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IEEE Conference on Computer Communications (INFOCOM)

Secret key agreement using a virtual wiretap channel

Setareh Sharifian, Fuchun Lin, Reihaneh Safavi–Naini

Published May 1, 2017• 10 citations
Publisher

Abstract

Key agreement using physical layer properties of communication channels is a well studied problem. iJam is a physical layer key agreement protocol that achieves security by creating a “virtual” wiretap channel for the adversary through a subprotocol between the sender and the receiver that uses self-jamming by the receiver. The protocol was implemented and its security was shown through extensive experiments. The self-jamming subprotocol of iJam was later modelled as a wiretap channel and used for designing a secure message transmission protocol with provable security. We use the same wiretap model of the subprotocol to design secret key agreement protocols with provable security. We propose two protocols that use the wiretap channel once from Alice to Bob, and a protocol that uses two wiretap channels, one from Alice to Bob, and one in the opposite direction. We provide security proof and efficiency analysis for the protocols. The protocols effectively give physical layer security protocols that can be implemented and have provable security. We discuss our results and propose directions for future research.

DOI
10.1109/infocom.2017.8057119

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Key Agreement over Wiretap Models with Non-Causal Side Information

Ali Zibaeenejad

The security of information is an indispensable element of a communication system when transmitted signals are vulnerable to eavesdropping. This issue is a challenging problem in a wireless network as propagated signals can be easily captured by unauthorized receivers, and so achieving a perfectly secure communication is a desire in such a wiretap channel. On the other hand, cryptographic algorithms usually lack to attain this goal due to the following restrictive assumptions made for their design. First, wiretappers basically have limited computational power and time. Second, each authorized party has often access to a reasonably large sequence of uniform random bits concealed from wiretappers. \nTo guarantee the security of information, Information Theory (IT) offers the following two approaches based on physical-layer security. \nFirst, IT suggests using wiretap (block) codes to securely and reliably transmit messages over a noisy wiretap channel. 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The Probability Transition Function (PTF) of the wiretap channel is controlled by a random sequence of Channel State Information (CSI), which is assumed to be non-causally available at Alice. The capacity of the public channel is C_P₁∈[0,∞) in the forward direction from Alice to Bob and C_P₂∈[0,∞) in the backward direction from Bob to Alice. For each model, the key capacity as a function of the pair (C_P₁, C_P₂) is denoted by C_K(C_P₁, C_P₂). We investigate the forward key capacity of each model, i.e., C_K(C_P₁, 0) in this thesis. We also study the key generation over the Gaussian model when Eve's channel is less noisy than Bob's. \nIn the DM model, the wiretap channel is a Discrete Memoryless State-dependent Wiretap Channel (DM-SWC) in which Bob and Eve each may also have access to a sequence of Side Information (SI) dependent on the CSI. We establish a Lower Bound (LB) and an Upper Bound (UB) on the forward key capacity of the DM model. When the model is less noisy in Bob's favor, another UB on the forward key capacity is derived. The achievable key agreement code is asymptotically optimum as C_P₁→ ∞. For any given DM model, there also exists a finite capacity C⁰_P₁, which is determined by the DM-SWC, such that the forward key capacity is achievable if C_P₁≥ C⁰_P₁. Moreover, the key generation is saturated at capacity C_P₁= C⁰_P₁, and thus increasing the public channel capacity beyond C⁰_P₁ makes no improvement on the forward key capacity of the DM model. If the CSI is fully known at Bob in addition to Alice, C⁰_P₁=0, and so the public channel has no contribution in key generation when the public channel is in the forward direction. \nThe achievable key agreement code of the DM model exploits both a random generator and the CSI as resources for key generation at Alice. The randomness property of channel states can be employed for key generation, and so the agreed keys depend on the CSI in general. However, a message is independent of the CSI in a secrecy problem. Hence, we justify that the forward key capacity can exceed both the main channel capacity and the secrecy capacity of the DM-SWC. \nIn the Gaussian model, the wiretap channel is a Gaussian State-dependent Wiretap Channel (G-SWC) with Additive White Gaussian Interference (AWGI) having average power Λ. For simplicity, no side information is assumed at Bob and Eve. \nBob's channel and Eve's channel suffer from Additive White Gaussian Noise (AWGN), where the correlation coefficient between noise of Bob's channel and that of Eve's channel is given by ϱ. \nWe prove that the forward key capacity of the Gaussian model is independent of ϱ. Moreover, we establish that the forward key capacity is positive unless Eve's channel is less noisy than Bob's. We also prove that the key capacity of the Gaussian model vanishes if the G-SWC is physically degraded in Eve's favor. However, we justify that obtaining a positive key capacity is feasible even if Eve's channel is less noisy than Bob's according to our achieved LB on the key capacity for case (C_P₁, C_P₂)→ (∞, ∞). Hence, the key capacity of the Gaussian model is a function of ϱ. \nIn this thesis, an LB on the forward key capacity of the Gaussian model is achieved. For a fixed Λ, the achievable key agreement code is optimum for any C_P₁∈[0,∞) in both low Signal-to-Interference Ratio (SIR) and high SIR regimes. We show that the forward key capacity is asymptotically independent of C_P₁ and Λ as the SIR goes to infinity, and thus the public channel and the interference have negligible contributions in key generation in the high SIR regime. On the other hand, the forward key capacity is a function of C_P₁ and Λ in the low SIR regime. 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This fact is an essential difference between this model and the DM model. \nFor C_P₁=0 and a fixed Λ, the forward key capacity of the Gaussian model exceeds the main channel capacity of the G-SWC in the low SIR regime. By simulations, we show that the interference enhances key generation in the low SIR regime. In this regime, we also justify that the positive effect of the interference on the (forward) key capacity is generally more than its positive effect on the secrecy capacity of the G-SWC, while the interference has no influence on the main channel capacity of the G-SWC.

