# High-Fidelity Steganography: A Covert Parity Bit Model-Based Approach
## 4 Proposed Scheme  
The DCT transform is a popular transform technique in the steganography field due to its strong energy compaction property. DCT-based schemes exploit this property by embedding in the large area that contains the high-frequency DCT components. Recent DCT-based schemes operate by substituting the high-frequency components with the confidential bits. This hiding procedure can produce stego signals with acceptable stego quality. This is true due to high-frequency DCT coefficients having less significance than low-frequency DCT coefficients, as shown in Figure 1. Based on Figure 1, the original signal can be restored with acceptable quality even after destroying the high-frequency component of the signal. Figure 1: Image showing the significance of each DCT component. In DCT model-based hiding schemes, the quality level of the stego signal is maximized by adopting a strategy to keep the layout of the high-frequency component of the signal instead of completely destroying the high-frequency coefficients. This is accomplished by modeling the high-frequency coefficients using the polynomial fitting approach. The DCT signal to be modeled is a nonlinear signal. The polynomial fitting approach has the ability to model nonlinear relationships, capturing complex patterns that linear regression cannot. By adjusting the polynomial's degree, the model can flexibly fit a wide range of data behaviors. Additionally, polynomial equations are relatively simple and interpretable, providing clear insights into the relationships between variables. Finally, the method is computationally efficient. There is a need to adopt a modeling technique that is simple but at the same time can capture complex nonlinear signals. Therefore, the proposed technique uses polynomial modeling. More information about polynomial fitting can be found in [22]. The DCT-based modeling technique proposed in [22] adopted the idea of superimposing a scaled-down version of the secret signal on the polynomial-generated signal to obtain the stego signal shown in Figure 2. The blue signal shown in Figure 2 represents the high-frequency portion of the cover image, which is completely destroyed in the DCT-based hiding schemes that adopt the concept of coefficients replacement. However, the scheme in [22] retains the overall shape of the high-frequency signal using polynomial modeling. Afterwards, the secret signal can be superimposed on the polynomial-generated signal after being down-scaled, with the resulting signal retaining the same structure as the polynomial-generated signal. The proposed scheme is based on the observation that, as shown in Figure 2, the points of the polynomial-generated signal are always in the middle, rather than above nor below the points of the original high-frequency DCT signal. Therefore, it is not a good idea for all stego pixels to be generated using an arithmetic addition between the samples of the scaled-down secret signal and the polynomial-generated signal. Instead, in this paper we aim to further maximize the similarity between the high-frequency DCT signal and the polynomial-generated signal. Instead of superimposing the scaled-down secret signal on the polynomial-generated signal, our scheme relies on the error between the high-frequency DCT signal and the polynomial-generated signal sample-by-sample. For a given sample, if the DCT sample is greater than the sample of the polynomial-generated signal, then the stego sample is obtained by _adding_ the secret sample to the polynomial sample. Otherwise, if the polynomial sample is greater than the DCT  
Figure 2: Hiding methodology of the steganography scheme proposed in [22]. sample, then the stego sample is obtained by _subtracting_ the value of the secret sample from the value of the DCT sample. To simplify, we add a parity bit calculation to the process. The parity bit is used to identify whether an addition or subtraction process is required within a specific sample. The parity-bit can obtain using  
\[P(x)=\left\{