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Entropy

Cooperative Jamming-Based Physical-Layer Group Secret and Private Key Generation

Shiming Fu, Tong Ling, Jun Yang, Yong Li

Published Sep 4, 2024• 1 citation
Publisher

Abstract

This paper explores physical layer group key generation in wireless relay networks with a star topology. In this setup, the relay node plays the role of either a trusted or untrusted central node, while one legitimate node (Alice) acts as the reference node. The channel between the relay and Alice serves as the reference channel. To enhance security during the channel measurement stage, a cooperative jamming-based scheme is proposed in this paper. This scheme allows the relay to obtain superimposed channel observations from both the reference channel and other relay channels. Then, a public discussion is utilized to enable all nodes to obtain estimates of the reference channel. Subsequently, the legitimate nodes can agree on a secret key (SK) that remains secret from the eavesdropper (Eve), or a private key (PK) that needs to be secret from both the relay and Eve. This paper also derives the lower and upper bounds of the SK/PK capacity. Notably, it demonstrates that there exists only a small constant difference between the SK/PK upper and lower bounds in the high signal-to-noise ratio (SNR) regime. Simulation results confirm the effectiveness of the proposed scheme for ensuring security and efficiency of group key generation.

DOI
10.3390/e26090758

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This paper explores physical layer group key generation in wireless relay networks with a star topology. In this setup, the relay node plays the role of either a trusted or untrusted central node, while one legitimate node (Alice) acts as the reference node. The channel between the relay and Alice serves as the reference channel. To enhance security during the channel measurement stage, a cooperative jamming-based scheme is proposed in this paper. This scheme allows the relay to obtain superimposed channel observations from both the reference channel and other relay channels. Then, a public discussion is utilized to enable all nodes to obtain estimates of the reference channel. Subsequently, the legitimate nodes can agree on a secret key (SK) that remains secret from the eavesdropper (Eve), or a private key (PK) that needs to be secret from both the relay and Eve. This paper also derives the lower and upper bounds of the SK/PK capacity. Notably, it demonstrates that there exists only a small constant difference between the SK/PK upper and lower bounds in the high signal-to-noise ratio (SNR) regime. Simulation results confirm the effectiveness of the proposed scheme for ensuring security and efficiency of group key generation.
This paper investigates the cooperative jamming based key generation scheme in a cooperative wireless network, where Alice and Bob aim to generate a secret key (SK) that is secret from Eve and a private key (PK) that is secret from both the relay and Eve, with the assistance of a relay. The correlation between legitimate channels and eavesdropping channels is considered. The SK and PK rates are evaluated based on minimum mean square error (MMSE) and zero forcing (ZF) estimation methods, respectively. The analytical expressions are further simplified with asymptotic forms in the high signal-to-noise ratio (SNR) regime. We demonstrate that the MMSE method is optimal to estimate channels, and the ZF method is asymptotically optimal in the high SNR regime. Moreover, we prove that the double-hop key generation strategy cannot achieve a higher rate than the single-hop strategy. Finally, numerical results validate the analysis and demonstrate that the cooperative jamming based key generation scheme significantly outperforms the traditional pairwise key generation scheme.
This paper investigates the performance of key generation between two nodes assisted by a relay in the presence of correlated eavesdropping channels. A cooperative jamming scheme is utilized to impose superimposed channel measurements on the relay and eavesdropper. Both lower and upper bounds on key capacities for both secret key (SK) and private key (PK) generation are evaluated, where the lower bounds are derived by using minimum mean square error and zero forcing methods for channel estimation, and the upper bounds are derived by formulating several enhanced discrete memoryless source (DMS) models. The analytical expressions are further simplified in the high signal-to-noise ratio (SNR) regime. We discover that one of the two legitimate channels should specialize in playing a role of jamming the relay or eavesdropper. We also demonstrate that the derived lower and upper bounds are tight when the eavesdropping channels are lowly or highly correlated. When the eavesdropping channels are uncorrelated, the SK and PK capacities can be determined since the corresponding upper and lower bounds are equal. Moreover, at high SNRs, a constant gap exists between the SK/PK upper and lower bounds as the correlation coefficient becomes one.
