By leveraging the no-cloning principle of quantum mechanics, unclonable cryptography enables us to achieve novel cryptographic protocols that are otherwise impossible classically. Two most notable examples of unclonable cryptography are quantum copy-protection and unclonable encryption. Most known constructions rely on the quantum random oracle model (as opposed to the plain model). Despite receiving a lot of attention in recent years, two important open questions still remain: copy-protection for point functions in the plain model, which is usually considered as feasibility demonstration, and unclonable encryption with unclonable indistinguishability security in the plain model. A core ingredient of these protocols is the so-called monogamy-of-entanglement (MoE) property. Such games allow quantifying the correlations between the outcomes of multiple non-communicating parties sharing entanglement in a particular context. Specifically, we define the games between a challenger and three players in which the first player is asked to split and share a quantum state between the two others, who are then simultaneously asked a question and need to output the correct answer. In this work, by relying on previous works of Coladangelo, Liu, Liu, and Zhandry (Crypto'21) and Culf and Vidick (Quantum'22), we establish a new MoE property for subspace coset states, which allows us to progress towards the aforementioned goals. However, it is not sufficient on its own, and we present two conjectures that would allow first to show that copy-protection of point functions exists in the plain model, with different challenge distributions (including arguably the most natural ones), and then that unclonable encryption with unclonable indistinguishability security exists in the plain model. We believe that our new MoE to be of independent interest, and it could be useful in other applications as well.

翻译：通过利用量子力学的不可克隆原理，不可克隆密码学使我们能够实现经典方法无法实现的新型密码协议。其中两个最显著的例子是量子复制保护与不可克隆加密。现有大多数构造依赖于量子随机预言模型（而非普通模型）。尽管近年来备受关注，但仍有两个重要开放问题悬而未决：通常被视为可行性验证的普通模型中点函数的复制保护，以及具备不可克隆不可区分安全性的普通模型中不可克隆加密。这些协议的核心要素是所谓的纠缠单调性（MoE）性质。此类博弈允许量化共享纠缠态的多个非通信方在特定情境下输出结果间的关联性。具体而言，我们定义了一个挑战者与三个参与者之间的博弈：首个参与者需将量子态拆分后共享给另外两人，这两人随后同时接受质询并需输出正确答案。本研究基于Coladangelo、Liu、Liu与Zhandry（Crypto'21）及Culf与Vidick（Quantum'22）的既有工作，建立了子空间陪集态的新型MoE性质，从而推动上述目标的实现。然而该性质本身尚不充分——我们提出两个猜想：其一可论证普通模型中点函数复制保护的存在性（涵盖不同挑战分布，包括最具自然性的情形），其二可论证普通模型中具备不可克隆不可区分安全性的不可克隆加密的存在性。我们认为本项MoE成果可能具有独立研究价值，并有望应用于其他场景。