# Enhanced Dual Reversible Data Hiding Using Combined Approaches
## 1 Introduction  
Multimedia communication and security technologies are important issues in both academia and industry. The most widely used method for information security is encryption, which encrypts information so that only authorized recipients can decrypt it. However, encrypted images have the problem of potentially attracting the attention of attackers. On the other hand, data hiding (DH) [1, 2, 3, 4, 5] is a method of covertly concealing secret data in multimedia media, with the advantage that attackers cannot easily determine the existence of the data. Due to these characteristics, DH is advantageous for covertly transmitting small amounts of confidential information to the receiving end and is therefore being extensively researched. DH techniques can be broadly divided into non-reversible data hiding (Non-RDH) and reversible data hiding (RDH). In Non-RDH, the cover image cannot be restored to its original state after extracting the hidden information. On the other hand, RDH [6, 7, 8, 9, 10, 11, 12, 13]allows for the perfect restoration of the original cover image after extracting the hidden data, making it ideal for applications requiring high fidelity such as medical images, military maps, and art preservation. Over the years, various RDH techniques have been developed to achieve an optimal trade-off between data embedding capacity and visual quality. A variety of RDH techniques, including difference expansion and histogram shifting, have been developed to balance embedding capacity and image quality. Notable methods include difference expansion (DE), proposed by [PERSON] [8; 9], Histogram Shifting (HS), introduced by [PERSON] et al. [10], and Prediction Error Expansion (PEE) [13]. These techniques have improved the performance of RDH by enhancing capacity and image quality. [PERSON] (2003) [8] introduced the difference expansion (DE) technique, which uses the difference between two adjacent pixels to hide data. The DE technique provides high embedding capacity and has the advantage of being able to restore the original image without loss. However, this method may have limited embedding capacity and may result in some degradation of image quality. [PERSON] et al. (2006) [10] proposed the Histogram Shifting (HS) technique, introducing a method of embedding data by shifting the positions of the peak and zero points in the image histogram. This method has relatively low embedding capacity but shows excellent performance in maintaining image quality. The HS technique became the foundation for RDH research, and various modified techniques were subsequently developed. [PERSON] (2004) [9] proposed a reversible watermarking technique that generalized the DE technique and applied it to quads. This method provides high embedding capacity and can restore the original image without loss. However, it requires complex calculations and may have limitations in real-time applications. [PERSON] et al. (2013) [14] proposed a high-fidelity RDH technique that combines Pixel Value Ordering (PVO) and prediction-error expansion (PEE). This method simultaneously provides high insertion capacity and excellent image quality, making it effective for use in various application areas. By combining PVO and PEE techniques, they reduced distortions that could occur during the data insertion process and improved the ability to restore the original image. Dual reversible data hiding (RDH) [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27] is a technique that simultaneously achieves high embedding capacity and good image quality. This method incorporates the concept of Secret Sharing (SS) [28; 29] to ensure data security and recoverability. SS is a technique that divides secret data into multiple pieces and distributes them, allowing the original data to be reconstructed only when pieces meeting specific conditions are gathered. Prominent examples of this method include Shamir's SS [28].