A method for establishing a fully private, information secure interconnection between a source and a destination over a data network with at least a portion of a public infrastructure. The method comprising at the source creating n shares of a source data according to a predetermined secret sharing scheme, and encrypting the n shares using (n, k) secret sharing. Further, defining for at least one node vi a directed edge (Vi1, Vi2) that has a k−1 capacity. All outgoing links of vi are connected to vi2. Additionally, using a maximum flow algorithm to define the maximum number of shares outgoing from vi2, and therefore from vi, on each outgoing link. The number of shares forwarded by node vi does not exceed the number of maximum shares that were defined by the maximum flow algorithm.