## 5 Conclusions and Future Works  
A novel reversible adversarial example generation method is proposed under black-box conditions. A differential evolution algorithm is utilized to generate minimal adversarial perturbations on the original image. RAEs are generated based on D-CSDPP algorithm. This method not only mislead the deep learning models in image classification tasks, but also allows the RAEs to be exactly restored to the original image. This feature is lacking in many existing methods. Furthermore, this method enables recognition control in computer vision. The proposed reversible method functions as a form of encryption for computer vision. Thus, only authorized models are allowed to recognize the images. The D-CSDPP can automatically detect the perturbed pixels, meaning that location information is not needed for original image restoration, resulting in a decrease in embedded data. As a result, APR is improved by more than 20%. Comparative experiments with different approaches demonstrate the effectiveness and detection performance of the proposed D-CSDPP. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Method** & **Model** & \(ASR_{A}\) & \(ASR_{RA}\uparrow\) & \(APR\uparrow\) \\ \hline \multirow{2}{*}{Proposed} & Inc-V3 & 27.20\% & 25.50\% & **93.75\%** \\  & IncRes-V2 & 27.60\% & 26.10\% & **94.57\%** \\ \hline \multirow{2}{*}{Post [24]} & Inc-V3 & 30.82\% & 19.92\% & 64.63\% \\  & IncRes-V2 & 37.23\% & 24.60\% & 66.08\% \\ \hline \multirow{2}{*}{In-the-loop [24]} & Inc-V3 & 30.82\% & 25.76\% & 83.58\% \\  & IncRes-V2 & 37.23\% & **30.91\%** & 83.02\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison with state-of-the-art methods. The PSNR and SSIM between the RAEs and the original images can reach up to 48.32 dB and 0.9986, respectively, indicating that the images generated by the proposed method are of high quality. This is also reflected in the visual results of the RAEs. The proposed method demonstrates effectiveness across various advanced models and datasets, highlighting its generalizability. Compared to SOTA methods, the proposed method achieves superior APR due to the high image quality of the RAEs. In the future, we will attempt to propose some methods for generating more robust and efficient adversarial perturbations. We will also try to enhance the efficiency of the optimization solving. Alternatively, we aim to further compress the required auxiliary information for image restoration. Conceptualization, L.L. and S.Y. ; methodology, L.L., S.Y., C.-C.C. ([PERSON]) and C.-C.C. ([PERSON]); software, S.Y. ; validation, S.Y. ; formal analysis, L.L., S.Y., C.-C.C. ([PERSON]) and C.-C.C. ([PERSON]); investigation, S.Y. ; resources, S.Y. ; data curation, S.Y. ; writing--original draft preparation, S.Y. ; writing--review and editing, L.L., S.Y., C.-C.C. ([PERSON]) and C.-C.C. ([PERSON]); visualization, S.Y. ; supervision, L.L., C.-C.C. ([PERSON]) and C.-C.C. ([PERSON]); project administration, L.L. All authors have read and agreed to the published version of the manuscript. This study was funded by National Natural Science Foundation of China (62466038), Jiangxi Provincial Key Laboratory of Image Processing and Pattern Recognition (2024 SSY03111), Technology Innovation Guidance Program Project (Special Project of Technology Cooperation, Science and Technology Department of Jiangxi Province) (20212 BDH81003), and the Innovation Foundation for Postgraduate Students of Nanchang Hangkong University (YC2023-102). Not applicable. Data Availability Statement: Data is contained within the article. This study was supported by National Natural Science Foundation of China (62466038), Jiangxi Provincial Key Laboratory of Image Processing and Pattern Recognition (2024 SSY03111), Technology Innovation Guidance Program Project (Special Project of Technology Cooperation, Science and Technology Department of Jiangxi Province) (20212 BDH81003), and the Innovation Foundation for Postgraduate Students of Nanchang Hangkong University (YC2023-102). The authors declare no conflicts of interest.