Constructing quantum Hash functions based on quantum walks on Johnson graphs

We present a quantum hash function in a quantum walk framework on Johnson graphs. In this quantum hash function, the message bit decides which coin operator, i.e., Grover operator or DFT operator, is applied on the coin at each step. Then a fixed conditional shift operator is applied to decide the movement of the walker. Compared with existing quantum-walk-based hash functions, the present hash function has a lower collision rate and quantum resource cost. It provides a clue for the construction of other cryptography protocols by introducing the quantum walk model into hash functions.