Quantum CopyProtection from Hidden Subspaces
Abstract
Quantum copyprotection is an innovative idea that uses the nocloning property of quantum information to copyprotect programs and was first put forward by [Aar09]. The general goal is that a program distributor can distribute a quantum state $\Psi\rangle$, 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. In the copyprotection with oracle setting, the user has access to a public oracle and can use the given quantum state and the oracle to compute on his/her own input for polynomially many times. However, the user is not able to produce an additional program(quantum or classical) that computes the same as P on almost all inputs. We present a first quantum copy protection scheme with a classical oracle for any unlearnable function families. The construction is based on membership oracles for hidden subspaces in $\mathbb{F}_2^n$, an idea derived from the public key quantum money scheme in[Aar12]. We prove the security of the scheme relative to a classical oracle, namely, the subspace membership oracle with the functionality of computing the secret function we want to copyprotect. The security proof builds on the quantum lower bound for the DirectProduct problem ([Aar12],[BDS16]) and the unlearnability of the copyprotected functions. We also show that existence of quantum copy protection and the quantum hardness of LearningwithErrors (LWE) will imply publicly verifiable quantum money.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.09674
 Bibcode:
 2020arXiv200409674A
 Keywords:

 Computer Science  Cryptography and Security;
 Quantum Physics