Radio Frequency IDentification(RFID) systems are being used in many applications such as the supply chain. The widespread usage of tags creates new threats of security and privacy in RFID systems. Many schemes have been proposed to provide security and privacy, based on basic cryptographic primitives such as hash function and encryption algorithm. However, it may be a burden on a resource-constrained tag. As considering the requirements on a tag, we propose a lightweight mutual authentication scheme based on trapdoor one-way property and challenge/reaponse approach. Even though the proposed scheme does not perform cryptograhic primitives, it guarantees security and privacy provided by the authentication schemes using cryptographic primitives. We expect this mutual authentication scheme to activate RFID systems in various applications.