The components of ensuring the warranty of automated systems, which are subject to increased requirements in connection with their use in many sensitive areas of public activity, including national security and defense, critical industrial technologies, energy and communications, banking, environmental protection , technologies of legitimate distance learning, etc. Certain components can significantly affect the quality and reliability of information services in regulatory conditions. In particular, the special role of the functional security of the cryptographic subsystem in terms of supporting the performance of the automated system for its tasks and functions in general, as well as in terms of ensuring the confidentiality and integrity of information. The components of the cryptographic subsystem have been identified, the poor or incorrect operation of which negatively affects the security of these subsystems. The types of the most dangerous attacks on these subsystems are analyzed, their classification from the point of view of possibility of realization in modern scientific and technical conditions and depending on capacity of available computing means and technologies on the basis of which the most real and dangerous variant of realization of remote attacks on software implementation of cryptographic subsystem is defined. . Based on the analysis, a method for evaluating the quality of cryptographic transformations based on a modified algorithm for solving the problem of finding solutions of systems of linear equations with distorted right-hand parts using the so-called decoding based on "lists" of first-order "shortened" Reed-Muller codes is proved. the correctness of the proposed algorithm.