# A Zero-Watermarking Algorithm Based on Scale-Invariant Feature Reconstruction Transform
## 1 Introduction  
In digital works, digital images are a widely used network information carrier. Image processing and the internet have made it easier to duplicate, modify, reproduce, and distribute digital images at low cost and with approximately immediate delivery without any degradation of quality [1]. Digital watermarking is a trend in security techniques that hides data using data embedding and data extraction processes. Therefore, it is very effective in encrypting data for applications running on limited resources and can be used to solve copyright disputes and other issues in digital products [2]. Digital watermarking can be classified into embedded watermarking and zero-watermarking based on whether it modifies the carrier information. Zero-watermarking does not modify the original data of the propagation carrier and is suitable for fields with high image-quality requirements. The key idea is to generate feature information based on the image's own data and bind it with copyright data through computation. This ensures the accurate expression of the original visual effect of the image. This technology is widely applied in sensitive digital image domains where information tampering is a concern, such as military radar images, patient pathology images [3], and artistic heritage images.  
In recent years, research on zero-watermarking has mainly focused on two steps: constructing various feature matrices and encrypting copyright information. In terms of local features, [PERSON] et al. [4] proposed a zero-watermarking algorithm based on image block features. The host image is divided into 8 \(\times\) 8 blocks, and the joint photographic experts group (JPEG) quantization matrix of each block is calculated to generate the actual block matrix. The mean value of this local block and the above block matrix are then input into aJacobian model to generate meaningful watermarking information. To distinguish watermarking information in similar images, [PERSON] et al. [5] proposed a zero-watermarking algorithm for distinguishing the similarity between fundus images in the medical field. They constructed image features by extracting the grayscale distinctiveness of the sector region in the fundus image and combined this feature with visual cryptography to enhance the security of the information. However, when the grayscale features of the fundus carrier image are partially truncated, the grayscale features in that part exhibit a stepped change. This leads to the extracted watermarking image containing more noise, indicating a lack of robustness in the algorithm. In terms of the geometric moment features of images, continuous orthogonal moments have become the main tool used in zero-watermarking algorithms. However, existing research has found defects in both computational accuracy and numerical stability when using integer-order continuous orthogonal moments, which affects the zero-watermarking performance. [PERSON] et al. [6] proposed a conversion from integer-order radial harmonic Fourier moments (IoRHFMs) to fractional-order radial harmonic Fourier moments (FoRHFMs). This conversion improves computational accuracy and helps alleviate the numerical instability issue associated with such moments. The algorithm exhibits strong robustness against geometric attacks and common attacks, surpassing the performance of the IoRHFM-based zero-watermarking algorithm. To enhance the security of digital images, [PERSON] et al. [7] proposed a robust digital image watermarking system with a fractional-order discrete-time chaotic system and discrete wavelet transform-singular value decomposition (DWT-SVD). The inclusion method inserts an encrypted image into the dynamics of an integer-order discrete-time chaotic system and the resulting cipher serves as a host image watermark.