Quantum hashing based on symmetric groups

TL;DR

This paper introduces a novel method for constructing quantum hash functions applicable to any finite group, extending previous abelian group-based approaches and integrating classical hash functions from NC^1.

Contribution

It presents a new group-agnostic approach to quantum hashing, enabling broader applicability and combining classical hash functions with quantum methods.

Findings

Constructs quantum hash functions for any finite group.

Integrates classical hash functions from NC^1 into quantum hashing.

Extends previous abelian group-based quantum hashing results.

Abstract

The notion of quantum hashing formalized by F. Ablayev and A. Vasiliev in 2013. F. Ablayev and M. Ablayev in 2014 introduced the notion of quantum hash generator which is convenient technical tool for constructing quantum hash func- tions. M. Ziatdinov in 2014 presented group approach for constructing quantum hash functions. All these mentioned above results present constructions of quan- tum hash functions based on abelian groups. This paper continue the research on quantum hashing. Our approach allows us to construct quantum hash function working on any (finite) group. Also our approach allows us to construct quantum hash functions based on classical hash function from $NC^1$.