A Modular Approach to Unclonable Cryptography

TL;DR

This work proposes a new notion called unclonable puncturable obfuscation (UPO), a candidate construction of UPO, and proves 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.

Abstract

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.

Figures (39)

• Figure 1: Applications of Unclonable Puncturable Obfuscation. ${\cal S}_{{\sf punc}}$ denotes cryptographic schemes satisfying puncturable property. ${\cal F}_{{\sf punc}}$ denotes cryptographic functionalities satisfying functionalities satisfying puncturable property. ${\cal F}_{{\sf evasive}}$ denotes functionalities that are evasive with respect to a distribution $\mathcal{D}$ satisfying preimage-sampleability property. The dashed lines denote corollaries of our main results. The blue-filled boxes represent primitives whose feasibility was unknown prior to our work. The red-filled boxes represent primitives for which we get qualitatively different results or from incomparable assumptions when compared to previous works.
• Figure 2: Security Experiment
• Figure 3: Generalized Security Experiment
• Figure 4: The $\mathsf{CLLZ}$$\mathrm{single\ }\mathrm{decryptor\ }\mathrm{encryption}$ scheme, see CLLZ21.
• Figure 5: Definition of a $\mathsf{CLLZ}\text{ }{post}\text{-}{processing}$$\mathsf{SDE}$ scheme.

Theorems & Definitions (142)

• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4
• Corollary 5
• Corollary 6
• Theorem 7: Informal
• Remark 8
• Definition 9: $\mathsf{UPO}$ Security
• Definition 10: Generalized $\mathsf{UPO}$ security