•Jun 20, 2012•2 citations

Wireless Physical Layer Security: On the Performance Limit of Secret-Key Agreement

Marwen Zorgui

Physical layer security (PLS) is a new paradigm aiming at securing communications between legitimate parties at the physical layer. Conventionally, achieving confidentiality in communication networks relies on cryptographic techniques such as public-key cryptography, secret-key distribution and symmetric encryption. Such techniques are deemed secure based on the assumption of limited computational abilities of a wiretapper. Given the relentless progress in computational capacities and the dynamic topology and proliferation of modern wireless networks, the relevance of the previous techniques in securing communications is more and more questionable and less and less reliable. In contrast to this paradigm, PLS does not assume a specific computational power at any eavesdropper, its premise to guarantee provable security via employing channel coding techniques at the physical layer exploiting the inherent randomness in most communication systems. In this dissertation, we investigate a particular aspect of PLS, which is secret-key agreement, also known as secret-sharing. In this setup, two legitimate parties try to distill a secret-key via the observation of correlated signals through a noisy wireless channel, in the presence of an eavesdropper who must be kept ignorant of the secret-key. Additionally, a noiseless public channel is made available to the legitimate parties to exchange public messages that are also accessible to the eavesdropper. Recall that key agreement is an important aspect toward realizing secure communications in the sense that the key can be used in a one-time pad scheme to send the confidential message. In the first part, our focus is on secret-sharing over Rayleigh fading quasi-static channels. We study the fundamental relationship relating the probability of error and a given target secret-key rate in the high power regime. This is characterized through the diversity multiplexing tradeoff (DMT) concept, that we define for our model and then characterize it. We show that the impact of the secrecy constraint is to reduce the effective number of transmit antennas by the number of antennas at the eavesdropper. Toward this characterization, we provide several schemes achieving the DMT and we highlight disparities between coding for the wiretap channel and coding for secret-key agreement. In the second part of the present work, we consider a fast-fading setting in which the wireless channels change during each channel use. We consider a correlated environment where transmit, legitimate receiver and eavesdropper antennas are correlated. We characterize the optimal strategy achieving the highest secret-key rate. We also identify the impact of correlation matrices and illustrate our analysis with various numerical results. Finally, we study the system from an energy-efficiency point of view and evaluate relevant metrics as the minimum energy required for sharing a secret-key bit and the wideband slope.

