# High-Fidelity Steganography: A Covert Parity Bit Model-Based Approach
## 4 Proposed Scheme
### Data Embedding  
The embedding algorithm is illustrated in Figure 4. First, the 2D-DCT is applied to the cover image. Next, the magnitude of the DCT is extracted, as hiding is performed in the magnitude of the DCT while the DCT phase is kept intact. It has been proven that the DCT phase contains more significant information than the magnitude; thus, keeping the phase intact can contribute to producing a stego image with good quality [22]. After that, column-by-column extraction is performed using the magnitude of the DCT. Next, each column is modeled using the polynomial fitting approach using a degree of order \(n\). Using the created polynomial model, a signal is generated that mimics the shape of the DCT signal. After that, the parity bit vector \(P(x)\) is generated by comparing the original DCT signal with the polynomial-generated signal. Figure 3: Hiding methodology of the proposed steganography scheme. In the meantime, the secret signal is prepared for the embedding process. First, the secret is downscaled using a rescaling factor \(k\). Then, the secret signal is multiplied with the parity vector \(P(x)\) using Equation (3). After that, the resulting multiplication signal is added to the polynomial-generated signal to obtain the DCT of the stego signal. Finally, the Inverse DCT (IDCT) is applied to the stego DCT signal to obtain the stego signal in the spatial domain. The rescaling factor \(k\) is a tuning parameter that controls the trade-off between stego quality and robustness. It is known that superimposing a small-scaled signal on a larger-scaled signal produces a signal that is similar to the larger signal. Therefore, decreasing the \(k\) value can improve the stego quality, as the secret column will be very small and the shape of the superimposed signal will not change much by superimposing this small signal. On the other hand, a very small secret signal can make the signal highly vulnerable to being destroyed by attacks such as data tampering. The proposed embedding algorithm is illustrated in the pseudocode shown in Algorithm 1. ```
1:Input:
2: cover: The cover image
3: secret: The secret image
4: n: The polynomial degree
5: k: The scaling factor
6:Output:
7: stego: The stego image
8: [covercct] \(\leftarrow\) DCT2(cover) \(\triangleright\) Apply 2D-DCT on the cover image
9: [sec] \(\leftarrow\) secret*(1/k) \(\triangleright\) Downscale the secret image using the scaling factor k
10: [column] \(\leftarrow\) EXTRACT(coverdct) \(\triangleright\) Extract DCT column (Column-by-column or zigzag)
11:for1:size(column) do\(\triangleright\) For every column, do the following: (for zigzag version, we have only 1 column)
12: [column_model] \(\leftarrow\) polymodel(column,n) \(\triangleright\) Apply polynomial modeling using a degree of n
13: [steg_column] \(\leftarrow\) column_model + b*sec \(\triangleright\) Superimpose sec over column_model
14:endfor
15: steg_dct \(\leftarrow\) Group(steg_column) \(\triangleright\) Group the columns and place them back into their original locations
16: [stego] \(\leftarrow\) IDCT2(steg_dct) \(\triangleright\) Apply the inverse 2D-DCT to obtain the stego image

Figure 4: The embedding algorithm (column\(-\)by\(-\)column). Another method to reduce the communication cost is the zigzag extraction method. Zigzag extraction of Discrete Cosine Transform (DCT) coefficients is preferred in image and video compression techniques such as the JPEG and MPEG standards due to several key advantages. The DCT transforms image data into frequency components, concentrating the most important visual information or lowest-frequency components in the top left-hand corner of the DCT block and high-frequency components, which are often less important and more noise-prone, positioned towards the bottom right-hand corner. Zigzag scanning starts from the top left and moves to the bottom right, effectively ordering the coefficients by their importance, which enhances the efficiency of compression algorithms.