## 2 Proposed Scheme
### Secret Embedding and Encryption Stage
the smooth image, the decimal value of the indicator (\(w_{1}w_{2}w_{3}\)) is the value of \(c^{*}(i,j)-1\) if \(c^{*}(i,j)\) is larger than 0 (the fallen cases are recorded under \"Label\" in Table 1). If it is a complex image, the values of \(c^{*}(i,j)\) equal to 7 and 8 fall into the same case; in such a situation, if \(c^{*}(i,j)\) is equal to 8, then the decimal value of (\(w_{1}w_{2}w_{3}\)) is adjusted to 7 (also recorded under \"Label\" in Table 1). For example, in Figure 1, the value \(c^{*}(i,j)\) generates the indicator (\(w_{1}w_{2}w_{3}\)) as 101 if the image is a complex image. Essentially, the value \(w_{1}w_{2}w_{3}\) can represent which case the pixel has fallen into, which indicates the hiding capacity. Next, the value of \(w_{1}w_{2}w_{3}\) is assigned to Equation (7), and the values of \(w_{1}^{*}\), \(w_{2}^{*}\) and \(w_{3}^{*}\) can be found to make the condition \(mC\) satisfy the value of \(w_{1}w_{2}w_{3}\) (as shown in Equation (7)). The Hamming coding matrix is used as the first round to shuffle the original values of \(w_{1}w_{2}w_{3}\) to produce the values of \(w_{1}^{*}\), \(w_{2}^{*}\) and \(w_{3}^{*}\). For example, if \(c^{*}(2,2)\) is equal to 5, \(w_{1}w_{2}w_{3}\) will be 101. While satisfying Equation (7)), the values of \(w_{1}^{*}\), \(w_{2}^{*}\) and \(w_{3}^{*}\) will be 1, 1, and 0, respectively. Subsequently, the value \(w_{1}^{*}w_{2}^{*}w_{3}^{*}\) is recalculated as \(w_{1}^{\prime}w_{2}^{\prime}w_{3}^{\prime}\) for the second round of shuffling with Equation (8), where \(r_{1}r_{2}r_{3}\) is generated by a random number generator with the key \(s_{1}\). In the previous example, if the value of \(r_{1}r_{2}r_{3}\) is 001, \(w_{1}^{\prime}w_{2}^{\prime}w_{3}^{\prime}\) will be \(110\oplus 001=111\). In the secret embedding and encryption step, the bit stream of the embedded pixel consists of three parts as shown in Figure 2, in which the embedded pixel is represented by \(p^{\prime}(i,j)\). The first part is for the Hamming encoding code, which expresses which case the given pixel \(p(i,j)\) falls into. The first three MSBs of the embedded pixel equate to the second-round shuffling result \(w_{1}^{\prime}w_{2}^{\prime}w_{3}^{\prime}\). As for the second part in Figure 2, the values of the \"Payload\" column in Table 1, depicted by \(payload(i,j)\), indicate the number of secret bits to-be embedded to the pixel \(p(i,j)\). In this part, the hiding capacity for different types of images is listed in Table 1. Here, the fallen cases, the code length, and pure payload are denoted by \"Label\", \"Capacity\", \"Code length\" and \"Payload\", respectively. The column \"Label\" indicates the decimal value of the indicator (\(w_{1}w_{2}w_{3}\)), \"Capacity\" refers to the amount of changeable bits for a given pixel, \"Code length\" is the code length of Hamming codes, and \"Payload\" represents the pure hiding capacity (i.e., the result of \"Capacity\" value minus the \"Code length\" value). For example, for a complex image, the payload is 3 if Label is 5 (i.e., \(6-3=3\)). If \(payload(i,j)\) is less than 0, no secret data are hidden. In addition, the original \(|payload(i,j)|\) MSBs of the pixel \(p(i,j)\) are regarded as part of the to-be hidden secret data, where \(|b|\) is the absolute value of \(b\). When \(payload(i,j)\) is larger than 0, the second part of the \(p^{\prime}(i,j)\), bits of the secret data, are equal to the values from the 4 th MSB bit to the \(payload(i,j)+3\)-th MSB bits of the \(p^{\prime}(i,j)\). The third part is the last (\(5-payload(i,j)\)) bits of \(p(i,j)\) if \(payload(i,j)\) is larger than 0; otherwise, the last five bits of the embedded pixel are kept the same as those of \(p(i,j)\).