Authentication of variable length messages in quantum key distribution
Department of Computer Science and Software Engineering, Miami University, 45056, Oxford, Ohio, USA
2 Department of Computer Science, University of Victoria, V8W 3P6, Victoria, BC, Canada
Accepted: 6 February 2022
Published online: 16 February 2022
Authentication plays a critical role in the security of quantum key distribution (QKD) protocols. We propose using Polynomial Hash and its variants for authentication of variable length messages in QKD protocols. Since universal hashing is used not only for authentication in QKD but also in other steps in QKD like error correction and privacy amplification, and also in several other areas of quantum cryptography, Polynomial Hash and its variants as the most efficient universal hash function families can be used in these important steps and areas, as well. We introduce and analyze several efficient variants of Polynomial Hash and, using deep results from number theory, prove that each variant gives an ε-almost-Δ-universal family of hash functions. We also give a general method for transforming any such family to an ε-almost-strongly universal family of hash functions. The latter families can then, among other applications, be used in the Wegman–Carter MAC construction which has been shown to provide a universally composable authentication method in QKD protocols. As Polynomial Hash has found many applications, our constructions and results are potentially of interest in various areas.
Key words: Quantum key distribution / Polynomial Hash / ε-almost-strongly universal / Polynomial congruence
© The Author(s) 2022
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