Radio Frequency Identification (RFID) has come under the spotlight as technology supporting ubiquitous society. But now, we face several security problems and challenges in RFID systems. Recent papers have reported that RFID systems have to achieve the following requirements: (1) Indistinguishability, (2) Forward Security, (3) Replay Attack resistance, (4) Tag Killing resistance, and (5) Ownership Transferability. We have to design RFID system that achieves the above-mentioned requirements. The previous security methods achieve only some of them individually, and no RFID system has been constructed that achieves all requirements. In this paper, we propose an RFID security method that achieves all requirements based on a hash function and a symmetric key cryptosystem. In addition, our proposed method provides not only high-security but also high-efficiency.