# Data Hiding of Multicompressed Images Based on Shamir Threshold Sharing
## 1 Introduction  
Traditional encryption protects the content of secret messages through the incomprehensibility of ciphertext. However, the incomprehensibility of ciphertext exposes the importance of the secret message, which easily arouses attackers' curiosity and attention. Thus, attackers would attempt to decipher the ciphertext or destroy the communication [1, 2]. Image-based data hiding (DH) methods have been used in the development of various applications in computer vision. In contrast to traditional cryptography, DH hides secret messages in multimedia files by taking advantage of the redundancy of multimedia files, while it does not cause significant perceptive distortion [3]. Even if an interceptor knows of the existence of the secret message, it is difficult to extract the secrets without authorization; accordingly, DH ensures the confidentiality and security of the secret message. DH can be applied in many fields, such as digital signature, fingerprint identification, authentication and secret communication [4]. Digital images are often used as the cover media because they are accessible and available in the redundancy [5]. DH in digital images has two principal standards: embedding capacity and the visual quality of the stego image. Embedding more secret data typically leads to more severe image distortion, so an excellent DH algorithm should embed secret data as much as possible, while ensuring that there is no obvious visual difference between the stego image and the original image. In accordance with the restoration of the cover image after secret message extraction, DH can be briefly divided into two classes, namely nonreversible DH (NRDH) and reversible DH (RDH). RDH should satisfy the visual quality requirement, and ensure that thereceiver can extract the secret message correctly and completely. In addition, RDH must restore the cover image completely with no distortion. Representative RDH algorithms typically include Difference Expansion (DE), image compression, Histogram Shifting (HS), Prediction Error Expansion (PEE), Pixel Value Order (PVO) [6; 7; 8; 9] and encrypted image reversible data hiding [10; 11]. Representative NRDH algorithms typically include Block Truncation Coding (BTC) [12], Absolute Moment Block Truncation Coding (AMBTC) [13; 14; 15] and Least Significant Bit (LSB) [16; 17; 18]. Although the traditional data hiding scheme can prevent malicious attackers from stealing the secret message embedded in the stego image to a certain extent, once the data hiding method is cracked by the attacker, the security of the secret message will be questioned [19]. Secret sharing is one of the important technologies to ensure the storage and transmission of secret messages. Instead of hiding secret messages on a single carrier, it splits the secret messages into n secrets and stores and transmits them separately. A subsecret is called a share, and an image embedded with the share as the secret message is called a shadow image. Only when \(m\) or more than \(m\) shares cooperate, the merging and extraction of secret messages can be completed. Therefore, the data hiding method based on secret sharing can improve the security of secret message in storage and transmission. The number \(m\) of shares used in secret message extraction is often smaller than the total number of splits \(n\); even if some shares are destroyed during storage and transmission, it does not affect the final secret message extraction, so this method can also improve the fault tolerance of the data hiding method. **(a)**: **Dual-image secret sharing data hiding**  
[PERSON] et al. first proposed dual-image data hiding based on Exploiting Modification Direction (EMD) in 2007 [20]. In this method, the binary secret message is converted into 5-based secret digitals, and then two binary secret digitals are embedded into a pixel pair.