Information-Theoretic Approach to Steganographic Systems

We propose a simple universal (that is, distribution- free) steganographic system in which covertexts with and without hidden texts are statistically indistinguishable. The stegosystem can be applied to any source generating i.i.d. covertexts with unknown distribution, and the hidden text is transmitted exactly, with zero probability of error. Sequences of covertexts with and without hidden information obey the same distribution (the stegosystem is perfectly secure). The proposed steganographic system has two important properties. First, the rate of transmission of hidden information approaches the Shannon entropy of the covertext source as the size of blocks used for hidden text encoding tends to infinity. Second, if the size of the alphabet of the covertext source and its minentropy tend to infinity then the number of bits of hidden text per letter of covertext tends to log(n!)/n where n is the (fixed) size of blocks used for hidden text encoding. Besides, the resource complexity of the proposed algorithms grows only polynomially.