A NISQ-friendly Coined Quantum Walk Algorithm for Chaos-based Cryptographic Applications

TL;DR

This paper introduces a depth-efficient LAQW quantum algorithm suitable for NISQ devices, demonstrating its application in chaos-based cryptography and key generation with reproducible 128-bit keys under simulated noise.

Contribution

The paper proposes a novel LAQW algorithm with significantly reduced circuit depth compared to existing models, enabling practical NISQ implementation for cryptographic purposes.

Findings

LAQW circuit depth scales as O(n^2 + nt), a reduction from O(n^2 t) in CAQW.

Reproducible 128-bit keys generated under simulated quantum noise.

LAQW demonstrates potential in cryptographic applications like key generation and image encryption.

Abstract

We present a novel lackadaisical alternating quantum walk (LAQW) algorithm whose circuit depth scales as $\mathcal{O}(n^2+nt)$ for a $n\times n$ lattice over $t$ time steps. We show that this is a significant depth reduction compared to the existing controlled alternating quantum walk (CAQW) model, which has a circuit depth that scales as $\mathcal{O}(n^2t)$ (Li et al., 2017, arXiv:1707.07389). This makes the implementation of the LAQW viable for Noisy Intermediate-scale Quantum (NISQ) devices. We then showcase the applicability of the LAQW algorithm by proposing a chaos-based symmetric-key generation scheme. Our approach uses the LAQW as a quantum entropy source from which reproducible random bitstring sequences are generated using the underlying probability distribution and subsequent post-processing methods. We provide a comprehensive evaluation of the LAQW algorithm and demonstrate the reproducibility of 128-bit keys under simulated quantum noise provided by IBM's FakeTorino backend. A direct comparison with the CAQW model, which has been used in image encryption and hash function schemes (Li et al., 2017, arXiv:1707.07389; Abd EL-Latif et al., 2020, ScienceDirect; Abd El-Latif, Abd El-Atty, and Venegas-Andraca, 2020, ScienceDirect), highlights the potential and usefulness of the LAQW model in cryptographic applications.