Unclonable Non-Interactive Zero-Knowledge

TL;DR

This paper introduces quantum-based non-interactive zero-knowledge proofs that are inherently unclonable, preventing adversaries from copying and distributing proofs, thus enhancing security in cryptographic protocols.

Contribution

It constructs the first unclonable NIZK proof system for NP, addressing a longstanding open question and enabling unclonable signatures of knowledge.

Findings

Successfully constructed unclonable NIZK proofs for NP

Proved unclonability prevents proof cloning and distribution

Applications include unclonable signatures of knowledge

Abstract

A non-interactive ZK (NIZK) proof enables verification of NP statements without revealing secrets about them. However, an adversary that obtains a NIZK proof may be able to clone this proof and distribute arbitrarily many copies of it to various entities: this is inevitable for any proof that takes the form of a classical string. In this paper, we ask whether it is possible to rely on quantum information in order to build NIZK proof systems that are impossible to clone. We define and construct unclonable non-interactive zero-knowledge arguments (of knowledge) for NP, addressing a question first posed by Aaronson (CCC 2009). Besides satisfying the zero-knowledge and argument of knowledge properties, these proofs additionally satisfy unclonability. Very roughly, this ensures that no adversary can split an honestly generated proof of membership of an instance $x$ in an NP language $\mathcal{L}$ and distribute copies to multiple entities that all obtain accepting proofs of membership of $x$ in $\mathcal{L}$. Our result has applications to unclonable signatures of knowledge, which we define and construct in this work; these non-interactively prevent replay attacks.