Chaotic or Hyper-chaotic Oscillator? Numerical Solution, Circuit Design, MATLAB HDL-Coder Implementation, VHDL Code, Sec
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Chaotic or Hyper-chaotic Oscillator? Numerical Solution, Circuit Design, MATLAB HDL-Coder Implementation, VHDL Code, Security Analysis, and FPGA Realization Talal Bonny1 Received: 3 November 2019 / Revised: 7 August 2020 / Accepted: 11 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Hyper-chaotic systems can exhibit a higher level of complexity in comparison with the chaotic systems. However, they require more resources when they are realized on a modular field-programmable gate array (FPGA). In this paper, we introduce full hardware/software comparison and security analysis of three-dimensional chaotic and four-dimensional hyper-chaotic oscillator systems. The two systems (previously implemented only in analog form) are realized on a modular FPGA hardware platform to generate high-speed random bit-streams. The realization is performed using two versions of VHDL code, one is generated automatically using a MATLAB HDL-Coder, and the optimized one which is manually written. The work explores the features of each oscillator system such as throughput, FPGA resources utilization, operating clock frequency, and security of the generated bit-streams, to show a compromise solution on these features. The experimental results show that the hyper-chaotic oscillator has higher level of security than the chaotic one, but it is slower and utilizes more FPGA resources. However, when the overall comparison measure figure of merit (FOM) is used, the chaotic system shows 188% better FOM than the hyper-chaotic system (for the automatically generated version) and 183% (for the manually written one). Keywords Chaotic oscillator · Hyper-chaotic oscillator · MATLAB HDL-Coder · VHDL · NIST · FPGA
1 Introduction Various chaotic systems have been introduced in the previous work through the past years, such as Chen [11], Chua [22], Colpits [23], Lorenz [27], and Rossler [35]. These systems are characterized by the impossibility to predict their behavior [42].
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Talal Bonny [email protected] Department of Computer Engineering, University of Sharjah, Sharjah, United Arab Emirates
Circuits, Systems, and Signal Processing
This makes the continuous-time chaotic oscillation a good candidate to generate truly random numbers [16], which can be used for a wide range of applications like eGovernment, e-identity card, e-Passport, e-Visa, e-Commerce, control [41,45], and public and private keys of symmetric, asymmetric [10], and hybrid crypto-systems [38]. Hyper-chaotic systems have also been introduced in the literature as a multidirectional expansion which leads to much more complex dynamical behaviors [36]. They are characterized by more than one positive Lyapunov exponent. Therefore, the hyper-chaotic system can exhibit a higher level of complexity in comparison with the chaotic system [19]. Hyperchaos has been found in many 4D circuits with capacitors, inductors, or by combining a memristor with cubic nonlinear characteristics [33], and a modified canonical Chua’s circuit [20]. This memristive s
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