Abstract. The paper analyzes the structure of families of automata without output mapping that are defined by recurrence relations on abstract finite quasigroups. The expediency of their use to design iterated hash functions with sufficiently high security is justified. It is shown how some families of reversible Mealy and Moore automata can be constructed based on these families of automata without output mapping. The expediency of using the proposed families of Mealy and Moore automata as the basis for construction of mathematical models for stream ciphers is justified.

Keywords: finite quasigroups, automata without output mapping, Mealy and Moore automata.