Abstract: A method for establishing a fully private, information theoretically secure interconnection between a source and a destination, over an unmanaged data network with at least a portion of a public infrastructure. Accordingly, n shares of the source data are created at the source according to a predetermined secret sharing scheme and the shares are sent to the data network, while encrypting the sent data using (n,k) secret sharing. A plurality of intermediating nodes are deployed in different locations over the network, to create a plurality of fully and/or partially independent paths in different directions on the path from the source to the destination, and with sufficient data separation. Then, the shares are sent over the plurality of fully and/or partially independent paths while forcing shares' carrying packets to pass through selected intermediate nodes, such that no router at any intermediating nodes intercepts k or more shares.