Image scrambler based on novel 4-D hyperchaotic system and magic square with fast Walsh–Hadamard transform

A novel 4-D hyperchaotic system that have seven positive parameters in third order with thirteen terms is proposed,in this paper, the proposed chaotic behavior is proved by analysis of the Lyapunov's exponent, fractional dimension, zero-one test, sensitivity dependent on initial condition (SDIC), phase portraits, and waveform analysis, this study offers an innovative designed image encryption algorithm depending on a 4-D chaotic system using fast discrete Walsh-Hadamard transform and magic matrix that is both effective and simple for image encryption and gives it a higher level of security. This new 4-D hyperchaotic system is used to produce a random key in this algorithm. The implemented and simulated results using mathematica programs and MATLAB programs were supplied qualitatively and in figures. The proposed system is hyperchaotic, according to testing results, because it possesses two Lyapunov positive exponents.