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A key agreement protocol is a tool by which two parties can share a common key for their subsequent communication .Many cryptographic protocols are based on the hardness of integer factorization and discrete logarithm problem. Very few protocols are based on search problems in non - abelian groups. In this paper, the authors present a tripartite key agreement protocol using triple decomposition search problem using which three parties may agree on a common shared key in two rounds. They have chosen discrete Heisenberg group and three cyclic sub groups as their platform to apply the above protocol.
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