Universal quantum hashing

In the paper we propose a method of quantum hashing which mostly combines the existing constructions of universal hash families with quantum one-way functions. Next, we define the concept of a quantum hash generator and present an approach for building a large number of various quantum hash functions. The construction is based on the integration of a classical $\varepsilon$-universal hash family and a given family of functions – quantum hash generator. The proposed construction combines the properties of robust representation of information by classical error-correcting codes together with the possibility of highly reliable representation of information by quantum systems. In particular, we present a quantum hash function based on the Reed–Solomon code and prove that this construction is optimal in the sense of the number of qubits needed.