Abstract
In this paper, we proposed a novel low power and high-speed FPGA implementation of the 4D memristor chaotic system with cubic nonlinearity based on Xilinx System Generator (XSG) model. Firstly, a pseudo-random number generator based on the proposed XSG FPGA implementation of the proposed 4D memristor chaotic system which implemented into Xilinx Spartan-6 X6SLX45 board with 32 fixed-point format. The aim of the FPGA implementation is increasing the frequency of the memristor chaotic random number generators. The FPGA implementation of the memristor chaotic system results show that the new design approach achieves a maximum frequency of 393 MHz and dissipates 117 m watt. The standard fifteen randomization tests are used to measure the quality of the proposed pseudo-random number generator based on the 4D memristor chaotic system and it gives an excellent randomization analysis. Also, the gray image encryption scheme based on the 4D memristor chaotic system has been introduced. The proposed cryptosystem has a large keyspace, very low correlation values, high entropy which is much closer to the ideal entropy value, a high number of pixels change rate and high unified average changing intensity values. The results and security analysis of the proposed encryption scheme demonstrate that the investigated encryption approach can protect high speed and high security against various attack.
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References
Akgul A, Calgan H, Koyuncu I, Pehlivan I, Istanbullu A (2015) Chaos-based engineering applications with a 3D chaotic system without equilibrium points. Nonlinear Dyn 84:481–495
Alçın M, Pehlivan İ, Koyuncu İ (2016) Hardware design and implementation of a novel ANN-based chaotic generator in FPGA. Optik 127:5500–5505
Alvarez G, Li S (2006) Some basic cryptographic requirements for chaos-based crypto systems. Int J Bifurcat Chaos 16(8):2129–2151
Johnson T (2015) Digital logic RLT & Verilog interview questions. Create Space Independent Publishing Platform
Azzaz MS, Tanougast C, Sadoudi C, Dandache A (2009) Real time FPGA implementation of Lorenz's chaotic generator for ciphering telecommunications. Joint IEEE North East Workshop on circuits and systems and Taisa Conf France, pp 1–4
Azzaz MS, Tanougast C, Sadoudi S, Fellah R, Dandache A (2013) A new auto-switched chaotic system and its FPGA implementation. Commun Nonlinear Sci Numer Simul 18:1792–1804
Barboza R, Chua LO (2008) The four-element chua’s circuit. Int J Bifurcat Chaos 18(4):943–955
Cgharles HR Jr, Lizy KJ (2017) Digital System Design Using VHDL, 3rd edn. Cengage Learning
Chai X, Yang K, Gan Z (2017) A new chaos-based image encryption algorithm with dynamic key selection mechanisms. Multimed Tools Appl 76:9907–9927
Chua L (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18(5):507–519
Rajagopal K, Akgul A, Jafari S, Karthikeyan A, Koyuncu I (2017) Chaotic chameleon: dynamic analyses, circuit implementation, FPGA design and fractional-order form with basic analyses. Chaos Soliton Fract 103:476–487. https://doi.org/10.1016/j.chaos.2017.07.007
Karakaya B, Celik V, Gulten A (2018) Realization of delayed cellular neural network model ON FPGA. 2018 Electric Electronics, Computer Science, Biomedical Engineerings' Meeting (EBBT), Istanbul, pp 1–4. https://doi.org/10.1109/EBBT.2018.8391449
Gerardo L, Torres E, Tlelo E, Mancillas C (2017) Hardware implementation of Pseudo-random number generator based on chaotic maps. Nonlinear Dyn 90:1661–1670
Guangya P, Fuhong M (2017) Multistability analysis, circuit implementations and application in image encryption of a novel memristive chaotic circuit. Nonlinear Dyn 90:1607–1625
Hidayat O, Mustafa T (2017) FPGA Implementations of Chaotic Quadratic Map for Cryptographic Applications. Turkish Journal of Science & Technology 12(2):113–119
Hua Z, Zhou Y, Huang H (2019) Cosine-transform-based chaotic system for image encryption. Inf Sci 480:403–419
IEEE computer society: IEEE standard for binary floating point arithmetic, ANSI/IEEE std. 754–1985 (1985)
Jakimoski G, Kocarev L (2001) Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans Circuits Systems I Fund Theory Appl 48(2):163–169
Johnson T (2017) Digital Logic RLT & Verilog. Create Space Independent Publishing Platform
Kar M, Mandal MK, Nandi D, Kumar A, Banik S (2016) Bit-plane encrypted image cryptosystem using chaotic, quadratic, and cubic maps, IETE Tech Rev 33(6):651–661. https://doi.org/10.1080/02564602.2015.1136245.
