QFactory: classically-instructed remote secret qubits preparation. (arXiv:1904.06303v1 [quant-ph])

The functionality of classically-instructed remotely prepared random secret
qubits was introduced in (Cojocaru et al 2018) as a way to enable classical
parties to participate in secure quantum computation and communications
protocols. The idea is that a classical party (client) instructs a quantum
party (server) to generate a qubit to the server's side that is random, unknown
to the server but known to the client. Such task is only possible under
computational assumptions. In this contribution we define a simpler (basic)
primitive consisting of only BB84 states, and give a protocol that realizes
this primitive and that is secure against the strongest possible adversary (an
arbitrarily deviating malicious server). The specific functions used, were
constructed based on known trapdoor one-way functions, resulting to the
security of our basic primitive being reduced to the hardness of the Learning
With Errors problem. We then give a number of extensions, building on this
basic module: extension to larger set of states (that includes non-Clifford
states); proper consideration of the abort case; and verifiablity on the module
level. The latter is based on "blind self-testing", a notion we introduced,
proved in a limited setting and conjectured its validity for the most general
case.

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