The work considers an important scientific and practical task of increasing the effectiveness of detecting violations of the integrity of information, in particular digital images, which is its common representation, which is becoming one of the main ones for specialists in the field of information and cyber security today. Undetected, unauthorized changes to information in a timely manner can lead to negative, catastrophic consequences for individuals, enterprises, banks, firms, and for humanity as a whole, when it comes to information that constitutes a state secret, contains data from the military industry, nuclear energy, chemical industry, etc., which determines the relevance of the problem under consideration.The main result of the work is an improved universal method for detecting violations of the integrity of a digital image, ready for practical implementation, the theoretical basis of which is based on the analysis of eigenvalues and eigenvectors of symmetric blocks of the image matrix, which correspond to the original blocks. The paper substantiates the method of symmetrization of the block matrix, which allows to significantly (by more than 23%) reduce computational and, as a result, time costs for image examination in comparison with& the time costs of the prototype method. It is proved that for the majority of the obtained symmetric blocks that correspond to the blocks of the original CG, the angle between the eigenvector corresponding to the maximum eigenvalue of the block and &the normalized vector of the modules of the eigenvalues is equal to a certain value that does not depend on the specifics of the original image, but is sensitive to its changes, which made it possible to ensure the universality of the method and incr&ease its efficiency in the sense of the accuracy of detecting a violation of the integrity of the image by more than 5%, compared to the analogue.The significance of the obtained results lies in ensuring, due to the use of the proposed method, an inc&rease in the efficiency of the process of detecting violations of the integrity of the image according to the criteria of computing (time) costs for the examination of one image and the accuracy of detection.
