The development of computer technology has determined the vector for the expansion of services based on the Internet and “G” technologies. The main requirements for modern services in the banking sector are security and reliability. At the same time, security is considered not only as ensuring the confidentiality and integrity of transactions, but also their authenticity. However, in the post-quantum period, US NIST specialists question the durability of modern means of providing basic security services based on symmetric and asymmetric cryptography algorithms. The increase in computing resources allows attackers to use modern threats in combination. Thus, there is a need to search for new and/or modify known algorithms for generating MAC (message authentication codes). In addition, the growth of services increases the amount of information that needs to be authenticated. Among the well-known hash algorithms, the hash functions of universal hashing are distinguished, which allow initially determining the number of collisions and their uniform distribution over the entire set of hash codes. Possibilities of modifying the cascade hashing algorithm UMAC (message authentication code based on universal hashing, universal MAC) based on the use of McEliece crypto-code construction on algebrogeometric (elliptic codes (EC), modified elliptic codes (MEC) and damaged codes (DC). This approach allows preserving the uniqueness property, in contrast to the classical UMAC scheme based on a block symmetric cipher (AES). The presented algorithms for evaluating the properties of universality and strict universality of hash codes make it possible to evaluate the security of the proposed hashing constructs based on universal hash functions, taking into account the preservation of the universality property