Simple hash function using discrete-time quantum walks

Hash functions play an essential role in many cryptographic applications such as digital signature, integrity authentication, and key derivation. Most of them are iteratively built based on the Merkle–Damgård (MD) structure. Unfortunately the traditional MD structure is suffering from various attacks, and thus the design of new hash functions is emerging. In this paper, inspired by quantum computation, we present a new hash function by introducing alternate single-qubit coin operators into discrete-time quantum walk. The present hash function is classical with classical input and output. The compressive function can be implemented by performing alternate single-qubit coin operators on the coin state controlled by a classical input binary message and then applying the global conditional shift operator on the position state and the coin state. The classical output hash value is generated by making amplification, truncation, and modular operation on the final probability distribution. Numerical simulation and performance comparison show that the present hash function has an excellent property of collision resistance and easier implementation than existing quantum-walk-based hash functions. It promotes more applications of quantum computation in the design of hash functions.