Quantum-inspired Hash Function Based on Parity-dependent Quantum Walks with Memory

TL;DR

This paper introduces a quantum-inspired hash function based on a novel controlled quantum walk model with memory, demonstrating strong statistical properties and robustness comparable to existing quantum walk-based hash functions.

Contribution

It proposes a new quantum-inspired hash function using a controlled quantum walk with memory, combining parity dependence and arbitrary memory lengths for improved performance.

Findings

Achieves near-ideal statistical performance

Comparable sensitivity, diffusion, and collision resistance to state-of-the-art methods

Robustness against parameter variations

Abstract

In this paper, we develop a generic controlled alternate quantum walk model (called CQWM-P) by combining parity-dependent quantum walks with distinct arbitrary memory lengths and then construct a quantum-inspired hash function (called QHFM-P) based on this model. Numerical simulation shows that QHFM-P has near-ideal statistical performance and is on a par with the state-of-the-art hash functions based on discrete quantum walks in terms of sensitivity of hash value to message, diffusion and confusion properties, uniform distribution property, and collision resistance property. Stability test illustrates that the statistical properties of the proposed hash function are robust with respect to the coin parameters, and theoretical analysis indicates that QHFM-P has the same computational complexity as that of its peers.