  This study distinguishes the weak fairness property from the strong fairness
property which is necessary in the quantum key agreement (QKA) and shows that
most of the existing QKAs cannot achieve the strong fairness property with a
key manipulation problem.To solve this problem, a model which describes the way
to design a QKA with the strong fairness property is proposed. Based on the
model, an example QKA is presented. Security analyses show that the proposed
QKA is effective to resist not only outsider's eavesdropping attack but also
insider's key manipulation.
