We first propose a 2D Location Based Encryption (LBE) scheme, where the setting includes a geography center system and the 2D triangle area including the set of locations. A user joining in the system is provided with a pre-arranged key, which belongs to her/his location. If the user’s location is belonging to this area, he/she can decrypt the message. Our proposed scheme achieves a constant ciphertext size in encryption algorithm and decryption cost. Beyond the 2D-LBE scheme, we explore the 3D-LBE scheme; whereby the location is set up in the 3D dimensions. This proposed scheme is an extension of 2D-LBE scheme, which the ciphertext is also constant. Both two schemes are proved in the selective model under the decisional wBDHI assumption.