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 proofs (of knowledge) for NP. Besides satisfying the zero-knowledge and proof 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.

翻译：非交互式ZK（NIZK）证明能够在无需泄露秘密的情况下验证NP语句。然而，获取NIZK证明的敌手可能能够克隆该证明，并将其任意多的副本分发给不同实体：对于任何采用经典字符串形式的证明而言，这是不可避免的。本文探讨是否可能借助量子信息构建不可克隆的NIZK证明系统。我们针对NP问题定义并构造了不可克隆的非交互式零知识（知识）证明。除了满足零知识性和知识证明属性外，这些证明还额外满足不可克隆性。粗略而言，这确保没有任何敌手能够将实例$x$在NP语言$\mathcal{L}$中成员关系的诚实生成证明进行拆分，并向多个实体分发副本，使得所有实体都能获得$x$在$\mathcal{L}$中成员关系的接受性证明。我们的结果可应用于不可克隆的知识签名——本文定义并构造了该签名，它能以非交互方式防止重放攻击。