Non-uniformity and Quantum Advice in the Quantum Random Oracle Model

TL;DR

This paper investigates the power of quantum advice in the quantum random oracle model, showing it is often comparable to classical advice but can be exponentially more effective in certain contrived scenarios, highlighting potential quantum advantages.

Contribution

It introduces a quantum-friendly multi-instance framework and demonstrates quantum advice's near-equivalence to classical advice in many security settings, with some cases of exponential separation.

Findings

Quantum advice is nearly as effective as classical advice in many security games.

A new quantum analogue of multi-instance frameworks is proposed.

Quantum advice can exponentially outperform classical advice in specific contrived games.

Abstract

QROM (quantum random oracle model), introduced by Boneh et al. (Asiacrypt 2011), captures all generic algorithms. However, it fails to describe non-uniform quantum algorithms with preprocessing power, which receives a piece of bounded classical or quantum advice. As non-uniform algorithms are largely believed to be the right model for attackers, starting from the work by Nayebi, Aaronson, Belovs, and Trevisan (QIC 2015), a line of works investigates non-uniform security in the random oracle model. Chung, Guo, Liu, and Qian (FOCS 2020) provide a framework and establish non-uniform security for many cryptographic applications. In this work, we continue the study on quantum advice in the QROM. We provide a new idea that generalizes the previous multi-instance framework, which we believe is more quantum-friendly and should be the quantum analogue of multi-instance games. To this end, we match the bounds with quantum advice to those with classical advice by Chung et al., showing quantum advice is almost as good/bad as classical advice for many natural security games in the QROM. Finally, we show that for some contrived games in the QROM, quantum advice can be exponentially better than classical advice for some parameter regimes. To our best knowledge, it provides some evidence of a general separation between quantum and classical advice relative to an unstructured oracle.