A multi-hop line network is considered, where each node can receive signals transmitted by its two neighbors. As such, the model embodies both the interference and broadcast aspects of wireless networks. The leftmost node wishes to send messages to the rightmost node, while keeping these messages confidential from all the intermediate relay nodes. In this setting where any or all of the relay nodes can be eavesdroppers, it is shown that end-to-end secure and reliable communication is possible. Notably, it is shown that an end-to-end secrecy rate that is independent of the number of hops, i.e., intermediate eavesdroppers, is achievable by means of a carefully designed transmission schedule, compute-and-forward relaying and coding strategy utilizing nested lattice codes. The achievable rate obtained indicates that imposing secrecy constraints penalizes the capacity by at most 1 bit per channel use. Therefore, it is concluded that information theoretic secrecy can be guaranteed for this model irrespective of eavesdropping relays and a fixed modest cost for the end-to-end rate.
A multi-hop line network is considered, where each node can receive signals transmitted by its two neighbors. As such, the model embodies both the interference and broadcast aspects of wireless networks. The leftmost node wishes to send messages to the rightmost node, while keeping these messages confidential from all the intermediate relay nodes. In this setting where any or all of the relay nodes can be eavesdroppers, it is shown that end-to-end secure and reliable communication is possible. Notably, it is shown that an end-to-end secrecy rate that is independent of the number of hops, i.e., intermediate eavesdroppers, is achievable by means of a carefully designed transmission schedule, compute-and-forward relaying and coding strategy utilizing nested lattice codes. The achievable rate obtained indicates that imposing secrecy constraints penalizes the capacity by at most 1 bit per channel use. Therefore, it is concluded that information theoretic secrecy can be guaranteed for this model irrespective of eavesdropping relays and a fixed modest cost for the end-to-end rate.
We consider a two-source two-destination two-hop relay network, where all data communication must be kept secret from the relay node. The model considered is the simplest primitive that embodies a multi-transmitter multi-receiver network that needs to communicate sharing an untrusted relay node. We focus on two scenarios. In the first scenario, each source aims to send two messages to be kept secret from the relay: a common message that should be decoded by both destinations, and a private message that should be decoded by the first destination while kept secret from the second one. We define an achievable rate region by utilizing stochastic encoding at the sources, the Gaussian noise cooperative jamming from the destinations, and compress-and-forward at the relay. In the second scenario, each source aims to send a confidential message to its intended destination, which should be kept secret from the other one as well as the relay. We define an achievable rate region using a combination of nested lattice codes and random binning at the sources, structured cooperative jamming from destinations, and scaled compute-and-forward at the relay. We also derive genie-aided outer bounds on the secrecy rate regions. We present numerical results that demonstrate the performance of the proposed achievable schemes. Overall, this paper provides insights into how to utilize an untrusted relay to communicate to destinations with different levels of security clearance, and how intentional interference is an enabler of communication.
We study, using information-theoretic security methods, the so-called symmetric two-hop channel with an untrusted relay. In this model, a source wants to send its message reliably and securely to the destination through an honest but curious relay. The relay acts as a passive eavesdropper. Our investigation, in line with the relevant literature, seeks to determine what rate, termed secrecy rate, is achievable. To do that, we consider a typical setting, with the destination cooperating with the source, sending a 'scrambling' signal to conceal the message from the relay. To derive the achievable secrecy rate, we propose a novel scheme based on nested lattice codes. We show that our scheme outperforms all existing schemes and it achieves the outer bound for this channel model within 0.33 bits.
We consider a source-destination pair that can communicate only through a chain of unauthenticated intermediate relay nodes over AWGN links. In this scenario, it is desirable to use these relays-as otherwise communicating with the destination is impossible-without the relays being able to decode the information flowing through them. This in turn is tantamount to treating the relays as eavesdroppers from whom the information needs to be kept secret. An important question then becomes that of identifying the limits of reliable and secure communication in this network in the information theoretic sense. In particular, we ask whether it is possible to achieve a non-vanishing perfect secrecy rate regardless of the number of hops. In this work, we find that the answer is yes and show that a constant secrecy rate for an arbitrary number of hops is achievable by employing the combination of a lattice code and a random code.
This paper considers the two-user interference relay channel where each source wishes to communicate to its destination a message that is confidential from the other destination. Furthermore, the relay, that is the enabler of communication, due to the absence of direct links, is untrusted. Thus, the messages from both sources need to be kept secret from the relay as well. We provide an achievable secure rate region for this network. The achievability scheme utilizes structured codes for message transmission, cooperative jamming and scaled compute-and-forward. In particular, the sources use nested lattice codes and stochastic encoding, while the destinations jam using lattice points. The relay decodes two integer combinations of the received lattice points and forwards, using Gaussian codewords, to both destinations. The achievability technique provides the insight that we can utilize the untrusted relay node as an encryption block in a two-hop interference relay channel with confidential messages.
