Multi-Copy Security in Unclonable Cryptography

Abstract: Unclonable cryptography leverages the quantum no-cloning principle to copy-protect cryptographic functionalities. While most existing works address the basic single-copy security, the stronger notion of multi-copy security remains largely unexplored. We introduce a generic compiler that upgrades collusion-resistant unclonable primitives to achieve multi-copy security, assuming only one-way functions. Using this framework, we obtain the first multi-copy secure constructions of public-key quantum money (termed quantum coins), single-decryptor encryption, unclonable encryption, and more. We also introduce an extended notion of quantum coins, called upgradable quantum coins, which allow weak (almost-public) verification under weaker assumptions and can be upgraded to full public verification under stronger assumptions by the bank simply publishing additional classical information. Along the way, we give a generic compiler that upgrades single-copy secure single-decryptor encryption to a collusion-resistant one, assuming the existence of functional encryption, and construct the first multi-challenge secure unclonable encryption scheme, which we believe are of independent interest.