This paper proposes FPGA realization of an IP core for generic fractional-order derivative based on Grünwald-Letnikov approximation. These results are essential for generating a highly secured nonlinear key for an encryption algorithm, which makes it resistant to various attacks. Third, the strength of chaos must be examined.
Second, the complete range of the chaotic and non-chaotic region of a system must be presented. First, a complete examination of the novel system must be performed with the appropriate chaos detection technique. Hence, it is crucial to realize three important facts.
But in most cases of chaotic maps, the test is performed only for certain random control parameter range, and its dynamics beyond that range is unknown. Further, the dynamics of the chaotic systems are better studied than the chaotic maps. Tests such as 0–1 test, three-state test and some entropy tests are seldom used. Whereas, phase portrait and bifurcation diagram are commonly used for chaotic systems. It is observed that the bifurcation diagram and Lyapunov exponent are the most highly used tests for chaotic maps. This paper analyzes the frequency of the chaos tests performed on 25 discrete chaotic maps and 18 continuous chaotic systems and reviewed for their effectiveness. Various chaos detection techniques are performed on them to examine and measure their complexity. Hence, novel chaotic dynamical systems are developed for this purpose with more advanced features and models. Chaos-based image encryption is increasingly used to protect images with high degree of security than other encryption techniques. The security concern in recent times has been rising exponentially, this has lead for highly secured image transmission.
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