Construction of S-box based on chaotic piecewise map: Watermark application

The spread of using communication technologies has made it necessary to take certain measures to prevent illegal copying. Watermarking techniques are of great potential value in this regard. The present study introduces a watermarking scheme as a block cypher. We use entropy for sorting the blocks. The sorted blocks after finite ridgelet transformation are hosting the logo. The logo's information encrypts before transferring into the blocks by the proposed S-box. We introduce a piecewise non-linear chaotic map for generating the S-box. The ergodic nature of introducing a map is proved by the invariant measure. The ergodic nature of the map is providing an excellent confusion property for encryption. The ability of the watermarked image to resist the attacks is an exam with statistical analysis(PSNR and MSE). The performance of generated S-box is studying with corresponding attacks (Non-linearity, SAC, BIC, LP, and DP). The results are close to the optimal value.