International Journal of Computer Science & Network Security

International Journal of Computer Science & Network Security (국제컴퓨터통신보호논문지학회)
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Cryptographic Protocols using Semidirect Products of Finite Groups

  • Lanel, G.H.J. (Department of Mathematics, University of Sri Jayewardenepura) ;
  • Jinasena, T.M.K.K. (Department of Computer Science, University of Sri Jayewardenepura) ;
  • Welihinda, B.A.K. (Department of Mathematics, University of Sri Jayewardenepura)
  • Received : 2021.08.16
  • Published : 2021.08.30
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Abstract

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 in fact any random path in Cayley graphs in the above cryptographic schemes and an application of the same concept to two previous cryptographic protocols based on a Generalized Discrete Logarithm Problem is discussed. Moreover, an alternative method of improving the security is also presented.

Keywords

Acknowledgement

We would like to express our thanks to the Editor, Reviewers of the open access journal IJCSNS and everyone who had given kind comments and support during our research.

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