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The use of the digital images in modern society is very common, making it difficult to name an industry where digital images are not used. However, in certain situations, the digital images may be direct or indirect digital evidence, such as in court cases. Tampering or violating the integrity of the digital images is one of the important issues in the information protection. The issue of the digital signal authentication by cybersecurity experts is a pressing issue in the present days. Therefore, the development of methods and algorithms for detecting the integrity of digital signals in general, and digital images in particular, is a very crucial task. Among all the possible variations in the integrity violation of digital images can be distinguished a separate group, in which the digital images are processed by various filters editors, such as blurring, sharpening, etc. The blurring is often applied to images not only when they are tampered, but also as a steganographic attack. Blur detection indicates the inability to use a digital image as the evidence of anything. One of the most effective blur detection methods known from the open sources is a method based on the analysis of singular values of blocks of a digital image matrix. The aim of this paper is to increase the efficiency of the blur detection in a digital image by modifying an algorithm based on the analysis of singular values. Computational experiments are performed to determine the number of parameters to be verified. The results obtained allow modifying the algorithm of the method of the blur detection in a digital image. The modification makes it possible to detect tampered access to a digital image. The modified algorithm is no less effective than the original algorithm, and allows analyzing fewer parameters in a shorter time. The computational complexity of the algorithm is determined by the second order polynomial that is acceptable in terms of the practical application. [ABSTRACT FROM AUTHOR]