Quantum hash function using discrete-time quantum walk on Hanoi network

TL;DR

This paper introduces a novel quantum hash function leveraging discrete-time quantum walks on a Hanoi network, enhancing collision resistance and efficiency for small message sizes compared to existing quantum walk-based hashes.

Contribution

It presents a new quantum hash function based on a Hanoi network, demonstrating improved collision resistance and applicability to small message lengths.

Findings

Highly collision resistant hash function.

Effective for small message bit-lengths.

Outperforms cycle-based quantum hash functions.

Abstract

Quantum walk based hash functions have attracted a lot of attention in recent years because of its faster execution time and robust resistance against attacks compared to classical hash functions. It has been observed that the underlying graph and the way message controls the quantum walk iteration steps play a crucial role for the robustness of the hash function. We propose a quantum hash function based on the discrete-time quantum walk on a Hanoi network--a one dimensional periodic lattice with extra long-range edges of a specific form--which is highly collision resistant. The message bits of our scheme control the flow of probability amplitude through the extra long-range edges and the conditional shift operators. Our method even works for messages with small bit-lengths, contrary to most of the quantum walk based hash functions defined on a cycle, which usually work for messages with bit-lengths more than the length of the cycle.