The proposed copy-protection scheme for point functions encodes the marked input in a quantum state using a random basis determined by the output of a hash function applied to the marked input. The scheme includes an additional hash of a random string to enable program evaluation. Security is analyzed through a sequence of hybrids, reducing to the security of a monogamy-of-entanglement game. The proof relies on a novel “simultaneous one-way-to-hiding” lemma, extending techniques from unclonable encryption.

The scheme achieves constant security, i.e., any adversary fails to simultaneously evaluate the program on different inputs with at least a constant probability. It avoids multi-qubit entanglement, using only BB84 states and computational/Hadamard basis measurements. The scheme is then extended to copy-protect compute-and-compare programs by copy-protecting the point function corresponding to the target output and providing the compute function in the clear.

The paper also shows that the copy-protection scheme satisfies distributional virtual black-box obfuscation in the QROM. It explores the relationship between copy-protection and obfuscation, demonstrating that the two functionalities are generally incomparable.

Furthermore, the authors introduce a stronger “secure software leasing” (SSL) definition, where an adversary, upon returning a leased program, cannot retain information to further evaluate the program. They provide an SSL scheme for compute-and-compare programs with negligible advantage in the QROM, leveraging a variant of the monogamy-of-entanglement property.

In summary, the paper makes progress on quantum copy-protection and secure software leasing in the QROM, providing new techniques and insights. However, achieving provable security with negligible advantage and removing the QROM requirement remain open questions for future research.