  We present a secure multi-party quantum summation protocol based on quantum
teleportation, in which a malicious, but non-collusive, third party (TP) helps
compute the summation. In our protocol, TP is in charge of entanglement
distribution and Bell states are shared between participants. Users encode the
qubits in their hand according to their private bits and perform Bell-state
measurements. After obtaining participants' measurement results, TP can figure
out the summation. The participants do not need to send their encoded states to
others, and the protocol is therefore congenitally free from Trojan horse
attacks. In addition, our protocol can be made secure against loss errors,
because the entanglement distribution occurs only once at the beginning of our
protocol. We show that our protocol is secure against attacks by the
participants as well as the outsiders.
