  Quantum mechanical effects have enabled the construction of cryptographic
primitives that are impossible classically. For example, quantum
copy-protection allows for a program to be encoded in a quantum state in such a
way that the program can be evaluated, but not copied. Many of these
cryptographic primitives are two-party protocols, where one party, Bob, has
full quantum computational capabilities, and the other party, Alice, is only
required to send random BB84 states to Bob. In this work, we show how such
protocols can generically be converted to ones where Alice is fully classical,
assuming that Bob cannot efficiently solve the LWE problem. In particular, this
means that all communication between (classical) Alice and (quantum) Bob is
classical, yet they can still make use of cryptographic primitives that would
be impossible if both parties were classical. We apply this conversion
procedure to obtain quantum cryptographic protocols with classical
communication for unclonable encryption, copy-protection, computing on
encrypted data, and verifiable blind delegated computation. The key technical
ingredient for our result is a protocol for classically-instructed parallel
remote state preparation of BB84 states. This is a multi-round protocol between
(classical) Alice and (quantum polynomial-time) Bob that allows Alice to
certify that Bob must have prepared $n$ uniformly random BB84 states (up to a
change of basis on his space). Furthermore, Alice knows which specific BB84
states Bob has prepared, while Bob himself does not. Hence, the situation at
the end of this protocol is (almost) equivalent to one where Alice sent $n$
random BB84 states to Bob. This allows us to replace the step of preparing and
sending BB84 states in existing protocols by our remote-state preparation
protocol in a generic and modular way.
