# A Novel CDMA-Based Secret Message Multiplexing Scheme by Image Data Hiding +
## 1 Introduction  
With the rapid development of information and communication technologies (ICT), smartphones have been an indispensable part of our daily life. Large amounts of data are transmitted on the Internet every day. Information security is becoming more and more important. In recent years, a lot of image-steganographic methods, also known as data hiding techniques, have been proposed to hide the secret data in the cover images. These techniques can be categorized into three major classes, which are the original domain hiding [1; 2; 3; 4; 5; 6; 7; 8; 9; 10], the compressed space domain hiding [11; 12; 13; 14], and the transform domain hiding [15; 16; 17; 18]. By embedding the secret data into a digital image with slight modification and transmitting the image on the Internet, the security of the secret data is improved. Nevertheless, among these techniques, there exists a common weakness. The secret data are stored in a single image. Being the only information carrier, once the image is lost or damaged, the secret data cannot be recovered correctly. To solve this problem, the secret sharing method is a feasible approach. The concept of secret sharing was proposed separately by [PERSON] [19] and [PERSON] [20] in 1979. It was called the (\(k\), \(n\)) threshold scheme. A secret is split into \(n\) pieces (\"shadows\" or \"shares\") and those pieces can be distributed to \(n\) participants at different locations. The secret can only be reconstructed from \(k\) or more pieces (\(k\leq n\)). In 1995, [PERSON] and [PERSON] [21] extended the secret sharing technique to the image field and proposed the visual cryptography technique, which was also called visual secret sharing (VSS). A secret image is divided into \(n\) shadows or shares to be held by \(n\) participants. The secret imagecan be revealed by stacking \(k\) or more shares. VSS schemes utilize the human visual system in the reconstruction of the secret image but suffer from pixel expansion problem. Thereafter, lots of novel secret image sharing (SIS) techniques were proposed to improve the VSS performance, such as the EMD-based scheme [22], Sudoku matrix scheme [23], turtle shell matrix scheme [24], maze matrix scheme [25], fractal matrix scheme [26], and so forth [27; 28; 29; 30; 31]. Those schemes utilize mathematical computation and well-designed reference matrices to construct meaningful shares and recover the secret image. In contrast to the secret sharing, we previously proposed an innovative secret message multiplexing scheme applied to a QR code [32], in which the secret extraction can be achieved by each participant independently without cooperating with others. This scheme is inspired by the concept of Code Division Multiple Access (CDMA) and enables a secret distributor delivering multiple secret messages to several participants simultaneously via a single QR Code. All the secret messages for different users are encoded into a CDMA codeword and embedded in the padding region of the cover QR code. By this way, everyone can read the public message of a marked QR code by any standard QR code reader, but only the authorized participant can extract the dedicated secret message using his or her specific secret key and has no knowledge about others' secret. Since the embedding capacity of the QR code is limited, this scheme is only feasible for small amount of secret message delivering. In this paper, we will implement the concept of secret multiplexing in the digital image and propose a novel CDMA-based secret message multiplexing scheme by image data hiding. In this scheme, we still consider a scenario where there is a secret distributor and several participants. The secret distributor is going to deliver multiple secret messages to all participants simultaneously via a single digital image. The secret messages for all users are encoded into a compound CDMA codeword and embedded in the grayscale image by modulo operation. At the receiving side, each participant will be assigned an exclusive spreading code.