A Stable Hash Function Based on Parity-Dependent Quantum Walks With Memory (August 2023)

In this article, we develop a generic controlled alternate quantum walk model by combining parity-dependent quantum walks with distinct arbitrary memory lengths and propose a hash function (called QHFM-P) based on this model. The statistical properties of the proposed scheme are stable with respect to the coin parameters of the underlying controlled quantum walks, and with certain parameter values, the collision resistance property of QHFM-P is better than that of the state-of-the-art hash functions based on discrete quantum walks. Moreover, the proposed hash function can also maintain near-ideal statistical performance when the input message is of small length. In addition, we derive a type of inappropriate initial states of hash functions based on 1-D one-particle quantum walks (with ordinary shift operator) on cycles, with which all messages will be mapped to the same hash value, regardless of the angles adopted by the coin parameters.