•Jan 1, 2015•0 citations
Key agreement using physical layer properties of communication channels is a well studied problem. iJam is a physical layer key agreement protocol that achieves security by creating a “virtual” wiretap channel for the adversary through a subprotocol between the sender and the receiver that uses self-jamming by the receiver. The protocol was implemented and its security was shown through extensive experiments. The self-jamming subprotocol of iJam was later modelled as a wiretap channel and used for designing a secure message transmission protocol with provable security. We use the same wiretap model of the subprotocol to design secret key agreement protocols with provable security. We propose two protocols that use the wiretap channel once from Alice to Bob, and a protocol that uses two wiretap channels, one from Alice to Bob, and one in the opposite direction. We provide security proof and efficiency analysis for the protocols. The protocols effectively give physical layer security protocols that can be implemented and have provable security. We discuss our results and propose directions for future research.
Secure communication ensures the integrity and confidentiality of communication between connected devices. An information-theoretic approach to secure communication gives the strongest confidentiality guarantee by assuming that the attacker has unlimited computing power. The earliest formal model and definition of information-theoretic secure communication is by Shannon, who employed a secret key shared between communicating parties to provide confidentiality. An alternative elegant information-theoretic approach to secure communication views the natural characteristics of the environment (i.e., channel’s noise) as a resource to build security functionalities. This approach was first proposed by Wyner, and the corresponding secure communication model is called the wiretap channel model. These two approaches introduce two primary resources for providing information-theoretic secure communication: the shared secret key and physical properties of the communication medium. In this thesis, we study how to employ the above two resources for secure message transmission. We study this by using channel’s noise in the wiretap channel model. In this model, a sender is connected to the receiver and the adversary through two noisy channels. We propose a new wiretap encoding scheme with strong secrecy that provides perfect secrecy and reliability, asymptotically. The construction treats the noise in the adversary’s channel as a source of randomness that is extracted and used to hide the message from the adversary. We realize the wiretap channel model using cooperative jamming to evaluate the performance of wiretap codes in practice. We consider a model called keyed wiretap channel that unifies Wyner’s model with Shannon’s model of perfect secrecy for information systems, and propose a keyed encoding schemes with strong secrecy and other properties that are attractive in practice. We also study two-party information-theoretic secret key agreement when the two parties have access to samples of a common source of randomness and use a single message transmission to arrive at a shared random key. We propose a secret key agreement protocol in this setting, prove its security, and show its superior performance compared to other known protocols with the same properties. Finally, we propose an information-theoretic secret key agreement over a virtual wiretap channel created by cooperative jamming.
The wiretap channel is a setting where one aims to obtain information-theoretic security of communicated data under the sole assumption that the channel from a sender Alice to an eavesdropper Eve is “noisier” than that from Alice to a receiver Bob. However, in practice, the difference between the two channels in terms of noise may be much smaller because of the wide spread application of high-performance communication technologies. Thus, establishing a wiretap channel over real channels is a challenging task. In this paper, we report a wiretap channel in the form of a “protocol” (a so-called virtual wiretap channel) realized by using a highly precise wireless clock-synchronization technology called the wireless two-way interferometry (abbreviated as Wi-Wi). Wi-Wi technology has already been implemented in wireless communication devices, and it measures the clock time difference and signal propagation time in a situation where the precisions of both values are mutually affected. That is, Alice or Bob can induce a noise on Eve's clock time difference measurement by physically introducing noise in the signal propagation time between Alice and Bob. We analyzed the proposed wiretap channel referred to as the Wi-Wi wiretap channel experimentally, and estimated its parameters (e.g., the error probabilities). We confirmed that the Wi-Wi wiretap channel works well as a virtual wiretap channel by simulating and experimentally demonstrating a well-known, provably secure, optimal wiretap code over it. The results show that Wi-Wi wiretap channel can serve as a physical layer security, useful for synchronized Internet of Things (IoT) devises.
