High-density and Secure Data Transmission via Linear Combinations

Original · EN

Suppose that there are n Senders and n Receivers. Our goal is to send long messages from Sender i to Receiver i such that no other receiver can retrieve the message intended for Receiver i. The task can easily be completed using n private channels between the pairs. Solutions, using one channel needs either encryption or switching elements for routing the messages to their addressee. The main result of the present work is a description of a network in which The Senders and the Receivers are connected with only nᵒ⁽¹⁾ channels; the encoding and de-coding is nothing else just very fast linear combinations of the message-bits; and there are no switching or routing-elements in the network, just linear combinations are computed, with fixed connections (channels or wires). In the proofs we do not use any unproven cryptographical or complexity theoretical assumptions.