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A Survey of Public-key Cryptography over Non-abelian Groups


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


Vol. 21  No. 4  pp. 289-300


Non-abelian group based Cryptography is a field which has become a latest trend in research due to increasing vulnerabilities associated with the abelian group based cryptosystems which are in use at present and the interesting algebraic properties associated that can be thought to provide higher security. When developing cryptographic primitives based on non-abelian groups, the researchers have tried to extend the similar layouts associated with the traditional underlying mathematical problems and assumptions by almost mimicking their operations which is fascinating even to observe. This survey contributes in highlighting the different analogous extensions of traditional assumptions presented by various authors and a set of open problems. Further, suggestions to apply the Hamiltonian Cycle/Path Problem in a similar direction is presented.


Cryptography, Diffie-Hellman, Discrete Logarithm Problem, El-Gamal, Hamiltonian Cycle/Path Problem, Non-abelian/Non-commutative.