A Simple Chaotic Flow with Hyperbolic Sinusoidal Function and Its Application to Voice Encryption

Abstract

In this article, a new chaotic system with hyperbolic sinusoidal function is introduced. This chaotic system provides a new category of chaotic flows which gives better perception of chaotic attractors. In the proposed chaotic flow with hyperbolic sinusoidal function, according to the changes of parameters of the system, the self-excited attractor and two forms of hidden attractors are occurred. Dynamic behavior of the offered chaotic flow is studied through eigenvalues, bifurcation diagrams, phase portraits, and spectrum of Lyapunov exponents. Moreover, the existence of double-scroll attractors in real word is considered via the Orcard-PSpice software through an electronic execution of the new chaotic flow and illustrative results between the numerical simulation and Orcard-PSpice outcomes are obtained. Lastly, random number generator (RNG) design is completed with the new chaos. Using the new RNG design, a novel voice encryption algorithm is suggested and voice encryption use and encryption analysis are performed.

Chaos in the Real World: Recent Applications to Communications, Computing, Distributed Sensing, Robotic Motion, Bio-Impedance Modelling and Encryption Systems

“…Herein two main topics are discussed. One issue regards the hardware implementations of encryption systems [18][19][20][21][22][23][24][25][26], whereas the other is related to the capability of chaotic systems to generate random numbers [27][28][29][30][31][32][33][34][35].…”

“…Since randomness and unpredictability are required by encryption, it is clear that chaos has good features in this regard, by virtue of the sensitive dependence on initial conditions, periodicity and reproduction. Some interesting manuscripts have been recently published on the topic [27][28][29][30][31][32][33][34][35]. For example, in [27] the dynamics of some discrete-time chaotic systems in the digital (i.e., finite-precision) domain is studied.…”

“…In [32], a novel chaotic system with hyperbolic sinusoidal function is introduced, where self-excited attractors and hidden attractors coexist. A chaotic circuit is designed and implemented.…”

“…A chaotic circuit is designed and implemented. By varying its parameters, it is shown that the chaotic circuit presents two sets of hidden attractors (with line of equilibria and no equilibrium point), which provide additional complexity to the system dynamics [32]. On the basis of these results, a random number generator is designed, which successfully passes all the NIST statistical tests [32].…”

“…In Section 5 it is shown how chaos can give significant insights to the quality assessments of fruits and vegetables [17]. Section 6 presents some applications of chaos to the hardware implementation of encryption systems [18][19][20][21][22][23][24][25][26] and to random number generation [27][28][29][30][31][32][33][34][35], including the use of chaos for secure transfer of medical images. Finally, Section 7 illustrates how chaos-based logic gates can be used for computing [36], whereas Section 8 highlights how chaos can be exploited in neuromorphic applications [37,38].…”