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— The protocol of Ko K., Lee S., are improved and generalized on base of metacyclic and nonmetacyclic p-groups of type Miller-Moreno (minimal non-abelian group). We show that the decomposition problem in this group is intractable. It is proved that the conjugacy problem in this group is also intractable. Further, we have constructed an algorithm of generating (designing) of common key for a non-commutative group with two mutually commuting subgroups has been constructed by us. Key-Words: CDH and CSP problems; non-commutative cryptography; Miller-Moreno p-group, generalization of CDH problem, conjugacy problem. Received: May 15, 2020. Revised: June 30, 2020. Re-revised: July 21, 2020. Accepted: August 4, 2020. Published: August 7, 2020.

An Application of Metacyclic and Miller Moreno P-groups to Establishment Protocol