Paper 2025/1264 Original: eprint.iacr.org/2025/1264 ↗

Copy Protecting Cryptographic Functionalities over Entropic Inputs

Abstract

We present improved definitions and constructions for copy-protected digital signatures and pseudorandom functions (PRFs). Our new security definitions support challenge messages or inputs chosen from arbitrary high min-entropy distributions and allow signing or evaluation queries. This extends prior definitions, which assumed uniformly random challenges and did not consider oracle access. We construct schemes that satisfy these stronger definitions using only polynomially secure indistinguishability obfuscation (iO) and one-way functions (OWFs), avoiding the subexponential assumptions and the Learning with Errors (LWE) assumption used in previous constructions, even in the uniform-challenge and query-free setting. Moreover, our constructions and security proofs are arguably simpler than existing ones. We also propose a new security notion for unclonable puncturable obfuscation (UPO), which primarily extends prior definitions to support challenge inputs drawn from arbitrary high min-entropy distributions, along with some additional refinements. We construct a UPO satisfying this notion from polynomially secure iO and the LWE assumption, thereby avoiding the subexponential assumptions and unproven conjectures required in previous constructions, even in the uniform-challenge setting. In fact, in the uniform-challenge case, we show that iO and OWFs alone suffice, further removing the need for LWE. Again, our constructions and security proofs are arguably simpler than existing ones. As applications, we show that a UPO satisfying this notion is sufficient to copy-protect a variety of puncturable functionalities beyond those studied in the prior work.