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Cryptographic Protocols using Semidirect Products of Finite Groups


G. H. J. Lanel, T. M. K. K. Jinasena, and B. A. K. Welihinda


Vol. 21  No. 8  pp. 17-27


Non-abelian group based cryptosystems are a latest research inspiration, since they offer better security due to their non-abelian properties. In this paper, we propose a novel approach to non-abelian group based public-key cryptographic protocols using semidirect products of finite groups. An intractable problem of determining automorphisms and generating elements of a group is introduced as the underlying mathematical problem for the suggested protocols. Then, we show that the difficult problem of determining paths and cycles of Cayley graphs including Hamiltonian paths and cycles could be reduced to this intractable problem. The applicability of Hamiltonian paths and cycles, and in fact any random path or cycle in Cayley graphs in the above cryptographic schemes is discussed and an alternative method of improving the security is also presented.


Algebraic span cryptanalysis, Cayley graphs, Hamiltonian Path/Cycle Problem, Non-abelian/Non-commutative, Semidirect products