  In this paper, a novel multi-party quantum private comparison (MQPC) protocol
with a semi-honest third party (TP) is proposed based on the entanglement
swapping of d-level cat states and d-level Bell states. Here, TP is allowed to
misbehave on his own but will not conspire with any party. In our protocol, n
parties employ unitary operations to encode their private secrets and can
compare the equality of their private secrets within one time execution of the
protocol. Our protocol can withstand both the outside attacks and the
participant attacks on the condition that none of the QKD methods is adopted to
generate keys for security. One party cannot obtain other parties' secrets
except for the case that their secrets are identical. The semi-honest TP cannot
learn any information about these parties' secrets except the end comparison
result on whether all private secrets from n parties are equal.
