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
⁺
= {x
₁
x
₂
⋯x
_k
|x
₁
∈ 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.