On the implementation of cubic public keys based on algebraic graphs over the finite commutative ring and their special symmetries

摘要

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 Kn 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 Kn with special invertible affine transformation of Kn. Finally we compute symbolically corresponding cubic public map g of Kn onto Kn. 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.