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IEEE Conference on Communications and Network Security

On full-duplex secure key generation with deterministic models

Rick Fritschek, Gerhard Wunder

Published Oct 1, 2017• 3 citations
Publisher

Abstract

The potential of full-duplex in communication design has been recently considered for emerging technologies such as 5G. Moreover, full-duplex can play a crucial role in upcoming secure communication scenarios too. However, results in the literature are limited and only explore scenarios, where the wireless channel is used either for key generation or for secure messaging. Our first contribution is the invention of a deterministic model for full-duplex communication which can analyse both scenarios, depending on the channel gain. Moreover, the properties of the model allow investigating scenarios, which were out of reach before, e.g. mixed channel gain randomness. Furthermore, it can incorporate a recently proposed scheme, called product signalling, which utilizes secure messaging and measures the channel gain bits at the same time. We demonstrate the utility of the model by investigating pilot signalling, i.e. secure key generation and secure messaging, for a two-way wiretap channel model. While pilot signalling is useful for channels with short coherence time, we will see that cooperative jamming is needed for channels with long coherence time. The bit-level nature of our model enables jamming schemes where users can jam individual levels at Eve, in contrast to previous achievable schemes where the users either send messages or jamming signals.

DOI
10.1109/cns.2017.8228687

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SECURE DEGREES OF FREEDOM OF WIRELESS NETWORKS

Jianwei Xie

This dissertation studies the security of wireless interference networks from an information-theoretic point of view. In this setting, several transmitter-receiver pairs wish to have secure communication against the eavesdropper(s). The central goal of this dissertation is to develop a framework based on information-theoretic principles to determine the complete solutions for the signaling schemes in different wireless interference networks with large transmit powers, and derive the corresponding fundamental limits in terms of the secure degrees of freedom (s.d.o.f.). Next, we study one-hop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel with helpers, Gaussian broadcast channel (BC) with confidential messages, Gaussian interference channel (IC) with confidential messages, and Gaussian multiple access (MAC) wiretap channel. 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We start with a model where each pair's payoff is their own secrecy rate. We then propose a refinement for the payoff function by explicitly accounting for the desire of the receiver to eavesdrop on the other party's communication. This payoff function captures the adversarial relationship between the users better. We determine the Nash equilibria for the binary deterministic channel for both payoff functions.

