Abstract: Most of the existing watermarking and encryption schemes are difficult to ensure the commutativity of watermarking and encryption as well as the visual quality of the protected image.These schemes complete watermark embedding and image encryption processes in a fixed order,and they modify the protected image content more or less.Few of them complete the commutativity of watermarking and encryption process without affecting the quality of the protected image content.Therefore,a homomorphic and commutative fragile zero-watermarking based on SVD (singular value decomposition) is proposed.At the sender side,the content owner adopts homomorphic modular encryption to encrypt the original image content,and the two stages of image encryption and watermarking generation do not affect each other.The zero-watermarking information can be generated from the encrypted image and the original host image,respectively.At the receiver end,the legitimate receiver first decrypts the image and then performs watermarking detection on the decrypted image content,and the extracted watermarking information can detect and locate the deliberately tampered area of the watermarked image.Experimental results confirm that the use of zero-watermarking will not lead to gray level value alteration of the image content,and the deliberately tampered area of the watermarked image can be located perfectly while ensuring the commutativity.

Key words: Commutative, Fragility, Homomorphic encryption, SVD, Zero-watermarking