# High-Fidelity Steganography: A Covert Parity Bit Model-Based Approach
## 4 Proposed Scheme
### Data Embedding
This method is particularly beneficial for run-length encoding (RLE), as it groups zero-valued high-frequency coefficients towards the end, producing longer runs of zeros and thereby improving compression rates. During quantization, high-frequency coefficients tend to become zero; thus, their clustering based on the zigzag order further enhances compression efficiency. Prioritizing low-frequency components helps to maintain image quality after compression by preserving essential image details. Moreover, zigzag scanning is a standardized method in JPEG and MPEG, ensuring compatibility across different platforms and devices. This standardized approach, coupled with the efficient ordering of coefficients, optimizes compression techniques and maintains good image quality, making zigzag extraction the preferred method for DCT coefficient handling in image and video compression. Moreover, instead of extracting column-by-column, in which case N number of columns need to be modeled, in zigzag extraction only one vector is modeled, meaning that only \(n+1\) polynomial coefficients need to be transmitted rather than \((n+1)\times N\times N\) polynomial coefficients. The zigzag version is shown in Figure 5.

### Data Extraction

The dimensions of the confidential image must be sent to the receiver along with the parity vector \(P(x)\) and the polynomial coefficients. To restore the confidential bits, the DCT is first performed on the stego signal. Because the area hosting the confidential bits is known, the magnitude of the DCT of the hosting area can be extracted. Next, using the sent polynomial coefficients, the polynomial signal \(M(x)\) is generated by the receiver. Using the parity vector received from the sender, extraction is achieved using

\[RE(x)=M(x)-\frac{P(x)}{k}ST(x), \tag{5}\]

Figure 5: The embedding algorithm (zigzag version). where \(RE(x)\) is the extracted sample at \(x\). To reduce the communication cost between the sender and receiver, the parity vector \(P(x)\) can be compressed efficiently using the RLE compression technique, as it contains binary data; the pseudocode of the proposed extraction step is shown in Algorithm 2. ```
1:Input:
2: stego: The stego image
3: p: The polynomial coefficients vector
4: k: The scaling factor
5:Output
6: secret: The secret image
7: [stegodct] \(\leftarrow\) DCT2(stego) \(\triangleright\) Apply 2D-DCT on the stego image
8: [column] \(\leftarrow\) EXTRACT(stegdct) \(\triangleright\) Extract DCT column (Column-by-column or zigzag)
9:for1:size(column) do\(\triangleright\) For every column, do the following: (for zigzag version, we have only 1 column)
10: [column_model] \(\leftarrow\) construct(n) \(\triangleright\) Construct the polynomial signal from the polynomial coefficients vector p
11: [secret_column] \(\leftarrow\) column - b* column_model\(\triangleright\) Get the secret column, b can be 0 or 1
12:endfor
13: secret_scaled \(\leftarrow\) Group(secret_column) \(\triangleright\) Group the columns and place them back into their original locations
14: [sec] \(\leftarrow\) secret_scaled*(k) \(\triangleright\) Upscale the secret image using the scaling factor k
```

**Algorithm 2** The algorithm of the proposed extraction scheme

## 5 Experimental Results

### Analysis of Results

This section presents the experimental results obtained by the proposed embedding scheme and provides a comprehensive analysis of the performance of the proposed technique. Section 5.2 presents a comparison between the results gathered by the proposed steganography technique and other recent steganography techniques. Section 5.3 examines the robustness of the proposed steganography scheme. Finally, Section 5.4 tests the robustness of the proposed steganography technique against depp learning steganalysis test. Figure 6 illustrates the original hosting image and the confidential image to be used. The hosting images, namely, \"Airplane\", \"Animal\", and \"Vegetables\", were deliberately selected due to their belonging to different classes in terms of statistical properties.