Quantum Copy-Protection from Hidden Subspaces

Quantum copy-protection is an innovative idea that uses the no-cloning property of quantum information to copy-protect programs and was first put forward by [Aar09]. The general goal is that a program distributor can distribute a quantum state |\psi>, whose classical description is secret to the users; a user can use this state to run the program P on his own input, but not be able to pirate this program P or create another state with the same functionality. We give a number of initial results in this area: We present a first quantum copy protection scheme for for any unlearnable function families relative to a classical oracle. The construction is based on membership oracles for hidden subspaces in F_n^2. We prove the security of this scheme relative to this classical oracle used, namely, the subspace membership oracle with the functionality of computing the secret function we want to copy-protect. The security proof builds on the quantum lower bound for the Direct-Product problem ([AC12, BDS16]) and the quantum unlearnability of the copy-protected functions. We point out the relationship between public-key quantum money and copy protection: any quantum copy protection schemes for quantum-CCA secure encryption or for certain post-quantum trapdoor functions will imply publicly verifiable quantum money, where former can be instantiated from the LWE assumption.