•Jan 1, 2014•0 citations
The potential of full-duplex in communication design has been recently considered for emerging technologies such as 5G. Moreover, full-duplex can play a crucial role in upcoming secure communication scenarios too. However, results in the literature are limited and only explore scenarios, where the wireless channel is used either for key generation or for secure messaging. Our first contribution is the invention of a deterministic model for full-duplex communication which can analyse both scenarios, depending on the channel gain. Moreover, the properties of the model allow investigating scenarios, which were out of reach before, e.g. mixed channel gain randomness. Furthermore, it can incorporate a recently proposed scheme, called product signalling, which utilizes secure messaging and measures the channel gain bits at the same time. We demonstrate the utility of the model by investigating pilot signalling, i.e. secure key generation and secure messaging, for a two-way wiretap channel model. While pilot signalling is useful for channels with short coherence time, we will see that cooperative jamming is needed for channels with long coherence time. The bit-level nature of our model enables jamming schemes where users can jam individual levels at Eve, in contrast to previous achievable schemes where the users either send messages or jamming signals.
This work considers the two-way wiretap channel in which two legitimate users, Alice and Bob, wish to exchange messages securely in the presence of a passive eavesdropper Eve. In the full-duplex scenario, where each node can transmit and receive simultaneously, we obtain new achievable secrecy rate regions based on the idea of allowing the two users to jointly optimize their channel prefixing distributions and binning codebooks in addition to key sharing. The new regions are shown to be strictly larger than the known ones for a wide class of discrete memoryless and Gaussian channels. In the half-duplex case, where a user can only transmit or receive on any given degree of freedom, we introduce the idea of randomized scheduling and establish the significant gain it offers in terms of the achievable secrecy sum-rate. We further develop an experimental setup based on a IEEE 802.15.4-enabled sensor boards, and use this testbed to show that one can exploit the two-way nature of the communication, via appropriately randomizing the transmit power levels and transmission schedule, to introduce significant ambiguity at a noiseless Eve.
This work considers the two way wiretap channel in which two legitimate users, Alice and Bob, wish to exchange messages securely in the presence of a passive eavesdropper Eve. In the full duplex scenario, where each node can transmit and receive simultaneously, we obtain new achievable secrecy rate regions based on the idea of allowing the two users to jointly optimize their channel prefixing distributions and binning codebooks; in addition to key sharing. The new regions are shown to be strictly larger than the known ones for a wide class of discrete memoryless and Gaussian channels. In the half duplex case, where a user can only transmit or receive on any given degree of freedom, we introduce the idea of randomized scheduling and establish the significant gain it offers in terms of the achievable secrecy sum-rate. We further develop an experimental setup based on a IEEE 802.15.4-enabled sensor boards to validate our theoretical analysis. Using this testbed, it is shown that one can exploit the two way nature of the communication, via appropriately randomizing the transmit power levels and transmission schedule, to introduce significant ambiguity at a noiseless Eve. To the best of our knowledge, this is one of the first attempts aiming towards building practical secrecy protocols inspired by information theoretic principles.
This paper presents a random pilot full-duplex (FD) secret key generation scheme designed to enhance security in static wireless environments. In these environments, where inherent channel randomness is limited, efficiently extracting secret keys poses a significant challenge. The proposed scheme leverages the benefits of both FD operation and random pilot transmission to overcome this limitation and enhance the physical layer security. In this scheme, one of the FD nodes transmits random pilot signals, unknown to the eavesdropper, during the channel probing phase to artificially increase the shared randomness between the legitimate communicating nodes. By considering correlated eavesdropping, we derive the lower and upper bounds for the achievable secret key rate (SKR). The results reveal that the proposed FD scheme outperforms the HD scheme even in the presence of residual SI. Furthermore, the secret key rate can be improved by better SIC channel estimation and lower eavesdropper channel correlation.
The two-way wiretap channel is considered in this paper. Two legitimate users, Alice and Bob, wish to exchange messages securely in the presence of a passive eavesdropper Eve. In the full-duplex scenario, where each node can transmit and receive simultaneously, new achievable secrecy rate regions are obtained based on the idea of allowing the two users to jointly optimize their channel prefixing distributions and binning codebooks in addition to key sharing. The new regions are shown to be strictly larger than the known ones for a wide class of discrete memoryless and Gaussian channels. In the half-duplex case, where a user can only transmit or receive on any given degree of freedom, the idea of randomized scheduling is introduced and shown to offer a significant gain in terms of the achievable secrecy sum-rate. A practical setup is further developed based on a near field wireless communication scenario, and it is shown that one can exploit the two-way nature of the communication, via appropriately randomizing the transmit power levels and transmission schedule, to introduce significant ambiguity at a noiseless Eve.
This work develops new achievable rate regions for the two way wiretap channel. In our setup, Alice and Bob wish to exchange messages securely in the presence of a passive eavesdropper Eve. In the full-duplex scenario, our achievability argument relies on allowing the two users to jointly optimize their channel prefixing distributions, such that the new channel conditions are favorable compared to that of Eve. Random binning and private key sharing over the channel are then used to exploit the secrecy advantage available in the equivalent cascade channel and to distribute the available secrecy rate among users. For the half-duplex case, we introduce the idea of randomized scheduling and establish the significant gain it offers in terms of the achievable secrecy sum-rate. We also quantify the gains that can be leveraged from the proposed schemes in the modulo-2 and Gaussian channels via numerical results in certain selected scenarios.
