Cryptographic scheme for group passwords distribution in steganographic systems

This paper proposes a new scheme of passwords distribution for user groups via a hidden communication channel. The previously known models explicitly demonstrated the presence of passwords and cannot be used in any hidden communication channel. The considered model assumes the presence of a coordinator who regulates the composition of the groups and is the source of the overwhelming proportion of messages. The composition of the groups is not known in advance and may change during transmission messages. It is assumed that the data transmitted in a container will consist of two parts: a service part, which contains information about groups and passwords, and a useful part, which contains the target message that encrypted with a group-password. The scheme is based on the Kronecker-Capelli theorem. To find a group password the subscriber-receiver, is included in the group, calculates the product of the roots of a joint system of linear algebraic equations. This system consists of n equations and contains n+1variables. For an outside subscriber, who is not included in the group, the system of equations has not a single solution. A subscriber in the group is able to calculate one variable by a predefined formula. Consequently, the system of equations for such subscriber has the unique solution. The paper describes the processes of changing a composition of groups: creating, adding a participant, removing. The removing users from a group is realized by reuniting members of the old group. The scheme provides the possibility of combining previously created subgroups into large group without significant overhead costs. The proposed scheme can be used in practice by some organization to manage its branches when communicating via hidden data transmission channels