FIELD: information technology.
SUBSTANCE: common elements Z and G of a non-commutative finite group "Г" generated such that G◦Z≠Z◦G, a first user generates their personal PK in form of two multi-bit binary numbers (MBN) X1 and W1, elements 
and 
of group "Г" are generated and an open key (OK) is generated for the first user in form of an element Y1 of the group "Г" using formula Y1=X1◦W1, where the symbol ◦ denotes a group operation of the group "Г", Y1 is sent to the second user, the second user generates their personal PK in form of two MBN x2 and w2, elements and 
of group "Г" are generated and OK is generated for the second user in form of an element Y2 of the group "Г" using the formula Y2=X2◦W2, and the sent to the first user, the first user generates a common key PK I form of an element K of the group "Г" depending on Y2 and PK of the first user, and the second user generates a common PK in form of an element K of the group "Г" depending on Y1 and PK of the second user.
EFFECT: faster generation of a common private key for remote users.
5 cl, 3 tbl, 4 ex, 1 app
