Abstract:Digital watermarking is the key technology to protect digital copyright. In this paper, the formal definition of the double watermarking algorithm is given firstly. Then, based on the Discrete Wavelet Transform (DWT), the SM4 block cipher algorithm, and the Paillier homomorphic cipher, a double watermarking algorithm in the ciphertext field is designed. When watermarking is embedded, the carrier image is transformed by triple DWT, and the band set is divided into the encryption part, the horizontal high-frequency LH3 watermarking part, and the vertical high-frequency HL3 watermarking part. The SM4 block cipher and Paillier public-key cipher are used to encrypt the frequency band coefficients of the encryption part and the watermark part, respectively. At the same time, the Paillier public-key cipher scheme is employed to encrypt the digital watermark information, and two user watermarks are embedded in the LH3 and HL3 ciphertext fields with the Least Significant Bit (LSB) method. Finally, a watermark ciphertext image is generated after the inverse wavelet transform of DWT. In the process of watermark extraction, due to the homomorphism of Paillier, the watermark can be extracted from the plaintext after decryption. Experimental results show that the algorithm is capable of fast encryption and decryption and good invisibility of watermarks.