## 4 Experiment and Security Analysis
### Embedding Capacity Analysis  
In this section, we discuss the embedding capacity of our proposed method. In phase-1, we conceal an \(n\)-ary secret message vector, \(d_{sb}\), and an \(m\)-ary secret message, \(d_{wm}\), in each pixel when synthesizing a stego image \(I^{\prime\prime}_{onset}\) using an optimal weighted color transfer. The embedding capacity (EC\({}_{1}\)) in bits in Phase-1 is shown in Equation (15), where  
Figure 8: The visual inspection of the test image “Kodim0”. Figure 10: The visual inspection of the test image “Kodim23”. Figure 9: The visual inspection of the test image “Kodim20”. \(\mathrm{W}\times\mathrm{H}\) represents the size of the stego image. Furthermore, the embedding rate (ER\({}_{1}\)) in bits-per-pixel (bpp) is shown in Equation (16), which depends on two parameters, \(n\) and \(m\), but is independent of the size of the stego image. \[\mathrm{EC}_{1}=\mathrm{EC}_{1}(\mathrm{SB})+\mathrm{EC}_{1}(\mathrm{WM})=(\log _{2}n^{3})\times\mathrm{W}\times\mathrm{H}+(\log_{2}m)\times\mathrm{W}\times \mathrm{H} \tag{15}\]  
\[\mathrm{ER}_{1}=(\log_{2}n\,+\log_{2}m^{\frac{1}{3}}) \tag{16}\]  
In phase-2, we adopt the weighted modulus reversible data hiding (WMRDH) for message concealment. We construct a 3-tuple dual-pixel, \(P^{\prime\prime}_{\mathbf{d}\mathbf{u}^{\prime}}\) consisting of three component pairs, \(P^{\prime\prime}_{\mathbf{n}^{\prime}}\), \(P^{\prime\prime}_{\mathbf{g}^{2}}\), and \(P^{\prime\prime}_{\mathbf{b}^{\prime}}\), in the Red, Green, and Blue channel, respectively, which are constructed from the input stego image, \(I^{\prime\prime}_{\mathbf{u}^{\prime}}\). Since each component pair can carry a \(k\)-ary secret message, two pixels, \(P^{\prime\prime}_{\mathbf{s}\mathbf{1}}\) and \(P^{\prime\prime}_{\mathbf{s}\mathbf{2}}\), in the respective dual stego images, \(I^{\prime\prime}_{\mathbf{s}\mathbf{1}}\) and \(I^{\prime\prime}_{\mathbf{s}\mathbf{2}}\), have three component pairs, thereby able to convey a \(k\)-ary 3-tuple secret message vector, \(\mathbf{d}_{\mathbf{d}\mathbf{u}}\). Consequently, the embedding capacity carried in dual stego images is expressed in Equation (17), and the embedding rate (number of bits-per-stego pixel and per-stego image) is shown in Equation (18). \[\mathrm{EC}_{2}=(3\times\log_{2}\mathrm{k})\times\mathrm{W}\times\mathrm{H} \tag{17}\]  
\[\mathrm{ER}_{2}=\frac{1}{2}\log_{2}k \tag{18}\]  
Table 7 shows the embedding capacities produced from two phases. The first phase, Phase-1, conceals an \(n\)-ary secret message vector, \(\mathbf{d}_{\mathbf{s}\mathbf{b}}\), denoted by EC\({}_{1}\)(SB) and \(m\)-ary secret message, \(d_{wm}\), denoted by EC\({}_{1}\)(WM). The embedding capacity, EC\({}_{1}\), is the sum of EC\({}_{1}\)(SB) and EC\({}_{1}\)(WM). The second phase, Phase-2, embeds a \(k\)-ary secret message in a component pair, thereby offering the embedding capacity, EC\({}_{2}\)(WMRDH), and the embedding rate, ER\({}_{2}\). In our experiments, we set \(n=3\), \(m=7\), and \(k=5\), implying that we embed 3-ary and 7-ary secret messages in Phase-1, producing the stego optimal weighted color-transferred image, \(I^{\prime\prime}_{\mathbf{u}^{\prime}}\). We then convey 5-ary secret messages in Phase-2, generating the dual stego images \(I^{\prime\prime}_{\mathbf{s}\mathbf{1}}\) and \(I^{\prime\prime}_{\mathbf{s}\mathbf{2}}\). Therefore, our algorithm can provide total embedding capacity between 38.08-57.12 million bits, equivalent to the embedding rate of 3.682 bits-per-pixel-per-stego image. Table 8 displays the timing results for six test images, including the optimal weight \((W^{*})\) in three channels, (a) time spent in determining the optimal weight, (b) timing of concurrently proceeding with the optimal weighted color-transfer and secret message embedding in Phase-1, (c) timing of reversible data-hiding weighted modulus in Phase-2. We also list the timing results for (d) the time required to extract secret message in Phase-2 and image restoration, and finally (e) the time spent in extracting secret messages in Phase-1.