Numerous illegal pirating sites and programs have emerged with the rapid development of digital network technology because digital media can be easily copied and tampered with. Digital watermarking technology

which is an effective solution to image copyright protection

content authentication

integrity

and other issues

has become a crucial research topic in recent years. The singular values of images received via singular value decomposition (SVD) are strongly resistant to various attacks. Therefore

scholars have proposed various SVD-based watermarking methods. We proposed the novel boost normed singular value decomposition (BN-SVD) to solve the problems of diagonal distortion and false positives

which are caused by SVD. The method involves establishing a parameter to identify the optimum scaling factor for efficient robustness to improve existing SVD algorithms. Considering the inconsistencies between invisibility and robustness caused by embedding watermarks in original images by traditional watermarking algorithms

a novel zero-watermarking scheme based on BN-SVD is proposed. Zero-watermarking is defined by the registration and certification processes. In registration

an algorithm uses the major characteristics of a digital image to construct zero-watermarking registration information. The information is stored in a centralized authentication center. In certification

the watermark information is restored by using the digital images to be certified and the data stored in a centralized authentication center. First

a low-frequency approximation sub-graph was established from an original image that was decomposed by discrete wavelet transform (DWT) to non-overlapping image blocks. The low-frequency approximation sub-graph generated a low-frequency coefficient matrix via discrete cosine transform (DCT). BN-SVD was used to each block matrix to achieve a maximum singular value. A characteristic vector was created by comparing the maximum singular value with the average of the maximum singular value. The watermark image was disposed with Arnold transformation and Logistic map to obtain an encrypted and scrambling watermark image. Finally

the characteristic vector was set as an initial value and the scrambling encrypted watermark image as a controlling input value are both sent into a cellular neural network (CNN). By setting up a feedback template

the control template and threshold value of CNN determined the specific reversible logic operation. The output image was the registration image of zero-watermarking. The registration image was saved in the certification center to verify the copyright of the image. Experimental results indicated that all watermark images extracted by the proposed method do not exhibit diagonal marks when heterogenic attacks are imposed on original images. The proposed method overcame the diagonal distortion problem in the diagonal experiment. A one-to-one relation between the singular value vector and the image was established by introducing a parameter where different images have various singular value vectors. Therefore

the major characteristic of different images can be represented by different singular value vectors in a false-positive rate experiment. The normalized correlation between the extracted watermark image from BN-SVD and the original watermark image was below 50%. A low false-positive rate was observed. In the robustness experiment

we imposed various types of attacks

including JPEG compression

noise

filtering

rotating

and shear on the images. In the JPEG compression attack

the normalized correlation reached up to 99%. In the noise attack

the normalized correlation exceeded 97%. In the filter attack

the normalized correlation exceeded 98%. In the rotating attack

the normalized correlation was higher than 96%. In the shear attack

the normalized correlation exceeded 98%. These results indicated the need to improve high-shear attacks. A parameter will be used to modify the singular values of a matrix

which enhances the robustness of the algorithm and eliminates the false-positive and diagonal distortion problems of SVD. Introducing CNN is advantageous because the attacker cannot determine specific parameters. Therefore

the attacker extract the watermark image by reversible logic operation to improve the security of the watermarking. The parallel image processing of CNN can be achieved with hardware

which makes the algorithm applicable in occasions with higher real-time requirement.