False Base Stations (FBSs) are nowadays proven to be a serious threat to location privacy. Apart from the location privacy threats, FBS causes several threats like Manin-the-Middle (MitM) attacks, eavesdropping, identity tracking, phishing attacks, etc. FBS-based two threats are presented in the 3GPP TR 33.809, namely, Authentication Relay Attack (ARA) and MitM attack. The corresponding solution mentioned for the ARA (which occurs because the user is connected with FBS) in TR 33.809 uses the real location of the user causing the location privacy issue. i.e., the user has to share its GPS location with the legitimate base station, even though it was not connected with the legitimate base station. In this regard, this work proposed an Elliptic Curve Cryptography (ECC) based proximity testing protocol termed as ECC based Private Equality Testing (EPET) to preserve the location privacy of the user under FBS.