Hash Function Based on Quantum Walks with Two-Step Memory

We propose a new quantum-walk-based hash function QHF2M by combining two types of quantum walks with two-step memory and numerically test its statistical performance. The test result shows that QHF2M 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. Moreover, both unequal and equivalent coin angles used by the underlying quantum walks can lead to near-ideal statistical performance. This result indicates that neither using quantum walks with different memory length nor adopting distinct coin angles is a necessary condition for constructing good quantum-walk-with-memory-based hash functions.