Group multiple-image encoding and watermarking using coupled logistic maps and gyrator wavelet transform

A novel method of group multiple-image encoding and watermarking using coupled logistic maps and gyrator wavelet transform is presented. The proposed method employs three different groups of multiple images. The color images of each group are individually segregated into R, G, and B channels. Each channel is first permutated by using a sequence of chaotic pairs generated with a system of two symmetrically coupled identical logistic maps and then gyrator transformed. The gyrator spectrum of each channel is multiplied together and then modulated by a random phase function to obtain a corresponding multiplex channel. The encoded multiplex image is restituted through a concatenation of R, G, and B multiplex channels. The phase and amplitude functions of the first, second, and third groups of encoded multiplex images are generated. The host image is a single-level 2D discrete wavelet transformed to decompose into LL, HL, LH, and HH subbands. HL, LH, and HH subbands are then replaced with phase functions of the first, second, and third groups, respectively. Finally, the resultant image is an inverse single-level 2D discrete wavelet transformed to construct a watermarked image. The three groups of multiple images are protected not only by the encryption algorithm but also visually by the host image. Thus, a high level of security can be achieved. Each group includes group decryption keys, and each image of the group comprises individual decryption keys beside parameters of coupled logistic maps and gyrator transform. As a result, the key space is very large. The decryption system can be realized by using an optoelectronic device. The numerical simulation results confirm the validity and security of the proposed scheme.