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 proved by analysis of Lyapunov's exponent, fractional dimension, zero-one test, sensitivity dependent on initial condition (SDIC), phase portraits, and waveform analysis, study offers an innovative designed image encryption algorithm depending a using fast discrete Walsh-Hadamard transform magic matrix both effective simple for gives it higher level security. This new used to produce random key algorithm. The implemented simulated results mathematica programs MATLAB were supplied qualitatively figures. hyperchaotic, according testing results, because possesses two Lyapunov exponents.