Signature Сodes for a Сlass of Multiple-Access Channels

In this paper we have investigated the mathematical problem of steganography and its applications at length. We have seen the dierent models (the active warden and the passive warden) and some methods to solve the problem. Two approaches (algebraic and probabilistic) were examined, and we have seen that there is a link between the problem of steganography and coding theory. To be exact, there is an equivalence between stego schemes and covering codes. So we monitored articles that propose the ways to construct eective covering codes. The particular problem of writing on dirty (and wet) paper was investigated. We have analyzed the perfor- mance of one interesting algorithm (ZZW) and proposed its improvement. In addition we have analyzed one important asymptotically optimal perfect stego scheme and its behavior in the noisy channel. It turns out that this scheme is perfect only in perfect environment and some curious errors occur in the messages during the transmission via a noisy channel (or a channel with a warden). To correct the aforementioned errors we need codes correcting deletions and insertions of symbols, but at nowadays there are codes correcting only one error of that type. Because of unsolved problems of additive number theory we can not construct codes that correct more insertions and deletions.