We study a two-terminal secret-key generation problem over a two-way, approximately reciprocal, block-fading channel. The channel gains between the legitimate terminals are not revealed to any terminal, whereas the channel gains of the eavesdropper are revealed perfectly to the eavesdropper. We study a separation based scheme that involves a training phase followed by a communication phase within each block. The training phase generates correlated estimates of the channel state sequence between the two terminals, whereas the communication phase generates correlated source sequences between the two terminals. A portion of the secret-key is generated from the correlated channel state sequences by creating omniscience between the legitimate terminals and the remainder of the secret-key is generated from the correlated source sequences. An upper bound on the secret-key capacity is also established by reducing the setup to a coherent channel by providing genie-aided side information to the receivers. We observe that the difference between the upper and lower bound decreases as 1/T in the high signal-to-noise-ratio (SNR) regime. Numerical results indicate that the proposed scheme achieves significant gains over the commonly used training-only schemes even for moderate SNR.
We study a two-terminal secret-key generation problem over a two-way, approximately reciprocal, block-fading channel. The channel gains between the legitimate terminals are not revealed to any terminal, whereas the channel gains of the eavesdropper are revealed perfectly to the eavesdropper. We study a separation based scheme that involves a training phase followed by a communication phase within each block. The training phase generates correlated estimates of the channel state sequence between the two terminals, whereas the communication phase generates correlated source sequences between the two terminals. A portion of the secret-key is generated from the correlated channel state sequences by creating omniscience between the legitimate terminals and the remainder of the secret-key is generated from the correlated source sequences. An upper bound on the secret-key capacity is also established by reducing the setup to a coherent channel by providing genie-aided side information to the receivers. We observe that the difference between the upper and lower bound decreases as 1/T in the high signal-to-noise-ratio (SNR) regime. Numerical results indicate that the proposed scheme achieves significant gains over the commonly used training-only schemes even for moderate SNR.
Fundamental limits of secret-key agreement over reciprocal wireless channels are investigated. We consider a two-way block-fading channel where the channel gains in the forward and reverse links between the legitimate terminals are correlated. The channel gains between the legitimate terminals are not revealed to any terminal, whereas the channel gains of the eavesdropper are revealed to the eavesdropper. We propose a two-phase transmission scheme, that reserves a certain portion of each coherence block for channel estimation, and the remainder of the coherence block for correlated source generation. The resulting secret-key involves contributions of both channel sequences and source sequences, with the contribution of the latter becoming dominant as the coherence period increases. We also establish an upper bound on the secret-key capacity, which has a form structurally similar to the lower bound. Our upper and lower bounds coincide in the limit of high signal-to-noise-ratio (SNR) and large coherence period, thus establishing the secret-key agreement capacity in this asymptotic regime. Numerical results indicate that the proposed scheme achieves significant gains over training-only schemes, even for moderate SNR and small coherence periods, thus implying the necessity of randomness-sharing in practical secret-key generation systems.
Motivated by recent interest in physical-layer secret-key generation over wireless fading channels, we study the non-coherent secret-key generation capacity of a block-fading wireless channel with channel reciprocity and bi-directional (two-way) communication. We assume a non-coherent main channel, i.e., the realization of channel gains on the main channel is not known to any terminal. The eavesdropper is assumed to have both perfect Channel State Information of its own channel and orthogonal observations from the forward and backward channels. As our main result, we establish new upper and lower bounds on the secret-key generation capacity with public discussion, which are structurally similar. The upper bound can be expressed as a sum of three terms-one of the terms arises due to channel reciprocity, while the other two terms correspond to communication on the forward and backward channels, respectively. In the limit of long coherence period, the contribution from channel reciprocity vanishes to zero, whereas the other terms prevail. The lower bound is based on a separation based scheme. In each coherence block, we use the first symbol for training while the remainder of the coherence block is devoted to source emulation, i.e., to generate correlated sources between the terminals. The lower bound expression also consists of three terms and admits an interpretation similar to the upper bound expression. For Rayleigh fading channels, in the high signal-to-noise ratio (SNR) regime, the gap between the upper and lower bounds is shown to vanish inversely with the coherence period. Numerical results indicate significant performance gains over training-only schemes even for moderate values of SNR and small coherence periods.
We study secret-key agreement with public discussion over a flat-fading wiretap channel model. The fading gains are correlated across the receivers and sampled independently at each time. Perfect receiver channel state information (CSI) is assumed, whereas a noisy CSI of the main channel is also available to the transmitter. We propose lower and upper bounds on the capacity. Our lower bound is achieved by a coding scheme that involves a separate binning of the receiver CSI sequence and its channel output sequence. In general it improves upon the joint-binning schemes considered in earlier works. Our upper and lower bounds coincide, establishing the capacity, when either the transmitter has no CSI or when the channel gains of the legitimate receiver and the eavesdropper are statistically independent.
We study the low SNR scaling of the non-coherent secret-key agreement capacity over a reciprocal, block-fading channel. For the restricted class of strategies, where one of the nodes is constrained to transmit pilot-only symbols, we show that the secret-key capacity scales as SNR ·log T if T ≤ 1/SNR, where T denotes the coherence period, and as SNR·log(1/SNR) otherwise. Our upper bound is inspired by the genie-aided argument of Borade and Zheng (IT-Trans 2010). Our lower bound is based on bursty communication, channel training, and secret message transmission.
We study the secret-key capacity in a joint source-channel coding setup-the terminals are connected over a discrete memoryless channel and have access to side information, modelled as a pair of discrete memoryless source sequences. As our main result, we establish the upper and lower bounds on the secret-key capacity. In the lower bound expression, the equivocation terms of the source and channel components are functionally additive even though the coding scheme generates a single secret-key by jointly taking into account the source and channel equivocations. Our bounds coincide, thus establishing the capacity, when the underlying wiretap channel can be decomposed into a set of independent, parallel, and reversely degraded channels. For the case of parallel Gaussian channels and jointly Gaussian sources we show that Gaussian codebooks achieve the secret-key capacity. In addition, when the eavesdropper also observes a correlated side information sequence, we establish the secret-key capacity when both the source and channel of the eavesdropper are a degraded version of the legitimate receiver. We finally also treat the case when a public discussion channel is available, propose a separation based coding scheme, and establish its optimality when the channel output symbols of the legitimate receiver and eavesdropper are conditionally independent given the input.
Abstract—We study the secret-key capacity in a joint source-channel coding setup—the terminals are connected over a discrete memoryless channel and have access to side information, modelled as a pair of discrete memoryless source sequences. As our main result, we establish the upper and lower bounds on the secret-key capacity. In the lower bound expression, the equivocation terms of the source and channel components are functionally additive even though the coding scheme generates a single secret-key by jointly taking into account the source and channel equivocations. Our bounds coincide, thus establishing the capacity, when the underlying wiretap channel can be decomposed into a set of independent, parallel, and reversely degraded channels. For the case of parallel Gaussian channels and jointly Gaussian sources we show that Gaussian codebooks achieve the secret-key capacity. In addition, when the eavesdropper also observes a correlated side information sequence, we establish the secret-key capacity when both the source and channel of the eavesdropper are a degraded version of the legitimate receiver. We finally also treat the case when a public discussion channel is available, propose a separation based coding scheme, and establish its optimality when the channel output symbols of the legitimate receiver and eavesdropper are conditionally independent given the input. Index Terms—Information theoretic security, joint sourcechannel coding, public discussion, secret-key agreement, wiretap channel. I.