To guarantee security between the tag and back-end server and implementation efficiency in low power tag, we propose two typed mutual authentication protocols in RFID system. One is static-ID authentication scheme which is well suitable in distributed server environments. The other is dynamic-ID scheme which is additively satisfied forward security. In proposed scheme, it does not need any random number generator in tag and requires only one(maximally three) hash operation(s) in tag or server to authenticate each other. Furthermore, we implement the proposed schemes in RFID smart card system and verify its normal operations.