Wireless sensor networks (WSNs) are resource-constrained and highly vulnerable to eavesdropping due to their broadcast nature. Traditional symmetric key cryptography provides strong security but imposes excessive computational and energy demands on sensor nodes. Physical layer–based secret key generation (SKG) offers a lightweight alternative by exploiting channel reciprocity and randomness; however, existing methods are mostly limited to two-user scenarios and lack scalability in multi-user settings. This paper introduces two scalable multi-user SKG frameworks: a sequential method and a star topology-based method. In the sequential method, users cooperatively relay random signals to derive a shared key, while the star topology leverages a central node for signal aggregation and redistribution. A comparative analysis reveals trade-offs between the proposed methods. The sequential method is more computationally efficient but sensitive to node failures, while the star topology offers lower delay at the cost of requiring a fully connected central node. Analyses and simulations confirm both methods’ effectiveness in key mismatch probability, key generation rate, and key randomness validated by the National Institute of Standards and Technology test suite.
Secret group key generation based on physical layer in wireless communications has a lot of practical applications. A few studies focused on the theoretical bounds of the secret key rate based on the sets of received signals rather than a particular secret key generation scheme. We propose a secret group key generation scheme for an arbitrary number of legitimate nodes, n, in mesh topology in the presence of a passive eavesdropper. In the scheme, after general pilot signal transmissions at all nodes, each node broadcasts a weighted combination of its received signals with optimized coefficients, so that legitimate nodes can obtain the information of channels used for group key generation while the eavesdropper cannot. We also apply different quantization schemes for quantizing and encoding the estimated channels into keys. To provide detailed transmissions and processing steps of group key generation, we also describe the proposed scheme for 4-node mesh topology case. The simulation results show that the proposed scheme achieves a higher secret group key rate and a lower key disagreement rate than a benchmark scheme.
This paper studies the problem of simultaneously generating a secret key (SK) and a private key (PK) between Alice and Bob, in a cooperative pairwise-independent network (PIN) with two relays. In the PIN, the pairwise source observed by every pair of terminals is independent of those sources observed by any other pairs. The SK needs to be protected from Eve, while the PK needs to be protected not only from Eve but also from the two relays. Two cooperative SK-PK generation algorithms are proposed: both of them first generate common randomness, based on the well-established pairwise key generation technique and the application of the one-time pad; but then, the two algorithms utilize the XOR operation and a specific random-binning-based SK-PK codebook to generate the expected keys, respectively. The achievable SK-PK rate regions of both the two proposed algorithms are analyzed. Of particular interest is the second algorithm with random-bing based codebook, whose achievable key rate region is demonstrated to be exactly the same as the derived outer bound, a crucial step for establishing the key capacity of this PIN model. Finally, the two proposed SK-PK generation algorithms are extended to a cooperative wireless network, where the correlated source observations are obtained from estimating wireless channels during a training phase.
Secret group key generation based on physical layer in wireless communications has a lot of practical applications. A few studies focused on the theoretical bounds of the secret key rate based on the sets of received signals rather than a particular secret key generation scheme. We propose a secret group key generation scheme for an arbitrary number of legitimate nodes, n, in mesh topology in the presence of a passive eavesdropper. In the scheme, after general pilot signal transmissions at all nodes, each node broadcasts a weighted combination of its received signals with optimized coefficients, so that legitimate nodes can obtain the information of channels used for group key generation while the eavesdropper cannot. We also apply different quantization schemes for quantizing and encoding the estimated channels into keys. To provide detailed transmissions and processing steps of group key generation, we also describe the proposed scheme for 4-node mesh topology case. The simulation results show that the proposed scheme achieves a higher secret group key rate and a lower key disagreement rate than a benchmark scheme.