Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Information Theory Workshop (ITW)

Key agreement in state-dependent channels with non-causal side information

Ali Zibaeenejad

Published Oct 1, 2011• 3 citations
Publisher

Abstract

Key agreement problem over a discrete memoryless state-dependent wiretap channel (DM-SWC) is addressed in this paper. Three parties have access to the wiretap channel: One transmitter, an authorized receiver, and an illegal receiver. The transmitter fully knows channel state information (CSI) in a non-causal form, while each receiver has access to a sequence of side information (SI) correlated with the CSI. Further to the DM-SWC, the parties can also exploit a unilateral public channel with a given capacity from the transmitter to the receivers. We have obtained a lower bound (LB) on the key capacity. The LB achieves the key capacity when the capacity of the public channel exceeds a fixed finite value determined by the DM-SWC. For any DM-SWC, the key capacity is consequently achievable as the public channel capacity becomes unlimited. An upper bound (UB) on the key capacity is obtained when the legal receiver is less noisy than the wiretapper.

DOI
10.1109/itw.2011.6089578

Related papers

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. 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.

•Jun 20, 2012•2 citations

Key Generation Over Wiretap Models With Non-Causal Side Information

Ali Zibaeenejad

The key agreement problem over a state-dependent wiretap channel with a parallel one-way public channel in the forward direction is studied. It is assumed that the channel state information (CSI) is non-causally known at the transmitter. In this paper, the effect of the public channel and the CSI on the key generation is investigated, and the key capacity as a function of public channel capacity CP, CK(CP), is sought for a discrete memoryless (DM) model and a Gaussian model, in which the CSI is an additive white Gaussian interference. For each model, a lower bound and an upper bound on the key capacity are derived, and CK(∞) is achieved as the bounds are asymptotically tight. For any DM wiretap channel, it is shown that there exists a finite capacity CP* beyond which CK(CP) = CK(CP*). If the CSI is also fully known at the legitimate receiver, it is proved that the public channel has no effect on the key capacity. For the Gaussian model, the achievable key rate is a strictly increasing function of CPin general. In addition, CK(CP) is attained in both the low signal-to-interference ratio (SIR) regime and the high SIR regime. In the low SIR regime, the public channel cooperates with the transmitter for the key generation from the known interference. In the high SIR regime, however, the public channel makes negligible contribution to the key generation.

IEEE Transactions on Information Forensics and Security•Feb 24, 2015•10 citations

Secret-Key Agreement With Channel State Information at the Transmitter

Ashish J. Khisti, Suhas N. Diggavi, Gregory W. Wornell

We study the capacity of secret-key agreement over a wiretap channel with state parameters. The transmitter, the legitimate receiver, and the eavesdropper are connected by a discrete memoryless wiretap channel with a memoryless state sequence. The transmitter and the legitimate receiver generate a secret-key that must be concealed from the eavesdropper. We assume that the state sequence is known noncausally to the transmitter and no public discussion channel is available. We derive lower and upper bounds on the secret-key capacity. The lower bound involves a source-channel codebook for constructing a common reconstruction sequence at the legitimate terminals and then mapping this sequence to a secret-key using a secret-key codebook. For the special case of Gaussian channels with additive interference (secret-keys from dirty paper channel) our bounds differ by 0.5 bit/symbol and coincide in the high signal-to-noise-ratio and high interference-to-noise-ratio regimes. In another special case-symmetric channel state information (CSI)-when the legitimate receiver is also revealed the state sequence, we establish optimality of our lower bound. In addition, only causal side information at the transmitter and the receiver suffices to attain the secret-key capacity in the case of symmetric CSI.

arXiv:1009.3052•IEEE Transactions on Information Forensics and Security•Jun 10, 2011•63 citations

