Analysis of the amplitude form of the quantum hash function

In this article, the properties of quantum hash functions are further explored. Previous findings show that so-called small-bias sets (special subsets of the set of elements of a cyclic group) generate a “phase” quantum hash function. Here, it was proved that they also generate an “amplitude” quantum hash function. Namely, it turned out that constructing small-bias sets while generating amplitude quantum functions yields a well-balanced combination of the cryptographic properties of unidirectionality and collision resistance. As a corollary of the obtained theorem, a general statement about the generation of new amplitude quantum hash functions based on universal hash families and small-bias sets was proved.