One-out-of-Many Unclonable Cryptography: Definitions, Constructions, and More

TL;DR

This paper introduces a new security notion called one-out-of-many unclonable security, constructs cryptographic primitives based on LWE, and advances unclonable cryptography by removing reliance on strong heuristics.

Contribution

It defines and constructs one-out-of-many unclonable cryptographic primitives from the LWE assumption, improving security notions and removing reliance on strong heuristics.

Findings

Constructed one-out-of-many unclonable encryption from LWE.

Developed a one-time strong anti-piracy secure SDE scheme in the standard model.

Achieved one-out-of-many copy-protection and predicate encryption from the new security notion.

Abstract

The no-cloning principle of quantum mechanics enables us to achieve amazing unclonable cryptographic primitives, which is impossible in classical cryptography. However, the security definitions for unclonable cryptography are tricky. Achieving desirable security notions for unclonability is a challenging task. In particular, there is no indistinguishable-secure unclonable encryption and quantum copy-protection for single-bit output point functions in the standard model. To tackle this problem, we introduce and study relaxed but meaningful security notions for unclonable cryptography in this work. We call the new security notion one-out-of-many unclonable security. We obtain the following results. - We show that one-time strong anti-piracy secure secret key single-decryptor encryption (SDE) implies one-out-of-many indistinguishable-secure unclonable encryption. - We construct a one-time strong anti-piracy secure secret key SDE scheme in the standard model from the LWE assumption. - We construct one-out-of-many copy-protection for single-bit output point functions from one-out-of-many indistinguishable-secure unclonable encryption and the LWE assumption. - We construct one-out-of-many unclonable predicate encryption (PE) from one-out-of-many indistinguishable-secure unclonable encryption and the LWE assumption. Thus, we obtain one-out-of-many indistinguishable-secure unclonable encryption, one-out-of-many copy-protection for single-bit output point functions, and one-out-of-many unclonable PE in the standard model from the LWE assumption. In addition, our one-time SDE scheme is the first SDE scheme that does not rely on any oracle heuristics and strong assumptions such as indistinguishability obfuscation and witness encryption.