The intercept-resent eavesdropping was explored in the polarization-drift quantum cryptography. Two-dimension model was used to describe the key distribution process. Model analysis and calculation provide precise relation between legitimate communicators and eavesdroppers. The loss of detection efficiency and fluctuation of QBER were obtained. The mutual information in the sifted keys shows that, comparing to BB84 protocol, the mutual information in B92 protocol is lower, which is caused by the simplified states from four states to two states. The information obtained by an eavesdropper can be more than that in the legitimate partners, which will threaten the privacy of the keys generated.