The Round Complexity of Proofs in the Bounded Quantum Storage Model

TL;DR

This paper explores how quantum memory limitations affect the complexity and design of interactive proof systems, demonstrating protocols that are efficient and secure under bounded quantum storage assumptions.

Contribution

It introduces protocols for proof systems in the bounded quantum storage model, including non-interactive proofs for NP and QMA, and compressed two-message quantum proofs.

Findings

Existence of non-interactive proof for NP and QMA in BQSM

Classical proof systems can be compressed into two-message quantum protocols

Zero-knowledge quantum protocols can be achieved with bounded prover memory

Abstract

The round complexity of interactive proof systems is a key question of practical and theoretical relevance in complexity theory and cryptography. Moreover, results such as QIP = QIP(3) (STOC'00) show that quantum resources significantly help in such a task. In this work, we initiate the study of round compression of protocols in the bounded quantum storage model (BQSM). In this model, the malicious parties have a bounded quantum memory and they cannot store the all the qubits that are transmitted in the protocol. Our main results in this setting are the following: 1. There is a non-interactive (statistical) witness indistinguishable proof for any language in NP (and even QMA) in BQSM in the plain model. We notice that in this protocol, only the memory of the verifier is bounded. 2. Any classical proof system can be compressed in a two-message quantum proof system in BQSM. Moreover, if the original proof system is zero-knowledge, the quantum protocol is zero-knowledge too. In this result, we assume that the prover has bounded memory. Finally, we give evidence towards the "tightness" of our results. First, we show that NIZK in the plain model against BQS adversaries is unlikely with standard techniques. Second, we prove that without the BQS model there is no 2-message zero-knowledge quantum interactive proof, even under computational assumptions.