## 3 Proposed Method
### Image Encryption
Case 2: When calculating \(Cap(2)\), since four 2 \(\times\) 2 sized pixel blocks are used as processing units, the embedding capacity is calculated in two cases: where there are unusable blocks in the four 2 \(\times\) 2 sized pixel blocks or where all four 2 \(\times\) 2 sized pixel blocks are usable. The embedding capacity of a pixel block with a partition size of 2 \(\times\) 2 in the cover image is calculated as follows:

\[Cap(2)=Cap2(0)+Cap2(1) \tag{11}\] \[Cap2(0)=\sum_{k_{1}=1}^{n_{1}}(md_{k_{1}}\times 3)-(t\times 3)-7\] (12) \[Cap2(1)=\sum_{k_{2}=1}^{n_{2}}(md_{k_{2}}\times 3)-15 \tag{13}\]

Equation (12) is used to compute the embedding capacity in the presence of unusable blocks, and (13) is used to compute the embedding capacity when both are usable, in units, where \(n_{1}\) is the number of units where there are unusable blocks and \(n_{2}\) is the number of units without unusable blocks; \(md_{k_{1}}\) is the result of summing the shared MSBs of the usable blocks in the \(k_{1}^{th}\) unit, and \(md_{k_{2}}\) is the result of summing the shared MSBs of all blocks in the \(k_{2}^{th}\) unit; \(t\) is the number of blocks usable in the unit. To evaluate the efficacy of the proposed method in enhancing the embedding capacity, a comparative analysis with prior methods was conducted. As shown in Table 2, where EC represents the embedding capacity, it can be seen that the proposed method exhibits superior embedding capacity for the majority of the images, except Barbara, Boat, Lake, and Peppers, for which the method proposed by [14] yielded the highest capacity. To further substantiate the effectiveness of the proposed method in improving embedding performance, an experimental setup involving 10,000 images selected from the BOSSbase1.01 dataset [30] was conducted. Among the 10,000 images, for 8056 images the largest embedding capacity was obtained by the proposed method; for 1333 images the largest embedding capacity was obtained by [14], and for 1301 of those 1333 images the largest embedding capacity was obtained by the proposed method rather than by [13], and the largest embedding capacity was obtained by [13] for only 610 images. Table 3 shows the experimental data for the 10,000 images extracted, where ER represents the embedding rate. It can be seen that the average embedding rate of the proposed method is 2.4731, which is better than the other two methods. Compared to [13], the average improved embedding rate of the proposed method in this paper is 0.2106, which is 0.0367 higher than that of [14], which is 0.1739. In Table 4, the embedding performance analysis of the proposed method compared with [13; 14] is shown. EC\({}_{1}\) represents the average embedding capacity of these images with improved embedding capacity compared with other methods, while \(\Delta\)EC\({}_{1}\) represents the average increase in the embedding capacity of these images. As shown in these images, compared with [13], the average embedding capacity of the proposed method was 674,057 bits, and the average embedding capacity was increased by 59,565 bits. Compared with [14], the average embedding capacity was increased by 12,347 bits. EC\({}_{2}\) represents the average embedding capacity of these images with decreased embedding capacity compared with other methods, while \(\Delta\)EC\({}_{2}\) represents the average reduction of the embedding capacity of these images. In these images, the average embedding capacity of the proposed method is 272,838 bits, and we can see a reduction of 8311 bits in the average embedding capacity compared to [13]. In addition, compared with [14], the average embedding capacity of the proposed method was 535,398 bits, and the average embedding capacity was reduced by 5381 bits. This shows that compared with [13; 14], the proposed method reduces the embedding performance in some cases but can improve the embedding performance in most cases. In summary, the proposed method exceeds the other two, in terms of embedding capacity, and exhibits superior embedding performance.