Churiwala S (2017) Designing with Xilinx FPGAs using Vivado. Springer International Publishing. https://doi.org/10.1007/978-3-319-42438-5
Karakaya B, Gulten A, Frasca M (2018) A true random bit generator based on a memristive chaotic circuit: analysis, design and FPGA implementation. Chaos, Solitons Fractals 119:143–149
Kim H, Hong S, Chang J (2014) Hilbert-curve based cryptographic transformation scheme for protecting data privacy on outsourced private spatial data. 2014 International Conference on Big Data and Smart Computing (BIGCOMP), Bangkok, pp 77–82. https://doi.org/10.1109/BIGCOMP.2014.6741411
Koppu V S, Viswanatham M (2017) A fast enhanced secure image chaotic cryptosystem based on hybrid chaotic magic transform. Model Simul Mater Sc 2017:1–12. https://doi.org/10.1155/2017/7470204
Koyuncu I, Ozcerit AT, Pehlivan I (2014) Implementation of FPGA-based real time novel chaotic oscillator. Nonlinear Dyn 77:49–59. https://doi.org/10.1007/s11071-014-1272-x
Li Y, Wang C, Chen H (2017) A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation. Opt Lasers Eng 90:238–246
Liang C, Su L, Wu J, Xiong J (2016) An innovative booth algorithm. 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), China, 2016, pp 1711–1715
Lin Z-h, Wang H-x (2009) Image encryption based on chaos with PWL memristor in Chua's circuit. 2009 International Conference on Communications, Circuits and Systems, Milpitas, CA, pp 964–968. https://doi.org/10.1109/ICCCAS.2009.5250354
Lin Z, Wang H (2010) Efficient image encryption using a chaos-based PWL memristor. IETE Tech Rev 27(4):318–325. https://doi.org/10.4103/0256-4602.64605
Liu LF, Miao SX (2016) A new image encryption algorithm based on logistic chaotic map with varying parameter. Springer Plus 5
Lynch S (2014) Dynamical Systems with Applications using MATLAB, 2nd edn. Springer International Publishing Switzerland 2004
Merah L, Ali-Pacha A, Said NH, Mamat M (2013) Design and FPGA implementation of Lorenz chaotic system for information security issues. Appl Math Sci 7:237–246
Mishra M, Routray A, Kumar S (2012) High Security Image Steganography with Modified Arnold’s Cat Map. Int J Comput Appl 37(9)
Muthuswamy B (2010) Implementing memristor based chaotic circuits. Int J Bifurcat Chaos 20(05):1335–1350. https://doi.org/10.1142/S0218127410026514
NIST (2010) A statistical test suite for random and Pseudo-random number generator for cryptographic applications
Koyuncu I, Ozcerit AT, Pehlivan I (2014) Implementation of FPGA-based real time novel chaotic oscillator. Nonlinear Dyn 77:49–59. https://doi.org/10.1007/s11071-014-1272-x
Sadoudi S, Azzaz MS, Djeddou M, Benssalah M (2009) An FPGA real-time implementation of the Chen’s chaotic system for securing chaotic communications. Int J Nonlin Sci Num 7(4):467–474
Deng Z, Zhong S (2019) A digital image encryption algorithm based on chaotic mapping. J Algorithms Comput Technol 13:1–11. https://doi.org/10.1177/1748302619853470
Tlelo-Cuautle E et al (2015) FPGA realization of multi-scroll chaotic oscillators. Commun Nonlinear Sci Numer Simul 27(1–3):66–80
Tolba MF, Fouda ME, Hezayyin HG, Madian AH, Radwan AG (2019) Memristor FPGA IP Core implementation for analog and digital applications. IEEE Trans Circuits Syst II Express Briefs 66(8):1381–1385
Tuna M, Fidan CB (2016) Electronic circuit design, “implementation and FPGA-based realization of a new 3D chaotic system with single equilibrium point”. Opt - Int J Light Electron Opt 127:11786–11799
Venkatachalam S, Lee HJ, Ko S (2018) Power Efficient Approximate Booth Multiplier. 2018 IEEE International Symposium on Circuits and Systems (ISCAS), Florence, pp 1–4
Wang X, Zhang H (2015) A color image encryption with heterogeneous bit-permutation and correlated chaos. Opt Commun 342:51–60
Wang S, Wang X, Zhou Y (2015) A memristor-based complex Lorenz system and its modified projective synchronization. Entropy 17(11):7628–7644
Wang Q, Yu S, Li C, Lü J, Fang X, Guyeux C, Bahi JM (2016) Theoretical design and FPGA-based implementation of higher-dimensional digital chaotic systems. IEEE Trans Circuits Syst I Regul Papers 63(3):401–412
Wang B, Zou FC, Cheng J (2017) A memristor-based chaotic system and its application in image encryption. Optik 154
Xilinx, Vivado (Apr. 2018) Design suite user guide: model-based DSP design using system generator (UG897), (v 2018.1). Xilinx
Xilinx, Inc. (2012) Synthesis and Simulation Design Guide. UG626 (v 14.5)
Yang C, Hu Q, Yu Y, Zhang R, Yao Y, Cai J (2015) Memristor-based Chaotic Circuit for Text/Image Encryption and Decryption. 8th International Symposium on Computational Intelligence and Design pp 447–450
Ye G, Wong KW (2012) An efficient chaotic image encryption algorithm based on a generalized Arnold map. Nonlinear Dyn 69(4):2079–2087
Zhang L (2017) Fixed-point FPGA model-based design and optimization for Henon map chaotic generator. 2017 IEEE 8th Latin American Symposium on Circuits & Systems (LASCAS), Bariloche, pp 1–4. https://doi.org/10.1109/LASCAS.2017.7948065
Zodpe H, Spkal A (2018) An efficient AES implementation using FPGA with enhanced security features. J King Saud Univ Eng Sci
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Hagras, E.A.A., Saber, M. Low power and high-speed FPGA implementation for 4D memristor chaotic system for image encryption. Multimed Tools Appl 79, 23203–23222 (2020). https://doi.org/10.1007/s11042-019-08517-w
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DOI: https://doi.org/10.1007/s11042-019-08517-w