2D hyperchaotic system based on Schaffer function for image encryption

Chaotic systems are the most essential tools for wide range of applications such as communication, water-marking, data compression and multimedia encryption. However, the existing chaotic systems suffer from low complexity and randomness. In this study, a novel 2D hyperchaotic system denoted as Schaffer map is conceived for high complexity required applications. It is inspired by the Schaffer function mostly used as optimization benchmark function to exploit its strict oscillation properties. The chaotic performance of 2D Schaffer map is evaluated over rigorous chaos indicators such as bifurcation and phase space trajectory diagrams, Lyapunov exponent (LE), sample entropy (SE), permutation entropy (PE), 0-1 test, correlation dimension (CD) and Kol-mogorov entropy (KE). The proposed chaotic system is verified through comparison with its recent counterparts. The 2D Schaffer map manifests the best ergodicity and erraticity characteristics. In addition, the applicability of the 2D Schaffer map is tested by implementing it to image encryption. The results show that the proposed 2D Schaffer map has excellent hyperchaotic performance thanks to its diversity property.