Secret key agreement on wiretap channel with transmitter side information

Ashish J. Khisti

The secret-key agreement problem over wiretap channels controlled by a state parameter is studied. The entire state sequence is known (non-causally) to the sender but not to the receiver and the eavesdropper. Upper and lower bounds on the secret-key capacity are established both with and without public discussion. In absence of public-discussion, our lower bound is strictly better than the best known lower bound for transmitting an independent secret message. This illustrates that the coding schemes for secret-key agreement are substantially different than secret-message transmission. For the special case of Gaussian channels, we establish the secret-key capacity when the legitimate receiver's signal-to-noise-ratio is greater than 0 dB. When a public discussion channel is available between the sender and the receiver, upper and lower bounds on the secret-key capacity are again established. These bounds coincide, yielding the capacity, when then the channels of the receiver and the eavesdropper satisfy an independent noise condition.

European Wireless Conference•Jan 1, 2010•11 citations

Secret key agreement on wiretap channels with transmitter side information

Ashish J. Khisti

Secret-key agreement protocols over wiretap channels controlled by a state parameter are studied. The entire state sequence is known (non-causally) to the sender but not to the receiver and the eavesdropper. Upper and lower bounds on the secret-key capacity are established both with and without public discussion. The proposed coding scheme involves constructing a codebook to create common reconstruction of the state sequence at the sender and the receiver and another secret-key codebook constructed by random binning. For the special case of Gaussian channels, with no public discussion, - the secret-key generation with dirty paper problem, the gap between our bounds is at-most 1/2 bit and the bounds coincide in the high signal-to-noise ratio and high interference-to-noise ratio regimes. In the presence of public discussion our bounds coincide, yielding the capacity, when then the channels of the receiver and the eavesdropper satisfy an in- dependent noise condition.

arXiv:1006.5901•Jun 30, 2010•7 citations

Key agreement over Gaussian wiretap models with known interference at the transmitter

