Аннотация:In addition to the quantum channel, an auxiliary classical authentic communication channel isrequired for quantum key distribution. To provide unconditional security in quantumcryptography, which based on the fundamental laws of quantum mechanics, informationtheoreticauthentication is required, and not authentication based on computational complexity.The paper provides a security proof of information-theoretic authentication in quantumcryptography using ε-ASU2 hash functions. The internal structure of ε-ASU2 hash functions isnot used in the proof, so these hash functions can be implemented by a different composition ofother hash functions, for example, including the composition ε-AXU2 functions with a reusedkey and subsequent encryption of the tag with a one-time pad key, which is taken from theprevious session of quantum key distribution. It is also shown that information-theoreticauthentication preserves composable security of the keys. This authentication method can alsobe used for key agrrement in in networks with trusted nodes (Molotkov 2022 Laser Phys. Lett.19 045201–9; Arbekov and Molotkov 2020 Laser Phys. Lett. 17 055202–8) and with quantumkey distribution.