RFID is one of the most protuberant systems in the field of ubiquitous computing. Since RFID tags have limited computation capabilities, numerous ultralightweight authentication protocols have been proposed to provide privacy and security. However all the previously proposed ultralightweight mutual authentication protocols have some security apprehensions and are vulnerable to various desynchronization and full disclosure attacks. This paper proposes a new ultralightweight mutual authentication protocol to provide robust confidentiality, integrity, and authentication (RCIA) in a cost effective manner. RCIA introduces a new ultralightweight primitive recursive hash, which efficiently detects the message tempering and also avoids all possible desynchronization attacks. RCIA involves only bitwise operations such as XOR, AND, left rotation, and recursive hash. Performance evaluation illustrates that RCIA requires less resources on tag in terms of on-chip memory, communication cost, and computational operations.