Theoretical foundations for constructing effective codewords for the code-controlled information embedding steganographic method

Abstract

Steganography is an important component of modern information security systems. At the same time, in the conditions of modern cyberspace, it is relevant to develop high-performance steganographic methods that would have a high level of resistance to possible attacks by compression, noise, and blur. One of such methods is the steganographic method with code-controlled information embedding, based on the idea of preliminary coding of the information being embedded using binary codewords, for which the transformants of the Walsh-Hadamard transform have the specified properties. A specific localization of disturbances in the Walsh-Hadamard transform domain of the container takes place because of the information embedding. In this paper, a theoretical basis has been formed for further improvement of the codewords used in the code-controlled information embedding steganographic method. It is shown that despite the fact that these codewords have an ideal effect only on a given transformant of the Walsh-Hadamard transform, they affect several transformants at once in the domain of the discrete cosine transform (DCT). The concept of the selectivity coefficient is introduced to estimate the level of selectivity of the impact on a given DCT transformant. It has been established that with an increase in the size of the blocks used, a tendency is observed to a decrease in the selectivity coefficient due to the presence of the “close neighbor” effect. This trend is conditioned by the involvement of the DCT transformants with similar frequencies that have similar resistance to possible attacks on the embedded message. In this case, the ratio of the sum of absolute values of low-frequency DCT transformants to the sum of absolute values of all other DCT transformants increases with the size of the codeword. In this paper it has been proven and practically confirmed that an increase in the size of a codeword leads to an increase in the resistance of the code-controlled information embedding steganographic method. Possible ways of further practical improvement of codewords used in the code-controlled information embedding steganographic method are theoretically substantiated.