This dissertation studies the security of wireless interference networks from an information-theoretic point of view. In this setting, several transmitter-receiver pairs wish to have secure communication against the eavesdropper(s). The central goal of this dissertation is to develop a framework based on information-theoretic principles to determine the complete solutions for the signaling schemes in different wireless interference networks with large transmit powers, and derive the corresponding fundamental limits in terms of the secure degrees of freedom (s.d.o.f.). Next, we study one-hop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel with helpers, Gaussian broadcast channel (BC) with confidential messages, Gaussian interference channel (IC) with confidential messages, and Gaussian multiple access (MAC) wiretap channel. The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the s.d.o.f. of the Gaussian wiretap channel with no helpers is zero. We show that the exact s.d.o.f. of the Gaussian wiretap channel with a helper is 1/2. Our achievable scheme is based on real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact s.d.o.f. in this case is M/(M+1). We then generalize this approach to more general network structures with multiple messages. We show that the sum s.d.o.f. of the Gaussian BC with confidential messages and M helpers is 1, the sum s.d.o.f. of the two-user IC with confidential messages is 2/3, the sum s.d.o.f. of the two-user IC with confidential messages and M helpers is 1, and the sum s.d.o.f. of the K-user MAC wiretap channel is K(K-1)/(K(K-1)+1). Then, we study the sum s.d.o.f. of multi-receiver networks. In this dissertation, we determine the exact sum s.d.o.f. of the K-user Gaussian IC. We consider three different secrecy constraints: 1) K-user IC with one external eavesdropper (IC-EE), 2) K-user IC with confidential messages (IC-CM), and 3) K-user IC with confidential messages and one external eavesdropper (IC-CM-EE). We show that for all of these three cases, the exact sum secure d.o.f. is K(K-1)/(2K-1). We show converses for IC-EE and IC-CM, which imply a converse for IC-CM-EE. We show achievability for IC-CM-EE, which implies achievability for IC-EE and IC-CM. We develop the converses by relating the channel inputs of interfering users to the reliable rates of the interfered users, and by quantifying the secrecy penalty in terms of the eavesdroppers' observations. Our achievability uses structured signaling, structured cooperative jamming, channel prefixing, and asymptotic real interference alignment. While the traditional interference alignment provides some amount of secrecy by mixing unintended signals in a smaller sub-space at every receiver, in order to attain the optimum sum s.d.o.f., we incorporate structured cooperative jamming into the achievable scheme, and intricately design the structure of all of the transmitted signals jointly. Next, we study the entire s.d.o.f. regions of multi-user network structures. In this dissertation, we determine the entire s.d.o.f. regions of the K-user MAC wiretap channel and the K-user IC with secrecy constraints. The converse for the MAC follows from a middle step in the converse of the sum s.d.o.f. The converse for the IC includes constraints both due to secrecy as well as due to interference. Although the portion of the region close to the optimum sum s.d.o.f. point is governed by the upper bounds due to secrecy constraints, the other portions of the region are governed by the upper bounds due to interference constraints. Different from the existing literature, in order to fully understand the characterization of the s.d.o.f. region of the IC, one has to study the 4-user case, i.e., the 2 or 3-user cases do not illustrate the generality of the problem. In order to prove the achievability, we use the polytope structure of the converse region. In both MAC and IC cases, we develop explicit schemes that achieve the extreme points of the polytope region given by the converse. Specifically, the extreme points of the MAC region are achieved by an m-user MAC wiretap channel with (K-m) helpers, i.e., by setting (K-m) users' secure rates to zero and utilizing them as pure (structured) cooperative jammers. The extreme points of the IC region are achieved by a (K-m)-user IC with confidential messages, m helpers, and N external eavesdroppers, for m>=1 and a finite N. As a byproduct of determining the entire s.d.o.f. regions of MAC and IC channels, we show that the sum s.d.o.f. is achieved only at one extreme point of the s.d.o.f. region, which is the symmetric-rate extreme point, for both MAC and IC channel models. Then, we determine the sum s.d.o.f. of two-unicast layered wireless networks. Without any secrecy constraints, the sum d.o.f. of this class of networks was shown to take only one of three possible values: 1, 3/2 and 2, for all network configurations. We consider the setting where, in addition to being reliably transmitted, each message is required to be kept information-theoretically secure from the unintended receiver. We show that the sum s.d.o.f. can only take one of five possible values: 0, 2/3, 1, 3/2,2, for all network configurations. To determine the sum s.d.o.f., we divide the class of two-unicast layered networks into several sub-classes, and propose an achievable scheme based on the specific structure of the networks in each sub-class. Our achievable schemes are based on real interference alignment, cooperative jamming, interference neutralization and cooperative jamming neutralization techniques. Next, we consider the Gaussian wiretap channel with M helpers, where no eavesdropper channel state information (CSI) is available at the legitimate entities. One of the key ingredients of our optimal achievable scheme with perfect CSI is to align cooperative jamming signals with the information symbols at the eavesdropper to limit the information leakage rate. This requires perfect eavesdropper CSI at the transmitters. We propose a new achievable scheme in which cooperative jamming signals span the entire space of the eavesdropper, but are not exactly aligned with the information symbols. We show that this scheme achieves the same s.d.o.f. of M/(M+1) but does not require any eavesdropper CSI; the transmitters blindly cooperative jam the eavesdropper. Then, we study the separability of the parallel MAC wiretap channel. Separability, when exists, is useful as it enables us to code separately over parallel channels, and still achieve the optimum overall performance. It is well-known that the parallel single-user channel, parallel MAC and parallel BC are all separable, however, the parallel IC is not separable in general. In this dissertation, we show that, while MAC is separable MAC wiretap channel is not separable in general. We prove this via a specific linear deterministic MAC wiretap channel. We then show that even the Gaussian MAC wiretap channel is inseparable in general. Finally, we show that, when the channel gains are drawn from continuous distributions, and when the s.d.o.f. region is considered, then the Gaussian MAC wiretap channel is almost surely separable. Finally, we study the two-user one-sided IC with confidential messages. In this IC, in addition to the usual selfishness of the users, the relationship between the users is adversarial in the sense of both receivers' desires to eavesdrop on the communication of the other pair. We develop a game-theoretic model for this setting. We start with a model where each pair's payoff is their own secrecy rate. We then propose a refinement for the payoff function by explicitly accounting for the desire of the receiver to eavesdrop on the other party's communication. This payoff function captures the adversarial relationship between the users better. We determine the Nash equilibria for the binary deterministic channel for both payoff functions.