur. J. A Glob. Perspect..

[40]  Elaine B. Barker,et al.  A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2000 .

[41]  Ljupco Kocarev,et al.  From chaotic maps to encryption schemes , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

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

[43]  Yong Feng,et al.  Chaos Synchronization Using A Robust Sliding Mode Observer By Transmitting A Scalar Signal , 2006, APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems.

[44]  Yicong Zhou,et al.  Cosine-transform-based chaotic system for image encryption , 2019, Inf. Sci..

[45]  X. Mou,et al.  On the security of a chaotic encryption scheme: problems with computerized chaos in finite computing precision , 2003 .

[46]  Lahcene Merah,et al.  Enhanced Chaos-based Pseudo Random Numbers Generator , 2018, 2018 International Conference on Applied Smart Systems (ICASS).

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

[48]  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.

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

[50]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[51]  Yicong Zhou,et al.  A new 1D chaotic system for image encryption , 2014, Signal Process..

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