In this paper, we propose a perfectly secure transmission scheme for an asymmetric bidirectional relay channel. The scheme is based on nested lattice coding with keys generated at both legitimate nodes, consisting of unshared random dithers. These keys are indexed by the past secret mutual transmissions and kept secret from other nodes. This model allows legitimate users to transmit safely their secret messages jointly with the artificial noise (dither) without the help of any dedicated internal or external jamming source. Besides, this scheme achieves perfect secrecy at the best known rate for the relay channel in presence of not only an untrusted relay, but also one passive eavesdropper at uplink and one at downlink, even if both eavesdropper channels are noiseless.
In this paper, we propose a perfectly secure transmission scheme for an asymmetric bidirectional relay channel. The scheme is based on nested lattice coding with keys generated at both legitimate nodes, consisting of unshared random dithers. These keys are indexed by the past secret mutual transmissions and kept secret from other nodes. This model allows legitimate users to transmit safely their secret messages jointly with the artificial noise (dither) without the help of any dedicated internal or external jamming source. Besides, this scheme achieves perfect secrecy at the best known rate for the relay channel in presence of not only an untrusted relay, but also one passive eavesdropper at uplink and one at downlink, even if both eavesdropper channels are noiseless.
In this work, we study two problems in information-theoretic security. Firstly, we study a wireless network where two nodes want to securely exchange messages via an honest-but-curious bidirectional relay. There is no direct link between the user nodes, and all communication must take place through the relay. The relay behaves like a passive eavesdropper, but otherwise follows the protocol it is assigned. Our objective is to design a scheme where the user nodes can reliably exchange messages such that the relay gets no information about the individual messages. We first describe a perfectly secure scheme using nested lattices, and show that our scheme achieves secrecy regardless of the distribution of the additive noise, and even if this distribution is unknown to the user nodes. Our scheme is explicit, in the sense that for any pair of nested lattices, we give the distribution used for randomization at the encoders to guarantee security. We then give a strongly secure lattice coding scheme, and we characterize the performance of both these schemes in the presence of Gaussian noise. We then extend our perfectly-secure and strongly-secure schemes to obtain a protocol that guarantees end-to-end secrecy in a multichip line network. We also briefly study the robustness of our bidirectional relaying schemes to channel imperfections.
In the second problem, we consider the scenario where multiple terminals have access to private correlated Gaussian sources and a public noiseless communication channel. The objective is to generate a group secret key using their sources and public communication in a way that an eavesdropper having access to the public communication can obtain no information about the key. We give a nested lattice-based protocol for generating strongly secure secret keys from independent and identically distributed copies of the correlated random variables. Under certain assumptions on the joint distribution of the sources, we derive achievable secret key rates.
The tools used in designing protocols for both these problems are nested lattice codes, which have been widely used in several problems of communication and security. In this thesis, we also study lattice constructions that permit polynomial-time encoding and decoding. In this regard, we first look at a class of lattices obtained from low-density parity-check (LDPC) codes, called Low-density Construction-A (LDA) lattices. We show that high-dimensional LDA lattices have several “goodness” properties that are desirable in many problems of communication and security. We also present a new class of low-complexity lattice coding schemes that achieve the capacity of the AWGN channel. Codes in this class are obtained by concatenating an inner Construction-A lattice code with an outer Reed-Solomon code or an expander code. We show that this class of codes can achieve the capacity of the AWGN channel with polynomial encoding and decoding complexities. Furthermore, the probability of error decays exponentially in the block length for a fixed transmission rate…
Secrecy capacity is analyzed in a Gaussian two-way relay wiretap channel (TRWC), where two legitimate source nodes wish to exchange their messages through a relay in the presence of an eavesdropper. We assume that all intended nodes operate in full-duplex mode and there is no direct path between two sources. In the Gaussian TRWC, we propose an achievable coding scheme composed of superposed lattice codes with both structured and random codebooks. A jamming strategy is further introduced at the two sources as well as at the relay to maximize the achievable secrecy rate regions, where each node allocates part of its power to jam the eavesdropper. Our result indicates that positive achievable secrecy rates are maintained even for the reversely degraded scenario. In addition, assuming two sources with equal power constraint, it is shown that the scheme asymptotically achieves within 1/2 bit from the cut-set bound based on the channel with no secrecy constraints, as the downlink phase is in the high signal-to-noise ratio regime.
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.
We study secret communication for broadcast channels with two legitimate receivers and one eavesdropper. The transmitter sends two independent confidential messages to the legitimate receivers which have to be kept secret from the eavesdropper. Here, each legitimate receiver is interested in one confidential message having the other one already as side information available. This problem arises for example in the broadcast phase in a bidirectional relay network, where a relay node establishes a bidirectional communication between two nodes while keeping the communication secure from an eavesdropper outside the network. We provide achievable rate regions and an outer bound on the secrecy capacity region.
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.
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.