Stream cipher based on post-commutative quasigroups

A quasigroup (A, ⊙) is said to be post-commutative if a ⊙ b = c implies a ⊙ c = b for all a, b, c ∈ Q. In this paper, we design a stream cipher based on post-commutative quasigroups and analyse its security. A lower bound of the total number of post-commutative quasigroups of a given order, and constructions of post-commutative quasigroups are also given in this paper.