  We define the functionality of delegated pseudo-secret random qubit generator
(PSRQG), where a classical client can instruct the preparation of a sequence of
random qubits at some distant party. Their classical description is
(computationally) unknown to any other party (including the distant party
preparing them) but known to the client. We emphasize the unique feature that
no quantum communication is required to implement PSRQG. This enables classical
clients to perform a class of quantum communication protocols with only a
public classical channel with a quantum server. A key such example is the
delegated universal blind quantum computing. Using our functionality one could
achieve a purely classical-client computational secure verifiable delegated
universal quantum computing (also referred to as verifiable blind quantum
computation). We give a concrete protocol (QFactory) implementing PSRQG, using
the Learning-With-Errors problem to construct a trapdoor one-way function with
certain desired properties (quantum-safe, two-regular, collision-resistant). We
then prove the security in the Quantum-Honest-But-Curious setting and briefly
discuss the extension to the malicious case.
