A New Multi-Scroll Chaotic System without Equilibrium Point and Its Application in Watermark Encryption

To enrich the topological forms and potential applications of non-equilibrium differential equations, a non-equilibrium seed system model is proposed. A grid multi-scroll hidden dynamical are gained through multi-level functions modulation. And then, based on PRNs coined by the proposed chaotic model, an fast watermarking scheme on basis of HAAR wavelet is proposed. Firstly, Haar wavelet transform is performed on the image to extract the low-frequency sub-band and then, the fast FFT is employed to calculate the time on extracted low-frequency sub-bands. By reducing the number of calculations for the moments, the running speed can be increased. Finally, in the watermark embedding and extracting stage, a new watermark quantization method based on Quantized Index Modulation (QIM) is proposed. By designing two watermark bit detectors, the coefficient values after wavelet transform are adjusted to ensure that the coefficient intervals remain uniform, thereby enhancing the overall anti-noise ability of watermark embedding, and it can improve the embedding extraction speed. The final test data show its excellent robustness and imperceptibility.