Quantum Hashing via Classical $ε$-universal Hashing Constructions
This work addresses the need for efficient quantum hashing in quantum computing, though it appears incremental as it builds on classical hashing techniques.
The paper tackles the problem of constructing quantum hash functions by introducing a quantum hash generator based on classical ε-universal hash families, achieving optimality in qubit usage with a specific Reed-Solomon code implementation.
In the paper, we define the concept of the quantum hash generator and offer design, which allows to build a large amount of different quantum hash functions. The construction is based on composition of classical $ε$-universal hash family and a given family of functions -- quantum hash generator. The proposed construction combines the properties of robust presentation of information by classical error-correcting codes together with the possibility of highly compressed presentation of information by quantum systems. In particularly, we present quantum hash function based on Reed-Solomon code, and we proved, that this construction is optimal in the sense of number of qubits needed.