Talking reliably, secretly, and efficiently: A “complete” characterization

We consider reliable and secure communication of information over a multipath network. A transmitter Alice sends messages to the receiver Bob in the presence of a hidden adversary Calvin. The adversary Calvin can both eavesdrop and jam on (possibly non-identical) subsets of transmission links. The goal is to communicate reliably (intended receiver can understand the messages) and secretly (adversary cannot understand the messages). Two kinds of jamming, additive and overwrite, are considered. Additive jamming corresponds to wireless network model while overwrite jamming corresponds to wired network model and storage systems. The multipath network consists of C parallel links. Calvin can both jam and eavesdrop any z
io
number of links, can eavesdrop (but not jam) any z
i/o
number of links, and can jam (but not eavesdrop) any z
o/i
number of links. We present the first “complete” information-theoretic characterization of maximum achievable rate as a function of the number of links that can be jammed and/or eavesdropped for equal and unequal link capacity multipath networks under additive and overwrite jamming in the large alphabet regime. Our achievability and converse proofs require non-trivial combination of information theoretic and coding theoretic ideas and our achievability schemes are computationally efficient. The PHaSE-Saving techniques
¹
are used for achievability while a “stochastic” singleton bound is obtained for converse.