In this paper, we present the design of the lightweight Ff family of privacy-preserving authentication protocols for RFID-systems. F f results from a systematic design based on a new algebraic framework focusing on the security and privacy of RFID authentication protocols. F f offers user-adjustable, strong authentication, and privacy against known algebraic attacks and recently popular SAT-solving attacks. In contrast to related work, Ff achieves these security properties without requiring an expensive cryptographic hash function. Ff is designed for a challenge-response protocol, where the tag sends random nonces and the results of HMAC-like computations of one of the nonces together with its secret key back to the reader. In this paper, the authentication and privacy of F f is evaluated using analytical and experimental methods. © 2011 IEEE.