ON THE IMPLEMENTATION OF PUBLIC KEY ALGORITHM BASED ON GRAPHS AND THEIR SYMMETRIES

Abstract

The paper devoted to implementation of the public key algorithm based on directed algebraic graphs over finite commutative ring $K$ and their symmetries. First we expand the key space $K^n$ of graph based encryption algorithm in such way that arbitrary chosen plaintext can be converted to arbitrary chosen ciphertext. Second, we conjugate chosen encryption map, which is a composition of several “elementary” cubical polynomial automorphisms of a free module $K^n$ with special invertible affine transformation of $K^n$. Finally we compute symbolically corresponding cubic public map $g$ of $K^n$ onto $K^n$. We evaluate time for the generation of $g$, time of execution of public map, number of monomial expression in the list of corresponding public rules.