  Multi-Party Quantum Computation (MPQC) has attracted a lot of attention as a
potential killer-app for quantum networks through it's ability to preserve
privacy and integrity of the highly valuable computations they would enable.
Contributing to the latest challenges in this field, we present a composable
protocol achieving blindness and verifiability even in the case of a single
honest client. The security of our protocol is reduced, in an
information-theoretically secure way, to that of a classical composable Secure
Multi-Party Computation (SMPC) used to coordinate the various parties. Our
scheme thus provides a statistically secure upgrade of such classical scheme to
a quantum one with the same level of security.
  In addition, (i) the clients can delegate their computation to a powerful
fully fault-tolerant server and only need to perform single qubit operations to
unlock the full potential of multi-party quantum computation; (ii) the amount
of quantum communication with the server is reduced to sending quantum states
at the beginning of the computation and receiving the output states at the end,
which is optimal and removes the need for interactive quantum communication;
and (iii) it has a low constant multiplicative qubit overhead compared to the
single-client delegated protocol it is built upon.
  The main technical ingredient of our paper is the bootstraping of the MPQC
construction by Double Blind Quantum Computation, a new composable resource for
blind multiparty quantum computation, that demonstrates the surprising fact
that the full protocol does not require verifiability of all components to
achieve security.
