A new algorithm for the construction of substitution box by using chaotic map

In the last few decades, security of digital information has become more important. This study focuses on the substitution of grayscale digital images. By using Cubic-Logistic map, a new substitution box is proposed which has been given the name Cubic-Logistic substitution box. Some substituted images have been examined which are substituted with the proposed and other existing substitution boxes. There is hardly any information in the substituted image which is substituted with the proposed substitution box, whereas patterns of the original image can be visualized in those substituted image which are substituted with other existing substitution boxes. Cubic-Logistic substitution box has also shown good statistical analysis such as strict avalanche criterion, differential approximation probability, linear approximation probability, nonlinearity, bit independent criterion, correlation and energy. These analyses of proposed Cubic-Logistic substitution box are then compared with the analysis of other existing substitution boxes such as Rijndael substitution box, Affine-Power-Affine substitution box and skipjack substitution box to show the strength of the proposed S-box.