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1 Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

1 2011

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The implementation of cubic public keys based on a new family of algebraic graphs

Klisowski M., Romańczuk U., Ustimenko V.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

2011

Vol. 11, no. 2

127--141

Families of edge transitive algebraic graphs defined over finite commutative rings were used for the development of stream ciphers, public key cryptosystems and key exchange protocols. We present the results of the first implementation of a public key algorithm based on the family of algebraic graphs, which are not edge transitive. The absence of an edge transitive group of symmetries means that the algorithm can not be described in group theoretical terms. We hope that it licates cryptanalysis of the algorithm. We discuss the connections between the security of algorithms and the discrete logarithm problem.The plainspace of the algorithm is Kn, where K is the chosen commutative ring. The graph theoretical encryption corresponds to walk on the bipartite graph with the partition sets which are isomorphic to Kn. We conjugate the chosen graph based 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 the corresponding cubic public map g of Kn onto Kn. We evaluate time for the generation of g, and the number of monomial expression in the list of corresponding public rules.