PROJECT TITLE :

An LP Characterization of the Secret-message Capacity of Three Erasure Networks With Feedback

ABSTRACT:

This paper presents precise capability characterizations for the case, when a principal, Alice, needs to securely send a message to a different principal, Bob, over three network configurations: the parallel edges network, the V-network, and therefore the triangle network. We assume that: one) a passive eavesdropper, Eve, overhears anybody edge within the network; a pair of) each edge corresponds to an independent broadcast packet erasure channel with arbitrary erasure possibilities; and 3) all legitimate nodes can publicly but causally acknowledge whether or not they received each packet or not. We tend to develop optimal achievability schemes that are expressed as linear programs (LPs) and share a two-part structure, where at the first phase, we create secret keys, and at the second part, we use them to encrypt the transmitted message. Our outer bounds also are expressed through LP formulations. We prove that our schemes are optimal by showing that the optimal resolution of the outer sure LP and the optimal solution of the achievability scheme LP coincide.