In this paper we propose a communication protocol for Radio Frequency Identification (RFID) systems that is based on the tags responding only to authenticated readers, otherwise tags always maintain RF silence. The protocol is practical from a deployment point of view and it not only meets the formal definitions of strong privacy and untraceability, but also addresses most, of the concerns raised by privacy advocates on behalf of consumers. Both passive and active RFID systems can use this protocol, and with slight modifications it can also be used on wireless-sensor networks. The protocol is expected to more efficiently utilize the RF spectrum by minimizing tag and reader collisions and as a result it should be possible to accommodate more readers and tags in a given area.