Statement of the problem of characterizing the secrecy of a common knowledge created by correlated observations and transmission over helping channels

We consider the following scenario. Two individuals receive correlated observations from a source and want to construct a coinciding realization of some random process. The individuals exchange a pair of messages at monologues. There is also an eavesdropper who receives exchanged messages, but does not have observations of individuals. We characterize the resulting processes constructed by the individuals and the eavesdropper by their entropies. Possible solutions to the problem of maximizing the difference between the entropy of the probability distribution constructed by individuals and the eavesdropper are presented for some numerical examples.