On the Concept of Cryptographic Quantum Hashing

TL;DR

This paper introduces a new concept of quantum-resistant hash functions that balance one-way and collision resistance, demonstrating their properties, construction, and implementation potential with current optical technology.

Contribution

It defines quantum-resistant hash functions combining pre-image and collision resistance, and presents explicit constructions suitable for optical implementation.

Findings

Quantum resistance properties are correlated in the quantum setting.

An explicit balanced quantum hash function is constructed.

Implementation with current optical technology is feasible.

Abstract

In the paper we define a notion of quantum resistant ($(\epsilon,\delta)$-resistant) hash function which combine together a notion of pre-image (one-way) resistance ($\epsilon$-resistance) property we define in the paper and the notion of collision resistance ($\delta$-resistance) properties. We show that in the quantum setting a one-way resistance property and collision resistance property are correlated: the "more" a quantum function is one-way resistant the "less" it collision resistant and vice versa. We present an explicit quantum hash function which is "balanced" one-way resistant and collision resistant and demonstrate how to build a large family quantum hash functions. Balanced quantum hash functions need a high degree of entanglement between the qubits. We use a "phase constructions" technique to express quantum hashing constructions, which is good to map hash states to coherent states in a superposition of time-bin modes. The later is ready to be implemented with current optical technology.