Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the key exchange with nonlinear polynomial maps of stable degree   We say that the sequence $g_n$, $n\ge 3$, $n \rightarrow \infty$ of
polynomial transformation bijective maps of free module $K^n$ over commutative
ring $K$ is a sequence of stable degree if the order of $g_n$ is growing with
$n$ and the degree of each nonidentical polynomial map of kind ${g_n}^k$ is an
independent constant $c$. A transformation $b={\tau}
  {g_n}^k {\tau}^{-1}$, where $\tau$ is 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 $C(K^n)$ of all regular
automorphisms of $K^n$. 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 $b^x=d$ to evaluate unknown $x$ in this form for the discrete logarithm
problem.
  In the paper we introduce the explicit constructions of sequences of elements
of stable degree for cases $c=3$ for each commutative ring $K$ containing at
least 3 regular elements and discuss the implementation of related key exchange
and public key algorithms.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph