  By introducing a semi-honest third party (TP), we propose in this paper a
novel QPC protocol using (n+1)- qubit (n \ge 2) Greenberger-Horne-Zeilinger
(GHZ) states as information carriers. The parameter n not only determines the
number of qubits contained in a GHZ state, but also determines the probability
that TP can successfully steal the participants' data and the qubit efficiency.
In the proposed protocol, we do not employ any other quantum technologies
(e.g., entanglement swapping and unitary operation) except necessary
technologies such as preparing quantum states and quantum measurements, which
can reduce the need for quantum devices. We use the keys generated by quantum
key distribution and bit-flipping for privacy protection, and decoy photons for
eavesdropping checking, making both external and internal attacks invalid.
Specifically, for external attacks, we take several well-known attack means
(e.g., the intercept-resend attack and the measurement-resend attack) as
examples to show that the attackers outside the protocol can not steal the
participants' data successfully, in which we provide the security proof of the
protocol against the entanglement-measurement attack. For internal attacks, we
show that TP cannot steal the participants' data and the participants cannot
steal each other's data. We also show that the existing attack means against
QPC protocols are invalid for our protocol.
