Optical asymmetric watermarking using 4D hyperchaotic system and modified equal modulus decomposition in hybrid multi resolution wavelet domain

In this paper, an asymmetric optical watermarking scheme using 4D hyperchaotic system with coherent superposition and modified equal modulus decomposition in hybrid multi-resolution wavelet domain is proposed. The 4D hyperchaotic system is used for generating permutation keystream for a pixel-swapping mechanism. The hybrid multi-resolution is generated using both the fractional Fourier transform of multiple orders and Walsh transform. The 4D hyperchaotic system's parameters and initial conditions along with the multiple fractional orders of the fractional Fourier transform increase the key-space and hence provide additional strength to the watermarking mechanism. The designed watermarking scheme is non-linear in nature and resists brute-force attack due to its large key-space. Computer-based simulations have been performed on grayscale images to verify the validity and performance of the scheme against various attacks including special attack. Results show that the proposed watermarking scheme not only offers high resistance to occlusion and noise attacks but is also invulnerable to the special attack.