Ali Zibaeenejad

We investigate the (forward) key capacity of a Gaussian state-dependent wiretap channel (G-SWC) paralleled with a public channel having capacity Cpϵ [0, ∞). This model consists of a sender, a main receiver, and a wiretapper. The channel state information (CSI) is an additive white Gaussian interference (AWGI) which is non-causally known at the sender. A lower bound (LB) on the key capacity is achieved by using a generalized version of the dirty paper coding (DPC) in which the transmitted signal is correlated with the interference. The correlation coefficient is to be determined by Cp. The achievable scheme is asymptotically optimum as Cp→ ∞. This optimum key capacity is also asymptotically achievable for any Cp≥ 0 in high signal to interference ratio (SIR) regime. In this regime, the public channel has negligible contribution in key generation. Generally, the CSI enhances the key capacity such that it exceeds the main channel capacity of the G-SWC in low SIR regime.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2012•0 citations
Key agreement problem over a discrete memoryless state-dependent wiretap channel (DM-SWC) is addressed in this paper. Three parties have access to the wiretap channel: One transmitter, an authorized receiver, and an illegal receiver. The transmitter fully knows channel state information (CSI) in a non-causal form, while each receiver has access to a sequence of side information (SI) correlated with the CSI. Further to the DM-SWC, the parties can also exploit a unilateral public channel with a given capacity from the transmitter to the receivers. We have obtained a lower bound (LB) on the key capacity. The LB achieves the key capacity when the capacity of the public channel exceeds a fixed finite value determined by the DM-SWC. For any DM-SWC, the key capacity is consequently achievable as the public channel capacity becomes unlimited. An upper bound (UB) on the key capacity is obtained when the legal receiver is less noisy than the wiretapper.
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.
The key agreement problem over a state-dependent wiretap channel with a parallel one-way public channel in the forward direction is studied. It is assumed that the channel state information (CSI) is non-causally known at the transmitter. In this paper, the effect of the public channel and the CSI on the key generation is investigated, and the key capacity as a function of public channel capacity CP, CK(CP), is sought for a discrete memoryless (DM) model and a Gaussian model, in which the CSI is an additive white Gaussian interference. For each model, a lower bound and an upper bound on the key capacity are derived, and CK(∞) is achieved as the bounds are asymptotically tight. For any DM wiretap channel, it is shown that there exists a finite capacity CP* beyond which CK(CP) = CK(CP*). If the CSI is also fully known at the legitimate receiver, it is proved that the public channel has no effect on the key capacity. For the Gaussian model, the achievable key rate is a strictly increasing function of CPin general. In addition, CK(CP) is attained in both the low signal-to-interference ratio (SIR) regime and the high SIR regime. In the low SIR regime, the public channel cooperates with the transmitter for the key generation from the known interference. In the high SIR regime, however, the public channel makes negligible contribution to the key generation.
We study the capacity of secret-key agreement over a wiretap channel with state parameters. The transmitter, the legitimate receiver, and the eavesdropper are connected by a discrete memoryless wiretap channel with a memoryless state sequence. The transmitter and the legitimate receiver generate a secret-key that must be concealed from the eavesdropper. We assume that the state sequence is known noncausally to the transmitter and no public discussion channel is available. We derive lower and upper bounds on the secret-key capacity. The lower bound involves a source-channel codebook for constructing a common reconstruction sequence at the legitimate terminals and then mapping this sequence to a secret-key using a secret-key codebook. For the special case of Gaussian channels with additive interference (secret-keys from dirty paper channel) our bounds differ by 0.5 bit/symbol and coincide in the high signal-to-noise-ratio and high interference-to-noise-ratio regimes. In another special case-symmetric channel state information (CSI)-when the legitimate receiver is also revealed the state sequence, we establish optimality of our lower bound. In addition, only causal side information at the transmitter and the receiver suffices to attain the secret-key capacity in the case of symmetric CSI.
The secret-key agreement problem over wiretap channels controlled by a state parameter is studied. The entire state sequence is known (non-causally) to the sender but not to the receiver and the eavesdropper. Upper and lower bounds on the secret-key capacity are established both with and without public discussion. In absence of public-discussion, our lower bound is strictly better than the best known lower bound for transmitting an independent secret message. This illustrates that the coding schemes for secret-key agreement are substantially different than secret-message transmission. For the special case of Gaussian channels, we establish the secret-key capacity when the legitimate receiver's signal-to-noise-ratio is greater than 0 dB. When a public discussion channel is available between the sender and the receiver, upper and lower bounds on the secret-key capacity are again established. These bounds coincide, yielding the capacity, when then the channels of the receiver and the eavesdropper satisfy an independent noise condition.
Secret-key agreement protocols over wiretap channels controlled by a state parameter are studied. The entire state sequence is known (non-causally) to the sender but not to the receiver and the eavesdropper. Upper and lower bounds on the secret-key capacity are established both with and without public discussion. The proposed coding scheme involves constructing a codebook to create common reconstruction of the state sequence at the sender and the receiver and another secret-key codebook constructed by random binning. For the special case of Gaussian channels, with no public discussion, - the secret-key generation with dirty paper problem, the gap between our bounds is at-most 1/2 bit and the bounds coincide in the high signal-to-noise ratio and high interference-to-noise ratio regimes. In the presence of public discussion our bounds coincide, yielding the capacity, when then the channels of the receiver and the eavesdropper satisfy an in- dependent noise condition.
We investigate the (forward) key capacity of a Gaussian state-dependent wiretap channel (G-SWC) paralleled with a public channel having capacity Cpϵ [0, ∞). This model consists of a sender, a main receiver, and a wiretapper. The channel state information (CSI) is an additive white Gaussian interference (AWGI) which is non-causally known at the sender. A lower bound (LB) on the key capacity is achieved by using a generalized version of the dirty paper coding (DPC) in which the transmitted signal is correlated with the interference. The correlation coefficient is to be determined by Cp. The achievable scheme is asymptotically optimum as Cp→ ∞. This optimum key capacity is also asymptotically achievable for any Cp≥ 0 in high signal to interference ratio (SIR) regime. In this regime, the public channel has negligible contribution in key generation. Generally, the CSI enhances the key capacity such that it exceeds the main channel capacity of the G-SWC in low SIR regime.