# High-Fidelity Steganography: A Covert Parity Bit Model-Based Approach
## 2 Related Works  
A common classification strategy for steganography techniques is based on the embedding domain. According to this approach, steganography schemes are categorized as either spatial domain schemes or frequency domain schemes. In spatial domain schemes, embedding is carried out directly in the native spatial domain of the host cover image [23; 24]. Examples of spatial domain schemes include Least-Significant-Bit (LSB) schemes [25; 26], histogram-based techniques [27; 28], and Pixel Value Difference (PVD) methods [29; 30]. In contrast, transform-based schemes embed confidential bits in the transform domain of the hosting signal. This transformation is performed using one of the primary frequency domain methods [31; 32; 33] or variations of these techniques such as Dual-Tree Complex Wavelet Transforms (DTCWT), Complex Wavelet Transforms (CWT), and Integer Wavelet Transform (IWT) [34]. For instance, a DFT-based hiding scheme was proposed in [35]. In this scheme, the confidential data are first encoded using the Lempel-Ziv-Welch (LZW) compression technique. The LZW encoded data are then encrypted by performing an XOR operation with pseudo-random numbers. To further enhance security, the XOR result is encrypted using the Data Encryption Standard (DES) encryption technique. Meanwhile, the host image is transformed to the frequency domain using the DFT transform, where the Coefficients Selection and Frequency Hopping (CSFH) algorithm is employed to randomly select the DFT coefficients. The encrypted secret data are then embedded in these selected coefficients. Finally, the inverse DFT is performed to transform the image back to the spatial domain. Another DWT-based hiding scheme was proposed in [36]. The proposed scheme successfully utilizes the three DWT bands, namely, horizontal, vertical, and diagonal, for hiding the confidential data. A secret key is generated to minimize the distortion in the cover image. Moreover, a blocking strategy is adopted to maintain the quality of the stego image by using a hiding strategy that elects matching blocks between the secret and cover image. Another DWT-based scheme that achieved acceptable imperceptibility and security levels was proposed in [37]. The proposed DWT scheme utilizes the Haar wavelet as the mother wavelet to minimize any data loss in the original hosting image. The Discrete Cosine Transform (DCT) is widely used in steganography due to its strong energy compaction properties. The DCT can represent a signal using only a few significant coefficients. This characteristic benefits steganography schemes, as the DCT domain has many insignificant coefficients. Consequently, high-payload steganography schemes can be effectively implemented using the DCT transform. Two parallel schemes were proposed in [38]. In the first scheme, the Rivest-Shamir-Adleman (RSA) encryption technique is utilized to encrypt a secret text message to generate the stego image. The second scheme is a parallelized chaotic 2D-DCT technique. The Duffing map is utilized to encode the confidential image into a uniform group of samples, which is later hidden in the frequency domain of the cover image. Another DCT-based scheme was proposed in [39]. This proposed method applies the DCT transform to the cover image, then scans the DCT coefficients in a zigzag manner. After that, the hiding positions are elected based on a proposed chaotic function. This proposed scheme shows acceptable results in terms of the imperceptibility level; however, experimental results show poor robustness against compression and geometric attacks [40]. Several recent papers have explored the DCT energy compaction limits within steganography techniques [5; 16; 18; 41]. These studies have confirmed that the DCT's strong energy compaction property is directly related to the inter-pixel correlation level of the cover image. Based on the findings, higher pixel correlation within the cover image leads to stronger energy compaction in the DCT, thereby enabling higher payload capacity.