In this work we propose a mutual authentication protocol for RFID (Radio Frequency Identification) systems incorporating low-cost RFID tags. These tags, due to their limited computational capabilities do not incorporate advanced cryptographic primitives. As a result, there are various threats against users' privacy and against the security of such systems. Our protocol, PMM, utilizes a hash function and a pseudorandom number generator that can be hardware implemented in a low-cost RFID tag. As we will demonstrate, our protocol offers a high level of security by preventing replay attacks, Denial-of-Service attacks, tracking attacks, tag spoofing and by offering forward security and an enhanced protection of user privacy.