*2.2. Previous Method*

The main idea is to form a mapping relationship between the carrier and the secret message, and then realize the coverless hiding of the secret data. The construction of the look-up table is based on the generation of hash code. Fatimah Shamsulddin Abdulsattar generates eigenvalues based on feature decomposition, and then calculates the hash code of the image block and builds a look-up table [34]. The look-up table contains the hash code and its location information. In the image, the main feature vector represents the direction of the maximum change between image pixels, and the largest feature value is related to the foremost feature vector. The hash code is calculated by the largest eigenvalue obtained by feature decomposition which is Equation (2).

$$\max \underline{\varepsilon}\_{jl} = \max \{ \underline{\varepsilon}\_{jl1}, \underline{\varepsilon}\_{jl2}, \underline{\varepsilon}\_{jl3}, \dots, \underline{\varepsilon}\_{jlk} \}, \tag{2}$$

where *max* \_ *ejl* denotes the largest value in the *l*-th sub-block and the block **Bjl** has *k* eigenvalues. The largest eigenvalue of adjacent image sub-blocks is arranged and combined in

light of the specific arrangements to obtain an 8-bit binary hash code. The arrangements in this method are displayed in Figure 1. If the arrangemen<sup>t</sup> Arr.1, as shown in Figure 1a, is selected in the process, the hash code is acquired by Equation (3). When another arrangemen<sup>t</sup> (Arr.2 or Arr.3 or Arr.4) is selected, the function is calculated according to Equation (4).

$$h\_{\mathbb{C}} = \begin{cases} 0, & \text{if } \max\\_{\mathcal{C}\_{jl}} > \max\\_{\mathcal{C}\_{\overline{\mathcal{B}}}} \\ 1, & \text{if } otherwise \end{cases} \tag{3}$$

where the *max* \_ *ejl* is the largest value in the *l*-th sub-block and *l* ∈ [1, 8].

$$h\_{\mathcal{L}} = \begin{cases} 0, & \text{if } \max\\_{\mathcal{E}\_{jl}} < \max\\_{\mathcal{E}\_{jl+1}} \\ 1, & \text{if } otherwise \end{cases} \tag{4}$$

where *l* ∈ [1, 8] and *l* = 5.

The hash code of each sub-block can be converted into the corresponding ASCII-code value [40]. The range of the ASCII code is [0, <sup>255</sup>]. The look-up table is created by putting the positions of the hash code and the hash code into the same table. When the sender hides the secret message, they can map the table with the data and record the location of the hash code, that is, by creating a location table to achieve coverless hiding. After receiving the location table and the original image, the receiver can establish the same look-up table and then extract the hidden secret from the look-up table in the light of the mapping relationship.

According to the above description, Fatimah Shamsulddin Abdulsattar uses eigenvalue decomposition to establish the hash code as the feature of the image and then establish the look-up table. The secret message is hidden according to the mapping relationship. Although their method does not require a large database and achieves a high hidden capacity, when the image block is set to a large size, the number of hash codes generated is less. There is a problem that the secret message has no mapping relationship. When the size of the secret message increases, the corresponding location table requires more space. In other words, there is room for improvement. Our method for this problem is increasing the diversity of hash code and further improving the hiding rate.

**Figure 1.** The four arrangements are used in [34]. (**a**) Arr.1, (**b**) Arr.2, (**c**) Arr.3, and (**d**) Arr.4.
