Quantum Watermarking Scheme Using Small-scale Quantum Circuits and Gray-code Scrambling

To solve the problem of watermark embedding and extracting of quantum color images, a method of using novel enhanced quantum representation and Gray-code scrambling was proposed. For the embedding process of quantum watermarking, at first, the position and color of pixels in watermark image were scrambled by the controlled-not gates, and then, the scrambled watermark with 2ⁿ×2ⁿ image size and 24 color qubits（8 qubits per channel） was expanded to an image with 2ⁿ⁺¹×2ⁿ⁺² image size and 3 color qubits（1 qubit per channel）. Finally, the color value of the expanded watermark image was added to the lowest qubit of color value of the carrier image sized 2ⁿ⁺¹×2ⁿ⁺² by modulo 2 additions. The watermark was extracted from the watermarked image by applying operations in the reverse order. The experimental results show that the proposed method is superior to the contrast method in terms of four items: visual quality, robustness performance under noises, scrambling effect of watermark image, and computational complexity.