# A Zero-Watermarking Algorithm Based on Scale-Invariant Feature Reconstruction Transform
## 3 Algorithm Process
### Distinguishability Test  
To test the distinguishability of the zero-watermarking algorithm for similar images, this paper presents an SIFRT feature extraction for five similar images. A comparative analysis is then performed to assess the image similarity level of the binary feature images generated under the proposed algorithm. This is intended to test whether the SIFRT feature matrices of similar images exhibit strong distinguishability. The content shown in Figure 9 consists of five similar images, with detailed displays of the binary feature images generated by the SIFRT zero-watermarking algorithm proposed in this paper. Based on this, we conducted a similarity analysis on the generated binary feature matrix, as shown in Figure 10. From a comparative analysis of the data in Figure 10, the following conclusions can be drawn. The NC values of the feature images generated from similar images are slightly higher compared to the similarity of the watermarking generated from incorrect keys, as shown in Figure 7, with NC values fluctuating at around 0.57 overall. This indicates that, even for images judged to be highly similar based on human physiological perception, the feature matrices generated by the SIRFT algorithm  
Figure 8: Comparison of feature similarity under approximate key conditions. Figure 7: Comparison of feature matrix similarity between different images. can effectively distinguish their differences, further enhancing the persuasiveness of the algorithm in professional applications. ### Distinguishability Test  
The performance of a digital watermarking can be measured from various perspectives. For embedding watermarkings, effectiveness and invisibility are important considerations. For zero-watermarking algorithms, invisibility may not be a concern because, theoretically, these algorithms do not modify the original image, thus eliminating visibility issues. Apart from security and distinguishability, zero-watermarking algorithms should also prioritize robustness, meaning whether the algorithm can still effectively extract copyright information after the copyright image has been subjected to a certain degree of attack, as shown in Table 1.  
From the analysis of Table 1, it can be observed that the copyright information of the experimental materials listed in Figure 6 is effectively preserved at the subjective visual level after various attacks. At the objective level, regarding JPEG compression attacks, the algorithm exhibits good robustness, with an NC mean value of 0.9985, close to 1, indicating that the feature data are well preserved under low JPEG compression. However, for image cropping attacks, where 1/16 of the content from the top left corner is removed, there is a certain degree of impact, with an NC mean value of 0.9668. Additionally, for attacks involving the addition of Gaussian noise, the NC mean value decreases to 0.9536, indicating the poorest robustness among the aforementioned attacks, suggesting room for improvement in subsequent iterations. Figure 10: Comparison of feature similarity between similar images. Figure 9: Details of feature extraction for similar images. To facilitate a more intuitive analysis of the performance of our algorithm and other zero-watermarking algorithms, we simulated how digital images were protected by selected mainstream zero-watermarking algorithms after undergoing various attack methods and intensities. Since the application scenarios of zero-watermarking technology mostly involve sensitive data, attackers typically refrain from employing irreversible attack methods to blur or steal copyrights. Undoubtedly, excessive attacks on digital images may lead to certain limitations and disturbances in the subsequent distribution and use of the images. Therefore, this section focuses on observing the integrity of the damaged copyright information extracted by some zero-watermarking algorithms under the conditions of cropping attacks, data compression attacks, and slight rotation attacks. The specific data are shown in Table 2.