The goal of this investigation is effective method of key exchange which based on non-commutative group G. The results of Ko et al. [6] is improved and generalized. The size of a minimal generating set for the commutator subgroup of Sylow 2-subgroups of alternating group is found. The structure of the commutator subgroup of Sylow 2-subgroups of the alternating group A 2 k is investigated and used in key exchange protocol which based on non-commutative group. We consider non-commutative

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... ation of CDH problem [4, 3] on base of metacyclic group of Miller-Moreno type (minimal non-abelian group). We show that conjugacy problem in this group is intractable. Effectivity of computation is provided due to using groups of residues by modulo n. The algorithm of generating (designing) common key in non-commutative group with 2 mutually commuting subgroups is constructed by us.