## 4 The SEME-TDHM Algorithm
### Encryption Process
Varied intensities of noise were added to the encrypted image for subsequent decryption, enabling us to assess the SEME

\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Schemes**} & \multicolumn{1}{c}{**Images**} & \multicolumn{3}{c}{**NPCR(\%)**} & \multicolumn{3}{c}{**UACI(\%)**} \\ \hline  & & R & G & B & **Average** & R & G & B & **Average** \\ \hline \hline \multirow{2}{*}{**Proposed**} & **Candy** & **99.6162** & **99.6116** & **99.6238** & **99.6172** & **33.4038** & **33.4758** & **33.4979** & **33.4592** \\  & **Baboon** & **99.6277** & **99.5960** & **99.6227** & **99.6155** & **33.4650** & **33.4630** & **33.4543** & **33.4607** \\  & **House** & **99.6257** & **99.6117** & **99.6121** & **99.6165** & **33.4427** & **33.4959** & **33.4661** & **33.4682** \\  & **Bird** & **99.6145** & **99.6071** & **99.6269** & **99.6162** & **33.4343** & **33.4754** & **33.4828** & **33.4639** \\  & **Peper** & **99.6082** & **99.6198** & **99.6251** & **99.6177** & **33.4833** & **33.4647** & **33.4500** & **33.4660** \\  & **Aircraft** & **99.6146** & **99.6191** & **99.6223** & **99.6187** & **33.4667** & **33.4634** & **33.4574** & **33.4558** \\  & **Mean** & **99.6178** & **99.6108** & **99.6221** & **99.6169** & **33.4658** & **33.4830** & **33.4697** & **33.4623** \\ Ref. [3] & Baboon & 99.6300 & 99.6300 & 99.6300 & 99.6300 & 33.4200 & 33.4400 & 33.5000 & 33.4533 \\  & **Peper** & 99.6300 & 99.6300 & 99.6300 & 33.4300 & 33.4400 & 33.4300 & 33.4300 \\ Ref. [4] & Baboon & 99.6227 & 99.6304 & 99.6052 & 99.6194 & 33.3952 & 33.4674 & 33.4584 & 33.4403 \\  & **Aircraft** & 99.6070 & 99.5983 & 99.6006 & 99.6020 & 33.4498 & 33.4504 & 33.4792 & 33.4598 \\ Ref. [19] & Baboon & 99.6229 & 99.6037 & 99.6009 & 99.6142 & 33.4263 & 33.4526 & 33.4868 & 33.4482 \\  & **Peper** & 99.5899 & 99.6037 & 99.60 TDHM algorithm's resistance to noise. The test results presented in Figure 14 demonstrate that the essential information from the original image is effectively recovered, underscoring the SEME-TDHM algorithm's robustness in the face of noise interference. Images are susceptible to loss during transmission or storage. To comprehensively assess the SEME-TDHM algorithm's performance, this study includes a simulation of data loss by cropping the encrypted image as shown in Figure 15. The results indicate that the greater the extent of image loss, the more obscured the original image appears upon decryption. However, even with significant loss, some recognizable details of the image are still visible to the naked eye. This underscores the SEME-TDHM algorithm's efficacy in resisting data loss to a certain extent. ### Analysis of Operating Speed

In addition to the encryption effect, the encryption efficiency is also an important factor in evaluating the image encryption algorithm [38]. Therefore, this section evaluates the processing speed of this algorithm and compares it with other algorithms. In this paper, the encryption and decryption time of different pixel grayscale maps was tested 20 times, and the average value was selected. The test results and comparisons are shown in Table 4. It can be seen that the encryption and decryption time is a bit long; this is because the encryption process has two rounds and involves bit level encryption. These operations enable our SEME-TDHM algorithm to effectively resist both chosen plaintext attacks and chosen ciphertext attacks. Although the encryption time is appropriately extended, its encryption performance is also improved. Although the experimental environment is different, the SEME-TDHM algorithm has better efficiency compared to similar environment algorithms. Therefore, the encryption and decryption speed of the SEME-TDHM algorithm meets the basic requirements of the application and is expected to be applied in the future. Figure 14: Noise test results of Candy, House and Pepper, Gaussian noise of (**a1–a3**) \(1\times 10^{-7}\), (**b1–b3**) \(1\times 10^{-6}\), Pepper and Salt noise of (**c1–c3**) 0.001, (**d1–d3**) 0.01.