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A new 3-D chaotic dynamical system with a peanut-shaped closed curve of equilibrium points is introduced in this work. Since the new chaotic system has infinite number of rest points, the new chaotic model exhibits hidden attractors. A detailed dynamic analysis of the new chaotic model using bifurcation diagrams and entropy analysis is described. The new nonlinear plant shows multi-stability and coexisting convergent attractors. A circuit model using MultiSim of the new 3-D chaotic model is designed for engineering applications. The new multi-stable chaotic system is simulated on a field-programmable gate array (FPGA) by applying two numerical methods, showing results in good agreement with numerical simulations. Consequently, we utilize the properties of our chaotic system in designing a new cipher colour image mechanism. Experimental results demonstrate the efficiency of the presented encryption mechanism, whose outcomes suggest promising applications for our chaotic system in various cryptographic applications.

Designing efficient and secure cryptosystems has been a preoccupation for many scientists and engineers for a long time wherein they use chaotic systems to design new cryptosystems. While one dimensional (1-D) chaotic maps possess powerful properties compared to higher dimension ones, they are vulnerable to various attacks due to their small key space, chaotic discontinuous ranges, and degradation in chaotic dynamical behaviours. Moreover, when simulated on a computer, every such chaotic system produces a periodic cycle. Meanwhile, quantum random walks exhibit the potential for deployment in efficient cryptosystem design, which makes it an excellent solution for this problem. In this context, we present a new method for constructing substitution boxes (S-boxes) based on cascaded quantum-inspired quantum walks and chaos inducement. the performance of the proposed S-box scheme is investigated via established S-box evaluation criterion and outcomes suggest that the constructed S-box has significant qualities for viable applications information security. Further, we present an efficient scheme for pseudo-random numbers generation (PRNG) whose sustainability over long periods remedies the periodicity problem associated with traditional cryptographic applications. Furthermore, by combining the two mechanisms, an atypical image encryption scheme is introduced. Simulation results and analysis validate that the proposed image encryption algorithm will offer gains in many cryptographic applications. Chaotic systems have attracted a great deal of attention across different scientific and engineering disciplines, especially in designing new cryptosystems and cryptanalysis. A chaotic system is an evolution map of a deterministic dynamical system that reconstructs the state of a system S 0 to a new state S 1 depending on the initial state of S 0 , a control parameter C, and time T 1. Chaotic maps exhibit the desired properties of ergodicity, unpredictability, and sensitivity to their control parameter(s) and initial value(s) that satisfy the requirements for cryptosystem confusion-diffusion properties 2-4. In fact, an inappropriate initial control parameter of a chaotic system can lead to non-chaotic behaviours, which implies the reduction in nonlinearity levels as well as circumvention of insecurity pitfalls 5,6. Currently, chaotic dynamical systems play a vital role in designing modern cryptographic applications, such as constructing S-boxes, generating pseudo-random numbers, designing image encryption algorithms and so on 7-16 , which are based on the unproven assumptions pertaining to computational complexity and that their constructions are based on mathematical models. However, with the development of quantum technologies, some of these traditional security mechanisms, and cryptographic applications may be effortlessly violated and abused 17-19. Among the computational models developed in quantum computation, quantum walks (QWs), which is a universal model of quantum computation that has been traditionally employed to de...