摘要：The method for a key agreement protocol (KAP) with application of a non-commutative group is presen-ted. The method is based on the two one-way functions (OWFs) and corresponding hard problems. One hard problem is left right factors' search problem (LRFSP) in non-commutative group presentation level, and another one is a postu-lated hard problem in the non-commutative group representation level or, in other words, action level. On the basis of LRFSP the first one-way function (OWF1) is constructed. Non-commutative group is treated as an endomorphic group of operators acting on a certain semimodule or module. In this case such semimodule is compatible with a non-commutative group and algebra generated by this non-commutative group. The requirements of semimodule compatibility to the introduced algebra are presented. On the basis of a hard problem postulation in non-commutative group action level the second OWF2 is constructed.
