This paper investigates a new family of RFID protocols called Ff that grew out of a proposal made at ESORICS 2007. This family has the property of having highly efficient implementations and simultaneously providing some security arguments which shares some features with the HB protocol family. In this work, we exhibit links between the Ff protocol and the LPN problem, and demonstrate two attacks against the Ff family of protocols which run with a time complexity of about 252 and 238 respectively against the instance proposed by the designers that has a 512-bit secret key. Our two attacks have the nice property that they only require interactions with the tag alone and does not involve the reader.