Security analysis of cryptosystem based on quasigroups

Consider quasigroup operations *₁, *₂, ⋯, *_n on a finite set A, we use them to define a transformation E⁽ⁿ⁾: A⁺ → A⁺, where A⁺ = {x₁x₂⋯x_k|x₁ ∈ A, k ≥ 1}. The function E⁽ⁿ⁾ have several useful properties suitable for many cryptographical purposes, and the encoding method based on quasigroups has remained unbroken. In this paper, we analyse the security of E⁽ⁿ⁾ and give an algorithm of partial break on the chosen plaintext attack.