Copy-Protection with Correlated Challenges: Point Functions and More via Decisional Coset Monogamy

Abstract: Copy-protection encodes a functionality in a reusable quantum state that cannot be split into two states (freeloader adversaries) which remain simultaneously useful. Prior plain-model results handle only independently sampled challenges; the more natural identical-challenge notion, also tied to unclonable bits and copy-protection of point functions, has remained open. We strengthen these definitions and prove plain-model security for our new stronger notions. For single-decryptor encryption (SDE) we define correlated challenge security, show it implies all previous SDE notions including identical-challenge security, and prove that the construction of Kitagawa and Yamakawa (TCC'25) achieves it assuming iO and one-way functions. We also nearly fully characterize the relations among prior SDE notions. For general functionalities we define correlated challenge unclonable puncturable obfuscation (UPO), allowing arbitrary correlations among challenge points and puncturing bits plus auxiliary information before and after splitting, and requiring only conditionally uniform bits and $λ<sup>c$ average conditional min-entropy in each point separately (thus, in particular, the points may be identical). Assuming post-quantum iO and quantum-hard LWE, we construct correlated UPO for polynomial-size keyed circuits with input length at least $λ<sup>c$, answering an open question of Ananth, Behera, Huang, Kitagawa, Yamakawa (EUROCRYPT'26) and of Cakan-Goyal (EUROCRYPT'26). We also obtain the first plain-model copy protection for point functions, $k$-point functions, and compute-and-compare programs, and identical-challenge copy protection for general puncturable functionalities.