Evaluation of the Probability of Breaking the Electronic Digital Signature Elements

This article analyzes the standards, algorithms, and hash functions used in electronic digital signature (EDS). It is determined that most of the modern hash functions and algorithms used in EDS schemes are based on elliptic curves above the field. Some of the collisions causes, methods, and algorithms for hash attacks are covered in the article. A mathematical apparatus for estimating the probability of hash functions breaking based on the "birthday paradox" is formed. The results of the probability of breaking for hash functions used in EDS were obtained. It is confirmed that in case of the same length of the hash, the probability of breaking the hash by the breaking the resistance to collisions method is much lower than using the method of breaking the strong resistance to collisions. It has been suggested that it is dangerous to add a key at the beginning or end of a message when working with key hash functions.