Problems of the Regional Energetics (May 2022)
The Sufficient Condition for Ensuring the Reliability of Perception of the Steganographic Message in the Walsh-Hadamard Transform Domain
Abstract
In view of the high compatibility of the Walsh-Hadamard transform to the architecture of mod-ern 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 reli-ability 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 do-main. This purpose was achieved by establishing the relationship between the Walsh-Hadamard transformants and the discrete cosine transform transformants, which was theoretically substan-tiated in two ways, and 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 Walsh-Hadamard trans-formants that correspond to the singular triples of the matrix corresponding to small (smallest) in value singular numbers, should change.
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