Delay Optimal Secrecy in Two-Relay Network

We consider a two-relay network in which a source aims to communicate a confidential message to a destination while keeping the message secret from the relay nodes. In the first hop, the channels from the source to the relays are assumed to be block-fading and the channel states change arbitrarily -possibly non-stationary and non-ergodic- across blocks. When the relay feedback on the states of the source-to-relay channels is available on the source with no delay, we provide an encoding strategy to achieve the optimal delay. We next consider the case in which there is one-block delayed relay feedback on the states of the source-to-relay channels. We show that for a set of channel state sequences, the optimal delay with one-block delayed feedback differs from the optimal delay with no-delayed feedback at most one block

Secret message capacity of a line network

We investigate the problem of information theoretically secure communication in a line network with erasure channels and state feedback. We consider a spectrum of cases for the private randomness that intermediate nodes can generate, ranging from having intermediate nodes generate unlimited private randomness, to having intermediate nodes generate no private randomness, and all cases in between. We characterize the secret message capacity when either only one of the channels is eavesdropped or all of the channels are eavesdropped, and we develop polynomial time algorithms that achieve these capacities. We also give an outer bound for the case where an arbitrary number of channels is eavesdropped. Our work is the first to characterize the secrecy capacity of a network of arbitrary size, with imperfect channels and feedback. As a side result, we derive the secret key and secret message capacity of an one-hop network, when the source has limited randomness

Secret Communication over Broadcast Erasure Channels with State-feedback

We consider a 1-to-$K$ communication scenario, where a source transmits private messages to $K$ receivers through a broadcast erasure channel, and the receivers feed back strictly causally and publicly their channel states after each transmission. We explore the achievable rate region when we require that the message to each receiver remains secret - in the information theoretical sense - from all the other receivers. We characterize the capacity of secure communication in all the cases where the capacity of the 1-to-$K$ communication scenario without the requirement of security is known. As a special case, we characterize the secret-message capacity of a single receiver point-to-point erasure channel with public state-feedback in the presence of a passive eavesdropper. We find that in all cases where we have an exact characterization, we can achieve the capacity by using linear complexity two-phase schemes: in the first phase we create appropriate secret keys, and in the second phase we use them to encrypt each message. We find that the amount of key we need is smaller than the size of the message, and equal to the amount of encrypted message the potential eavesdroppers jointly collect. Moreover, we prove that a dishonest receiver that provides deceptive feedback cannot diminish the rate experienced by the honest receivers. We also develop a converse proof which reflects the two-phase structure of our achievability scheme. As a side result, our technique leads to a new outer bound proof for the non-secure communication problem

Coding against a Limited-view Adversary: The Effect of Causality and Feedback

We consider the problem of communication over a multi-path network in the presence of a causal adversary. The limited-view causal adversary is able to eavesdrop on a subset of links and also jam on a potentially overlapping subset of links based on the current and past information. To ensure that the communication takes place reliably and secretly, resilient network codes with necessary redundancy are needed. We study two adversarial models - additive and overwrite jamming and we optionally assume passive feedback from decoder to encoder, i.e., the encoder sees everything that the decoder sees. The problem assumes transmissions are in the large alphabet regime. For both jamming models, we find the capacity under four scenarios - reliability without feedback, reliability and secrecy without feedback, reliability with passive feedback, reliability and secrecy with passive feedback. We observe that, in comparison to the non-causal setting, the capacity with a causal adversary is strictly increased for a wide variety of parameter settings and present our intuition through several examples.Comment: 15 page

Capacities of erasure networks

textWe have investigated, in various multiple senses, the “capacity” of several models of erasure networks. The defining characteristic of a memoryless erasure network is that each channel between any two nodes is an independent erasure channel. The models that we explore differ in the absence or presence of interference at either the transmitters, the receivers, or both; and in the availability of feedback at the transmitters. The crux of this work involves the investigation and analysis of several different performance measures for these networks: traditional information capacity (including multicast capacity and feeback capacity), secrecy capacity, and transport capacity.Electrical and Computer Engineerin