Complete characterization of perfectly secure stego-systems with mutually independent embedding operation

Without any assumption on the cover source, this paper presents a complete characterization of all perfectly secure stego-systems that employ mutually independent embedding operation. It is shown that for a fixed embedding operation, the only perfectly secure stego-systems are those whose cover distribution is an element of a linear vector space with basis vectors determined by the embedding operation. Moreover, we also prove that such stego-systems are perfectly secure if and only if the Fisher information with respect to the embedding change rate is zero and thus Fisher information can be seen as an equivalent descriptor of steganographic security. This result is important for deriving steganographic capacity of imperfect stego-systems with covers modeled as Markov chains [1]. It also suggests that Fisher information could be used for benchmarking.