Abstract: We present a family of parameterized hash functions allowing for flexibility between security and performance. The family consists of three basic hash functions: HaF-256, HaF-512 and HaF-1024 with message digests equal to 256, 512 and 1024 bits, respectively. Details of functions\' structure are presented. Method for obtaining function\'s S-box is described along with the rationale behind it. Security considerations are discussed.