Wyner [96] proved that unconditionally secure communication over noisy channels is possible if the wiretapping channel is noisier than the main channel. The work has developed the following belief: Physical-channel characteristics are great resources to build security functionalities in the information-theoretic framework. We follow this belief and investigate the three problems of secret key establishment, manipulation detection, and distance bounding verification over physical-layer channels. We investigate secret key establishment (SKE) between Alice and Bob when they are connected through a pair of noisy wiretap channels with leakage to Eve. Our results show the possibility of SKE even in cases where the main channels are noisier than Eve's channels. We then notice two implicit assumptions of this work: (i) local randomness is freely available, and (ii) the wiretap channels are independent. We remove Assumption (i) by considering no local randomness for the parties. The results appreciate the role of noise as a single resource for randomness derivation and key generation in this setting. Regarding the second assumption, we consider the general two-way wiretap channel, where simultaneous data transmission can help achieve higher key rates. We show under what condition our security requirements can be strengthened without sacrificing the SK capacity. We consider manipulation detection against physical-layer adversaries noticing their limitations. We define leakage-resilient algebraic manipulation detection (LR-AMD) codes and prove optimal LR-AMD code constructions in general and special leakage scenarios. We show two applications of these codes: (i) robust nonperfect secret sharing and (ii) manipulation detection over wiretap channels. We then discuss how these codes can be composed with other primitives to guarantee bitwise manipulation detection and SKE against active adversaries over binary wiretap channels. Distance bounding verification (DBV) allows a verifier to check an upper bound on a claimed distance from a prover. We study DBV over physical channels with security against distance fraud (DFA), ma a fraud (MFA) and terrorist fraud (TFA) attacks. We show efficient DFA- and MFA-secure protocols only using physical channel properties. We further prove that TFA-security becomes feasible if the parties' communication is limited by the bounded retrieval model (BRM).
The security of information is an indispensable element of a communication system when transmitted signals are vulnerable to eavesdropping. This issue is a challenging problem in a wireless network as propagated signals can be easily captured by unauthorized receivers, and so achieving a perfectly secure communication is a desire in such a wiretap channel. On the other hand, cryptographic algorithms usually lack to attain this goal due to the following restrictive assumptions made for their design. First, wiretappers basically have limited computational power and time. Second, each authorized party has often access to a reasonably large sequence of uniform random bits concealed from wiretappers. \nTo guarantee the security of information, Information Theory (IT) offers the following two approaches based on physical-layer security. \nFirst, IT suggests using wiretap (block) codes to securely and reliably transmit messages over a noisy wiretap channel. No confidential common key is usually required for the wiretap codes. The secrecy problem investigates an optimum wiretap code that achieves the secrecy capacity of a given wiretap channel. \nSecond, IT introduces key agreement (block) codes to exchange keys between legitimate parties over a wiretap model. The agreed keys are to be reliable, secure, and (uniformly) random, at least in an asymptotic sense, such that they can be finally employed in symmetric key cryptography for data transmission. The key agreement problem investigates an optimum key agreement code that obtains the key capacity of a given wiretap model. \nIn this thesis, we study the key agreement problem for two wiretap models: a Discrete Memoryless (DM) model and a Gaussian model. Each model consists of a wiretap channel \nparalleled with an authenticated public channel. The wiretap channel is from a transmitter, called Alice, to an authorized receiver, called Bob, and to a wiretapper, called Eve. The Probability Transition Function (PTF) of the wiretap channel is controlled by a random sequence of Channel State Information (CSI), which is assumed to be non-causally available at Alice. The capacity of the public channel is C_P₁∈[0,∞) in the forward direction from Alice to Bob and C_P₂∈[0,∞) in the backward direction from Bob to Alice. For each model, the key capacity as a function of the pair (C_P₁, C_P₂) is denoted by C_K(C_P₁, C_P₂). We investigate the forward key capacity of each model, i.e., C_K(C_P₁, 0) in this thesis. We also study the key generation over the Gaussian model when Eve's channel is less noisy than Bob's. \nIn the DM model, the wiretap channel is a Discrete Memoryless State-dependent Wiretap Channel (DM-SWC) in which Bob and Eve each may also have access to a sequence of Side Information (SI) dependent on the CSI. We establish a Lower Bound (LB) and an Upper Bound (UB) on the forward key capacity of the DM model. When the model is less noisy in Bob's favor, another UB on the forward key capacity is derived. The achievable key agreement code is asymptotically optimum as C_P₁→ ∞. For any given DM model, there also exists a finite capacity C⁰_P₁, which is determined by the DM-SWC, such that the forward key capacity is achievable if C_P₁≥ C⁰_P₁. Moreover, the key generation is saturated at capacity C_P₁= C⁰_P₁, and thus increasing the public channel capacity beyond C⁰_P₁ makes no improvement on the forward key capacity of the DM model. If the CSI is fully known at Bob in addition to Alice, C⁰_P₁=0, and so the public channel has no contribution in key generation when the public channel is in the forward direction. \nThe achievable key agreement code of the DM model exploits both a random generator and the CSI as resources for key generation at Alice. The randomness property of channel states can be employed for key generation, and so the agreed keys depend on the CSI in general. However, a message is independent of the CSI in a secrecy problem. Hence, we justify that the forward key capacity can exceed both the main channel capacity and the secrecy capacity of the DM-SWC. \nIn the Gaussian model, the wiretap channel is a Gaussian State-dependent Wiretap Channel (G-SWC) with Additive White Gaussian Interference (AWGI) having average power Λ. For simplicity, no side information is assumed at Bob and Eve. \nBob's channel and Eve's channel suffer from Additive White Gaussian Noise (AWGN), where the correlation coefficient between noise of Bob's channel and that of Eve's channel is given by ϱ. \nWe prove that the forward key capacity of the Gaussian model is independent of ϱ. Moreover, we establish that the forward key capacity is positive unless Eve's channel is less noisy than Bob's. We also prove that the key capacity of the Gaussian model vanishes if the G-SWC is physically degraded in Eve's favor. However, we justify that obtaining a positive key capacity is feasible even if Eve's channel is less noisy than Bob's according to our achieved LB on the key capacity for case (C_P₁, C_P₂)→ (∞, ∞). Hence, the key capacity of the Gaussian model is a function of ϱ. \nIn this thesis, an LB on the forward key capacity of the Gaussian model is achieved. For a fixed Λ, the achievable key agreement code is optimum for any C_P₁∈[0,∞) in both low Signal-to-Interference Ratio (SIR) and high SIR regimes. We show that the forward key capacity is asymptotically independent of C_P₁ and Λ as the SIR goes to infinity, and thus the public channel and the interference have negligible contributions in key generation in the high SIR regime. On the other hand, the forward key capacity is a function of C_P₁ and Λ in the low SIR regime. Contributions of the interference and the public channel in key generation are significant in the low SIR regime that will be illustrated by simulations. \nThe proposed key agreement code asymptotically achieves the forward key capacity of the Gaussian model for any SIR as C_P₁→ ∞. Hence, C_K(∞,0) is calculated, and it is suggested as a UB on C_K(C_P₁,0). Using simulations, we also compute the minimum required C_P₁ for which the forward key capacity is upper bounded within a given tolerance. \nThe achievable key agreement code is designed based on a generalized version of the Dirty Paper Coding (DPC) in which transmitted signals are correlated with the CSI. The correlation coefficient is to be determined by C_P₁. In contrast to the DM model, the LB on the forward key capacity of a Gaussian model is a strictly increasing function of C_P₁ according to our simulations. This fact is an essential difference between this model and the DM model. \nFor C_P₁=0 and a fixed Λ, the forward key capacity of the Gaussian model exceeds the main channel capacity of the G-SWC in the low SIR regime. By simulations, we show that the interference enhances key generation in the low SIR regime. In this regime, we also justify that the positive effect of the interference on the (forward) key capacity is generally more than its positive effect on the secrecy capacity of the G-SWC, while the interference has no influence on the main channel capacity of the G-SWC.
Physical layer security (PLS) is a new paradigm aiming at securing communications between legitimate parties at the physical layer. Conventionally, achieving confidentiality in communication networks relies on cryptographic techniques such as public-key cryptography, secret-key distribution and symmetric encryption. Such techniques are deemed secure based on the assumption of limited computational abilities of a wiretapper. Given the relentless progress in computational capacities and the dynamic topology and proliferation of modern wireless networks, the relevance of the previous techniques in securing communications is more and more questionable and less and less reliable. In contrast to this paradigm, PLS does not assume a specific computational power at any eavesdropper, its premise to guarantee provable security via employing channel coding techniques at the physical layer exploiting the inherent randomness in most communication systems. In this dissertation, we investigate a particular aspect of PLS, which is secret-key agreement, also known as secret-sharing. In this setup, two legitimate parties try to distill a secret-key via the observation of correlated signals through a noisy wireless channel, in the presence of an eavesdropper who must be kept ignorant of the secret-key. Additionally, a noiseless public channel is made available to the legitimate parties to exchange public messages that are also accessible to the eavesdropper. Recall that key agreement is an important aspect toward realizing secure communications in the sense that the key can be used in a one-time pad scheme to send the confidential message. In the first part, our focus is on secret-sharing over Rayleigh fading quasi-static channels. We study the fundamental relationship relating the probability of error and a given target secret-key rate in the high power regime. This is characterized through the diversity multiplexing tradeoff (DMT) concept, that we define for our model and then characterize it. We show that the impact of the secrecy constraint is to reduce the effective number of transmit antennas by the number of antennas at the eavesdropper. Toward this characterization, we provide several schemes achieving the DMT and we highlight disparities between coding for the wiretap channel and coding for secret-key agreement. In the second part of the present work, we consider a fast-fading setting in which the wireless channels change during each channel use. We consider a correlated environment where transmit, legitimate receiver and eavesdropper antennas are correlated. We characterize the optimal strategy achieving the highest secret-key rate. We also identify the impact of correlation matrices and illustrate our analysis with various numerical results. Finally, we study the system from an energy-efficiency point of view and evaluate relevant metrics as the minimum energy required for sharing a secret-key bit and the wideband slope.