# Dual Partial Reversible Data Hiding Using Enhanced Hamming Code
## 1 Introduction  
Although the internet facilitates global communication, it cannot always be regarded as a fully secure channel, especially when handling sensitive information. Therefore, appropriate security protocols must be employed to ensure that confidential information is exchanged safely. A common approach to defending internet communications is to encrypt messages during transmission. However, because encrypted messages are often easy to recognize, they may themselves become targets of attack. An alternative method known as data hiding (DH) [1, 2, 3, 4] involves embedding information within digital media. Because this process can appear the same as ordinary data transmission, it tends to draw less attention from potential attackers. Leveraging this characteristic can further strengthen the security of data exchanges. DH can be broadly classified into reversible (RDH) and non-reversible (N-RDH) methods. RDH techniques have the characteristic that the original cover image can be fully restored after extracting the hidden data from the stego image. Several representative RDH algorithms have been proposed to date, including difference expansion (DE)-based methods [5, 6, 7], histogram shifting (HS) techniques [8, 9, 10], and prediction error expansion (PEE) [11]. First introduced by [PERSON] in [5], the DE approach has demonstrated excellent performance in terms of embedding capacity. The histogram shifting (HS) method [8], firstintroduced in 2006, is regarded as an improvement over previous techniques due to the relatively lower distortion it causes to the cover medium. However, RDH schemes require a location map to embed data and recover the original cover image. While this method achieves good visual quality and reasonable embedding capacity, it has the drawback of requiring the transmission of two peak points and a zero-point pair to the receiver. PEE [11] involves obtaining prediction errors from the neighborhood of each pixel and embedding information bits into the expanded errors. If the difference between the original and predicted pixels is large, the embedding process can cause significant distortion to the cover image. DH methods based on ordered prediction can reduce distortion at low embedding rates. On the other hand, secret sharing [12] has the feature that while \(n\) participants create \(n\) shadows using the same cover image to share data, the data can only be reconstructed when there are shadows of \(k(k\leq n)\) participants. If the number of participants is less than \(k\), then data reconstruction will fail. In terms of data confidentiality, secret sharing is very powerful and can be used in various applications. Dual image-based RDH [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26] adopts some features of secret sharing, utilizing \(n(=k=2)\) cover images. Thus, two shadow images are required to recover the original image. [PERSON] et al. (2007) [13] introduced a dual-image RDH method using the exploitation modification direction (EMD). In their approach, two quinary secret data points are used to form a pair of stego pixels, with cover pixel pairs referenced according to the main and secondary diagonals of the EMD matrix. Later, [PERSON] et al. (2013) [14] proposed an improved method for enhancing the visual quality of the stego images. [PERSON] and [PERSON] (2013) [15] enhanced the visual quality of stego images by limiting modifications during the data hiding process to at most plus or minus one. [PERSON] et al. [16] proposed an asymmetric dual-image RDH method in which the first stego image is generated using the EMD technique and the second is created based on three rule analyses applied to the first image. As a result, the first stego image experiences greater distortion compared to the second. [PERSON] et al. (2015) [17] discovered that the LSB-matching technique, originally used in N-RDH, could be adapted for dual-image schemes.