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：非交互式零知识（NIZK）证明能够在无需泄露秘密的情况下验证NP陈述的真伪。然而，获取NIZK证明的攻击者可能能够克隆该证明，并将其任意数量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，这种克隆不可避免。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。我们定义并构建了针对NP问题的不可克隆非交互式零知识（知识）证明。除满足零知识和知识证明性质外，这些证明还额外满足不可克隆性。大致而言，该性质确保：对于实例$x$属于NP语言$\mathcal{L}$这一事实，任何攻击者都无法将诚实生成的成员资格证明拆分后分发给多个实体，使得它们均能获得关于$x$属于$\mathcal{L}$的接受性成员资格证明。我们的研究成果可应用于不可克隆知识签名（本文定义并构造了该概念），这类签名能以非交互方式防止重放攻击。