Scientific approach to probabilistic assessment of information protection against imposing false messages in telecommunication systems

Abstract

To date, in all economically developed countries of the world, multibillion-dollar scientific and exploratory research is being carried out on the problems of building quantum-resistant cryptographic systems. In particular, work is being carried out on the analysis, development and research of models, methods and computational algorithms for post-quantum cryptographic transformations, their possible standardization and implementation. At the same time, it is necessary to have an objective, scientifically based approach for assessing the level of information security, which can be guaranteed when implementing one or another protection mechanism. This paper presents formulated scientific approaches, derived expressions making it possible to evaluate the strength of MAC codes as mechanisms for ensuring the authenticity, integrity, and authenticity of messages. It is shown that it is necessary to use the statistics of joint message distributions for accurate calculation of the MAC codes simulation and collision stability. It is proved that the lower limits for the probabilities of imitation and substitution ignore the statistical properties of authenticators arrays. They are based on the pseudo-randomness model of f(x) function and determine the minimum requirements for the key space size and the MAC values space. The upper bounds for the imitation and substitution probabilities are related to combinatorial properties of the MAC arrays and evaluate the value of collisions in the space of MAC values f(x) and messages for the worst case choice of keys and messages. Collision characteristics of MAC codes are considered. The derived equations make it possible to solve accurately the problem of determining the number of experiments indispensable to create a collision with a certain probability on a set of MAC code values. The MAS stability estimates for one of the types of hash functions are obtained using the derived equations.