  Recently, Sun et al. [Quant Inf Proc DOI: 10.1007/s11128-013-0569-x]
presented an efficient multi-party quantum key agreement (QKA) protocol by
employing single particles and unitary operations. The aim of this protocol is
to fairly and securely negotiate a secret session key among $N$ parties with a
high qubit efficiency. In addition, the authors claimed that no participant can
learn anything more than his/her prescribed output in this protocol, i.e., the
sub-secret keys of the participants can be kept secret during the protocol.
However, here we points out that the sub-secret of a participant in Sun et
al.'s protocol can be eavesdropped by the two participants next to him/her. In
addition, a certain number of dishonest participants can fully determine the
final shared key in this protocol. Finally, we discuss the factors that should
be considered when designing a really fair and secure QKA protocol.
