The Sufficient Condition for Ensuring the Reliability of Perception of the Steganographic Message in the Walsh-Hadamard Transform Domain

In view of the high compatibility of the Walsh-Hadamard transform to the architecture of modern computing facilities, it is sensible to use it in methods of steganography and steganalysis. Now, there are some efficient steganographic methods that use the Walsh-Hadamard transform domain for information embedding presented in the literature. It is known that to ensure the reliability of the steganographic message perception, information should be embedded in its high-frequency components; nevertheless, the issues of the correspondence of the Walsh-Hadamard transformants to the frequency components of the original matrix of the cover image are poorly researched. The purpose of this paper is to develop a formal sufficient condition for ensuring the reliability of perception of steganographic messages in the Walsh-Hadamard transform domain. This purpose was achieved by establishing the relationship between the Walsh-Hadamard transformants and the discrete cosine transform transformants, which was theoretically substantiated in two ways, and also experimentally confirmed. Based on the established relationship between the Walsh-Hadamard transform and the discrete cosine transform, as well as the components of the singular value decomposition of the corresponding matrices, a sufficient condition has been developed to ensure the reliability of the perception of steganographic messages in the Walsh-Hadamard transform domain. The sufficient condition consists in the fact that after embedding of additional information using any steganographic method, those WalshHadamard transformants that correspond to the singular triples of the matrix corresponding to small (smallest) in value singular numbers, should change.