In this paper, we present the design of the lightweight $F_f$ family of privacy-preserving authentication protocols for RFID-systems. $F_f$ is based on a new algebraic framework for reasoning about and analyzing this kind of authentication protocols. $F_f$ offers user-adjustable, strong authenticity and privacy against known algebraic and also recent SAT-solving attacks. In contrast to related work, $F_f$ achieves these two security properties without requiring an expensive cryptographic hash function. $F_f$ 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. In this paper, the authenticity and privacy of $F_f$ is evaluated using analytical and experimental methods.
