In order to protect privacy of fingerprint when remote authentication is carried out by using equipment with limited computing resource, a scheme which performs the minutiae matching based on bitonic sorting network is adopted. The protocol achieves high efficiency on computation and communication by computing private two-party set intersection problem with garbled circuit. The processing of the garbled gates is pipelined to avoid the need to store the entire circuit and to improve the running time. The proposed scheme is capable of implementing remote authentication on mobile phone or embedded equipment with less memory.