In this paper, we consider communication on a two-hop channel in which a source wants to send information reliably and securely to the destination via a relay. We consider both the untrusted relay case and the external eavesdropper case. In the untrusted relay case, the relay behaves as an eavesdropper, and there is a cooperative node, which sends a jamming signal to confuse the relay when it is receiving from the source. In the external eavesdropper case, the relay is trusted, and there is an external node eavesdropping the communication. We propose two secure transmission schemes using the scaled compute-and-forward technique. One of the schemes is based on a random binning code, and the other one is based on a lattice chain code. It is proved that in the high signal-to-noise-ratio (SNR) scenario and/or the limited relay power scenario, if the destination is used as the jammer, both schemes outperform all existing schemes and achieve the upper bound. In particular, if the SNR is large and the source, the relay, and the cooperative jammer have identical power and channels, both schemes achieve the upper bound for secrecy rate, which is merely 1/2 bit per channel use lower than the channel capacity without secrecy constraints. We also prove that one of our schemes achieves a positive secrecy rate in the external eavesdropper case in which the relay is trusted and there exists an external eavesdropper.
This dissertation studies the fundamental rate limits of wireless communication systems through which confidential messages can be transmitted without being intercepted by an adversary. It is assumed that the adversary is subject to noise and interference, as are the legitimate nodes in the system. The security guarantees offered are irrespective of the computational power of the adversary.
Three themes are developed in parallel throughout the dissertation. The first theme explores the relationship between cooperation and secrecy. In wireless networks, cooperation from intermediate relay nodes are essential for facilitating long range communications. This dissertation considers a series of network models where the information from a source to a destination needs to be kept confidential from intermediate relays. Four different network models with untrusted relay nodes are considered: the three-node relay channel, the two-hop link, the two-way relay channel and the multi-hop line network. These models are studied for relays that are honest but curious. That is, the relay nodes are legitimate nodes with lower security clearance, that willingly carry out the designated relay schemes. Secrecy capacity lower and upper bounds for each channel model are found and cases where secrecy capacity can be found are identified. Next the two-hop link is studied where the relay turns malicious in that it can manipulate the signals being relayed and carry out a Byzantine attack. In this case, two requirements must be satisfied simultaneously: The message must be kept confidential from the relay node, and, any modification carried out by the relay node must be detected reliably by the legitimate parties. The dissertation shows that both requirements can be fulfilled for this model with arbitrarily small overhead.
The next two themes developed in this dissertation serve as the technical foundation for the first theme. One establishes the foundation for providing secrecy using structured codes. Traditionally, the achievability proofs for information theoretic secrecy rely on Shannon’s random codebook generation argument in which the codebook does not exhibit structure. In this dissertation, it is shown that by imposing structure requirements in random codebook generation, higher rates for secure communication can be achieved than known results obtained using the conventional approach. This dissertation develops the necessary tool and general methodology for computing the secrecy rate when a nested lattice structure is used in codebook generation. Two results are presented that rely on this foundation. First, it is proved that, for a class of Gaussian channel models with interference and secrecy constraints, structured codes outperform Gaussian signaling at medium to high SNR. Second, this tool is used to develop a strong secrecy scheme for the two-hop link with an untrusted relay, which in turn is the centerpiece of the Byzantine detection scheme developed in this dissertation.
The third theme is methods of proving strong secrecy. Information theoretic secrecy results often rely on the weak secrecy constraint which provides only asymptotic guarantees with respect to the information rate leaked to the adversary. As this would likely be insufficient in a practical system, a non-asymptotic, strong secrecy guarantee must be sought. More often than not, weak secrecy rates can be strengthened to strong secrecy rates in a straightforward manner, leading back to the justification of proving weak secrecy only. This dissertation challenges this conventional wisdom and identifies two cases where this approach does not follow. In both cases, direct strong secrecy proofs are established. These are: the two-hop link with a Byzantine relay, and models with arbitrarily varying eavesdropper channel considered in the last chapter of this dissertation.
The latter model is motivated by the need to bring the theory of providing unconditional secrecy guarantees closer to practice. In particular, the dissertation addresses the case where the channel that the adversary (eavesdropper) experiences is completely unknown to the legitimate parties. To do so, a multiple input-multiple output (MIMO) wiretap channel is considered where the eavesdropper’s channel is arbitrarily varying. A coding theorem is derived for with this setting. The secrecy rate obtained from this coding theorem is tight in terms of secure degree of freedom, which is a high SNR characterization of the secrecy capacity. In addition, the secure degree of freedom regions for the MIMO multiple access (MAC) wiretap channel and the MIMO broadcast wiretap channel are derived when the legitimate nodes have the same number of antennas, identifying the high SNR characterization of the fundamental transmission limits for these models.