Abstract: In order to solve the problems of high false alarm, poor robustness and security in the SVD (singular value decomposition) watermarking algorithms, this paper proposes a fast zero-watermarking algorithm with both the double encryption and strong robustness based on matrix Schur decomposition. Firstly, the matrix Schur decom-position is used on the low-frequency blocks of original images to obtain a stable value. Then, it extracts the abs-olute value of diagonal elements containing the largest energy elements of the upper triangular matrix of Schur decomposition block matrix so that it constructs a transition matrix. Next, to obtain the characteristic matrix, the average value of the matrix is compared with each element value to generate a perceptual Hash binary sequence. In addition, the chaotic map-encrypted feature matrix and the Fibonacci transform-encrypted watermark information are operated to obtain a zero-watermark. Finally, the registration is completed in the third party copyright certification center of IPR (intellectual property rights). Experimental results show that the NC value of watermark extracted from random carriers is less than 0.5, which can effectively solve the problem of high false alarm. Compared with the robust zero watermark based on integer wavelet transform, the performance of noise immunity is improved by 2.43%. In contrast with the time-domain watermarking algorithm, the resistance to JPEG raises up to 4.88% in performance.

Key words: singular value decomposition (SVD), false alarm rate, zero-watermarking, matrix Schur decomposition, perceptual Hash, Fibonacci transform

摘要： 为解决奇异值分解水印算法中所产生高虚警、鲁棒性不强以及安全性不高的问题，提出一种基于矩阵Schur分解的双重加密快速鲁棒零水印算法。该算法先将原始图像低频块进行矩阵Schur分解得到稳定值；提取Schur分解的块上三角矩阵对角线元素中含有最大能量元素的绝对值，并将其构造过渡矩阵；将该矩阵的平均值与每一个元素值进行比较生成感知哈希二值序列，构造特征矩阵；再将经过混沌映射加密的特征矩阵与斐波那契（Fibonacci）变换加密后的水印信息进行逻辑运算得到零水印；最后在第三方版权认证中心（intellectual property rights，IPR）完成注册。实验表明，在随机载体图像中所提取的水印[NC]值均在0.5以下，有效地解决高虚警问题；与基于整数小波变换的鲁棒零水印相比，抵抗噪声攻击的性能提高了2.43%；与时域水印算法相比，抵抗JPEG压缩攻击的性能提高了4.88%。

关键词: 奇异值分解（SVD）, 虚警率, 零水印, 矩阵Schur分解, 感知哈希, 斐波那契变换