# A Novel Adaptive Image Data Hiding and Encryption Scheme Using Constructive Image Abstraction
## 3 Experimental Results and Analysis
### Analysis of Security
#### 3.2.5 Image Sensitivity Analysis  
Differential attacks are a crucial process in undermining the encryption security because a malicious hacker is likely to reveal vital information from two ciphered images containing a subtle change in their plaintext images. A competent encryption algorithm must be able to detect the slightest variation between two input images, even a single bit of difference. The sensitivity of an image is an indicator of its ability to thwart differential attacks. The most commonly used metrics to evaluate image sensitivity are the number of pixel change rates (NPCR) and the unified average changed intensity (UACI) [40, 41, 42]. Equations (13)-(15) define NPCR and UACI. These equations utilize the pixel values of input images \(I_{1}\) and \(I_{2}\), denoted as \(I_{1}(i,j)\) and \(I_{2}(i,j)\):  
\[D(i,j)=\begin{cases}0\;if\;I_{1}(i,j)=I_{2}(i,j)\\ 1\;if\;I_{1}(i,j)\
eq I_{2}(i,j)\end{cases} \tag{13}\]  
\[NPCR(I_{1},I_{2})=\frac{\sum_{i,j}D(i,j)}{W\times H}\times 100\% \tag{14}\]  
\[UACI(I_{1},I_{2})=\frac{1}{W\times H}\left(\sum_{i,j}\frac{|I_{1}(i,j)-I_{2}( i,j)|}{255}\right)\times 100\% \tag{15}\]  
The NPCR and UACI results are reported in Table 7. All statistics are close to the ideal value of 99.6094 and 33.4635 [41], respectively, indicating that our encryption scheme can effectively defeat the differential attack.  
We note that the values of NPCR and UACI are influenced by the resolutions of the input images. Moreover, the optimal range of NPCR/UACI values that would render the ciphered image immune to malicious attacks remains uncertain. To address this issue, [PERSON] et al. [41] established the criteria for statistical hypothesis tests by calculating the means and standard deviations of NPCR and UACI.  
To perform the hypothesis test, we used 10 abstracted stego test images. For each image, we altered the least significant bit (LSB) of the R-channel in the center and the four corner pixels, generating five corresponding stego images that differed by one bit from the original. After image encryption, we calculated the NPCR and UACI values for each image  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Image** & **Channel** & **NPCR (\%)** & **UACI (\%)** \\ \hline \multirow{3}{*}{507 (HDR)} & R & 99.602208 & 33.456771 \\  & G & 99.607187 & 33.461968 \\ \cline{1-1}  & B & 99.608628 & 33.462320 \\ \cline{1-1}  & E & 99.605300 & 33.471379 \\ \hline \multirow{3}{*}{NCHU Main Gate (LDR)} & R & 99.604538 & 33.470771 \\ \cline{1-1}  & G & 99.604538 & 33.468483 \\ \cline{1-1}  & B & 99.606941 & 33.447217 \\ \hline \hline \end{tabular}
\end{table}
Table 7: NPCR and UACI statistics for two encrypted abstracted stego images.  
Figure 9: The test results of the local Shannon entropy for all 10 ciphered abstracted stego images.  
pair, the original and the altered one, to analyze their statistical significance. Figure 10 shows the NPCR and UACI results, averaged over five test cases.  
Results shown in Table 7 and Figure 10 indicate that our encryption scheme exhibits a significant degree of image sensitivity, making it capable of withstanding differential attacks. This conclusion is supported by the fact that all NPCR values are greater than the threshold, and all UACI results fall within the bounds defined by the lower and upper limits, indicating that our scheme has successfully passed both the NPCR and UACI statistical tests.