Theoretical Foundations of Digital Content Integrity Expertise

In the context of the rapid development of information technologies, their implementation in the process of functioning of critical infrastructure, in particular energy, of any state is extremely rele-vant. At the same time, the continuity and quality of functioning of any automated system in the digital space critically depends on ensuring the integrity of the information used. The effectiveness of digital content integrity expertise methods is determined by their theoretical foundations. Existing theoretical approaches do not allow obtaining a final solution to this problem. The aim of this work is to develop a general approach to the analysis of the state of information systems, based on the theory of matrices, for its use in the examination of the integrity of digital content. The objective was achieved by investigating the perturbation properties of singular values and singular vectors of the image (or video frame) matrix as a result of perturbation for original and non-original contents. The most important results of the work are: substantiation for non-original content of the destruction of the monotony of the trend of the func-tion of dependence of the disturbance of the singular number on its number, which takes place for orig-inal content; substantiation of the fundamental possibility of estimating the magnitude of the perturbing effect. The significance of the obtained results lies in their subsequent use for the development of uni-versal methods for examining the integrity of digital images, video, in particular steganoanalytical meth-ods, which make it possible not only to identify the fact of integrity violation, but also to assess the magnitude of the perturbing effect, which is extremely important in steganoanalysis, where this value characterizes the throughput of a hidden communication channels.