On the key exchange and multivariate encryption with nonlinear polynomial maps of stable degree

We say that the sequence gn, n ≥ 3, n → ∞ of polynomial transformation bijective maps of free module Kn over commutative ring K is a sequence of stable degree if the order of gn is growing with n and the degree of each nonidentical polynomial map of kind gn is an independent constant c. Transformation b = τgnkτ−1, where τ is the affine bijection, n is large and k is relatively small, can be used as a base of group theoretical Diffie-Hellman key exchange algorithm for the Cremona group C(Kn) of all regular automorphisms of Kn. The specific feature of this method is that the order of the base may be unknown for the adversary because of the complexity of its computation. The exchange can be implemented by tools of Computer Algebra (symbolic computations). The adversary can not use the degree of righthandside in bx = d to evaluate unknown x in this form for the discrete