Color watermarking algorithm combining the quantum discrete cosine transform with the sinusoidal–tent map

To overcome the drawbacks of the existing sinusoidal map and tent map, this paper proposes the design of a sinusoidal–tent (ST) map. The test results indicate that the new chaotic system exhibits more significant advantages in chaos control. Compared with the sinusoidal map and tent map, the proposed sinusoidal–tent map performs better in terms of bifurcation diagram and Lyapunov exponents. The trajectories of the sinusoidal–tent map can occupy all the phase planes over (0,4), while those of the two classic maps only occupy a small phase space, and the Lyapunov exponents of the ST map are all positive within the range of control parameters, higher than those of seed maps. Simultaneously, a novel quantum scrambling operation is devised based on the sinusoidal–tent map to avoid the periodicity of the quantum Arnold scrambling method. Initially, two chaotic sequences are generated to scramble the pixel positions of the watermark image, further enhancing the security of the watermarking algorithm. Subsequently, the host image is processed by the quantum discrete cosine transform, and finally, the scrambled watermark image is inserted into the medium-frequency band of the transformed host image, ensuring the invisibility of the watermarking. According to the simulation results, the quantum watermarking algorithm has excellent invisibility and robustness.