We explore a new pathway to designing unclonable cryptographic primitives. We propose a new notion called unclonable puncturable obfuscation (UPO) and study its implications for unclonable cryptography. Using UPO, we present modular (and arguably, simple) constructions of many primitives in unclonable cryptography, including public-key quantum money, quantum copy-protection for many classes of functionalities, unclonable encryption, and single-decryption encryption. Notably, we obtain the following new results assuming the existence of UPO: We show that any cryptographic functionality can be copy-protected as long as this functionality satisfies a notion of security, which we term as puncturable security. Prior feasibility results focused on copy-protecting specific cryptographic functionalities. We show that copy-protection exists for any class of evasive functions as long as the associated distribution satisfies a preimage-sampleability condition. Prior works demonstrated copy-protection for point functions, which follows as a special case of our result. We show that unclonable encryption exists in the plain model. Prior works demonstrated feasibility results in the quantum random oracle model. We put forward a candidate construction of UPO and prove two notions of security, each based on the existence of (post-quantum) sub-exponentially secure indistinguishability obfuscation and one-way functions, the quantum hardness of learning with errors, and a new conjecture called simultaneous inner product conjecture.

翻译：我们探索了一条设计不可克隆密码原语的新路径。我们提出一种称为不可克隆可穿刺混淆（UPO）的新概念，并研究其对不可克隆密码学的意义。利用UPO，我们给出了不可克隆密码学中多种原语的模块化（且可论证地简单）构造，包括公钥量子货币、多种功能类别的量子复制保护、不可克隆加密以及单解密加密。值得注意的是，在假设UPO存在的前提下，我们获得了以下新结果：我们证明，只要任何密码学功能满足一种我们称为“可穿刺安全性”的安全概念，该功能就能被复制保护。先前的可行性结果主要集中在复制保护特定密码学功能上。我们证明，只要相关分布满足原像可采样条件，任何逃避函数类别的复制保护都存在。先前工作展示了对点函数的复制保护，这作为我们结果的一个特例适用。我们证明，在普通模型下存在不可克隆加密。先前工作在量子随机预言机模型中展示了可行性结果。我们提出了一个UPO候选构造，并证明了两种安全性概念，每种都基于（后量子）次指数不可区分混淆和单向函数的存在性、学习带误差问题的量子困难性，以及一个称为同时内积猜想的新猜想。