A Novel S-Box Design Algorithm and fuzzy-PID controller Design for a 5-d Burke-Shaw System with Hidden Hyperchaos

This paper presents a new S-Box design algorithm of hidden hyperchaos in a 5-D hyperchaotic Burke–Shaw system, which is obtained by adding feedback controllers to the classic Burke–Shaw system. Of particular interest is that the hidden hyperchaotic attractors can be generated with three positive Lyapunov exponents in the proposed system with only one stable equilibrium. In addition, a new Pseudo Random Number Generator (PRNG) is developed by using the new 5-D Burke–Shaw system. Then, the S-Box design algorithm is developed based on the new PRNG. Furthermore, generated bit series have passed all NIST tests, which are run on bit series from the new PRNG. According to performance analysis, generated S-Box has better value than the chaos-based S-Box on the literature. Finally, Fuzzy-PID controller design is discussed for 5-D Burke–Shaw system with hidden hyperchaos. These results show the effectiveness of controller.