USING INTEGRAL ESTIMATES OF COLLISION PROBABILITY IN HASH FUNCTIONS DURING THE TRAINING OF FUTURE IT SPECIALISTS

Abstract

The article substantiates the pedagogical feasibility of using integral calculus methods to estimate collision probabilities in hash functions in the process of training future IT specialists. The relevance of the study is due to the need to improve the quality of mathematical training of future information security specialists and to form in them the ability to apply mathematical methods to analyze the cryptographic stability of information protection algorithms. The paper shows that traditional combinatorial approaches to estimating collision probabilities in hash functions are often difficult for students to perceive and do not provide an adequate level of awareness of the applied content of mathematical models. A teaching methodology based on the use of integral estimates is proposed, which allows approximating discrete probabilistic processes by continuous models and applying graphical interpretation of the results. This approach contributes to a better understanding of the birthday paradox and its connection with the problem of collisions in hash functions. In order to assess the pedagogical effectiveness of the proposed approach, a pedagogical experiment involving control and experimental groups of students was conducted. In the experimental group, the study of the topic was carried out using integral models and graphical interpretation of probabilities, while traditional combinatorial methods were applied in the control group. The test results demonstrated an increase in the level of material mastery in the experimental group, which was confirmed by statistical verification. The obtained results indicate the feasibility of using integrals as an effective tool for collision analysis in hash functions and confirm their pedagogical value in teaching the mathematical foundations of cryptography.