Mathematical models of hybrid crypto-code constructions in the UMAC algorithm

Abstract

In the post-quantum period, the issue of data authentication in critical informationcommunication and cyber-physical systems becomes acute. On the one hand, computing resources provide the ability to increase the amount of transmitted data, on the other hand, it is practically impossible to ensure stability in authentication mechanisms. Research in this area demonstrates that one of the promising directions is the use of crypto-code constructions based on McEliece and Niederreiter schemes based on algebraic geometric codes, and fast authentication algorithms. The authors propose the use of McEliece crypto-code constructions based on modified elliptic codes with damage in the cascade UMAC algorithm. This approach provides the required levels of robustness, the efficiency of generating the MAC code, as well the universality property of the UMAC algorithm, which allows using collision properties as additional identifiers in large databases.