An Application of Metacyclic and Miller-Moreno p-Groups to Generalization of Diffie-Hellman Protocol

摘要

The results of Ko K., Lee S., are improved and generalized on the basis of metacyclic p-group G of type Miller-Moreno (minimal non-abelian group). We show that the decomposition problem in this group is intractable. The conjugacy search problem in a group G is the problem of recovering an x ∈ G from given g ∈ G and h= x-~1gx. We show that the conjugacy problem in this group is intractable. The algorithm of generating (designing) of common key in a non-commutative group with two mutually commuting subgroups has been constructed by us. An application of general metacyclic group to control an entropy of key space is considered.