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 copy-protection (CP) and unclonable encryption (UE). Most known constructions rely on the QROM (as opposed to the plain model). Despite receiving a lot of attention in recent years, two important open questions still remain: CP for point functions in the plain model, which is usually considered as feasibility demonstration, and UE 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 [CLLZ21, CV22], 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 CP of point functions exists in the plain model, with different challenge distributions, and then that UE 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. To highlight this last point, we leverage our new MoE property to show the existence of a tokenized signature scheme with a new security definition, called unclonable unforgeability.

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条件下无法达成的新型密码协议。不可克隆密码学两个最显著的例子是复制保护（CP）和不可克隆加密（UE）。目前已知的大多数构造依赖于量子随机预言机模型（QROM），而非明文模型。尽管近年来受到广泛关注，仍存在两个重要的开放性问题：明文模型下点函数的复制保护（通常被视为可行性验证），以及明文模型下具有不可克隆不可区分安全性的不可克隆加密。这些协议的核心要素是所谓的纠缠单配性（MoE）特性。此类博弈允许量化在特定情境下共享纠缠的多个非通信方结果之间的关联性。具体而言，我们定义了挑战者与三个参与者之间的博弈：首先要求第一个参与者将量子态拆分并共享给另外两个参与者，随后同时向这两个参与者提问并要求输出正确答案。在本工作中，基于先前研究[CLLZ21, CV22]，我们为子空间陪集态建立了新的纠缠单配性特性，这使我们能够朝着上述目标推进。然而，仅凭该特性尚不充分，我们提出两个猜想：首先可证明明文模型下存在针对不同挑战分布的点函数复制保护，进而证明明文模型下存在具有不可克隆不可区分安全性的不可克隆加密。我们相信新的纠缠单配性特性具有独立研究价值，并可能在其他应用场景中发挥作用。为强调这一点，我们利用新的纠缠单配性特性证明了一种具有新型安全定义（称为不可克隆不可伪造性）的令牌化签名方案的存在性。