Mathematical analysis of extended matrix coding for steganography

Steganographic coding is an important technique for ensuring the security of steganography. It allows more secret messages to be embedded with a few modifications. As a typical representative of steganographic coding, the mechanism of extended matrix coding is described in detail. And a mathematical analysis is carried out when the secret message is a 0-1 random signal. According to the hierarchical mapping structure of hash function in the encoding process, a series of probabilities of each of extension-layers are obtained. The cost of setting symbol bits is also calculated. The quantitative relationship between the maximum permitted layer L and the embedding efficiency of stegosystem is confirmed. By theoretical analysis, we conclude that the performance of extended matrix coding is worse than that of original matrix coding when the secret message is a stochastic signal. The former will only be superior when the secret message is a black type logo.