Physical-layer Group Secret-Key (GSK) generation is an effective way of synthesizing symmetric keys across multiple nodes in wireless networks. Unlike the case of two-user key generation, GSK generation necessitates some nodes to act as facilitators, which broadcast linear combinations of the channel realizations thereby assisting all the nodes to witness the intended common source of randomness. However, in practice, radio devices are designed to transmit symbols from finite complex constellations, and as a result, the channel realizations are typically quantized by the facilitator which in turn impacts the overall secret-key rate. Identifying this issue, we propose a class of GSK generation protocols, called Symmetrically Quantized GSK (SQGSK) protocols, in a network of three nodes. In the proposed protocols, due to quantization of symbols at the facilitator, the other two nodes also quantize their channel realizations, and use them appropriately to generate the keys. Under special conditions, we analytically show that the SQGSK protocols provide higher key-rate than the baselines wherein only the facilitator quantizes the channel realizations. We use extensive simulations to demonstrate the benefits of the proposed protocols when the facilitator employs finite constellations such as 4-, 16-, and 64-QAM.
Physical-layer Group Secret-Key (GSK) generation is an effective way of synthesizing symmetric keys across multiple nodes in wireless networks. Unlike the case of two-user key generation, GSK generation necessitates some nodes to act as facilitators, which broadcast linear combinations of the channel realizations thereby assisting all the nodes to witness the intended common source of randomness. However, in practice, radio devices are designed to transmit symbols from finite complex constellations, and as a result, the channel realizations are typically quantized by the facilitator which in turn impacts the overall secret-key rate. Identifying this issue, we propose a class of GSK generation protocols, called Symmetrically Quantized GSK (SQGSK) protocols, in a network of three nodes. In the proposed protocols, due to quantization of symbols at the facilitator, the other two nodes also quantize their channel realizations, and use them appropriately to generate the keys. Under special conditions, we analytically show that the SQGSK protocols provide higher key-rate than the baselines wherein only the facilitator quantizes the channel realizations. We use extensive simulations to demonstrate the benefits of the proposed protocols when the facilitator employs finite constellations such as 4-, 16-, and 64-QAM.
Group secret-key (GSK) generation using temporal variation in wireless channels is an effective way of synthesizing symmetric keys across multiple nodes (more than two) in wireless networks. Unlike the case of two-node key-generation, GSK generation necessitates some nodes to act as facilitators by transmitting linear combinations of the channel realizations. However, in practice, radio devices are designed to transmit baseband signals from finite complex constellations. Due to such constraints, the linear combinations of channel realizations are typically quantized by the facilitator which in turn impacts the overall secret-key rate. Identifying this issue, we propose a practical GSK generation protocol in a network of three nodes. Under special conditions, we analytically show that the proposed method provides higher key-rate than the case when only the facilitator quantizes the channel realizations before transmission. Through simulations, we show that the proposed method yields higher key-rate than the baselines when the facilitator employs finite constellations such as 4-, 16-, and 64-QAM.
It is well known that physical-layer Group Secret-Key (GSK) generation techniques allow multiple nodes of a wireless network to synthesize a common secret-key, which can be subsequently used to keep their group messages confidential. As one of its salient features, the wireless nodes involved in physical-layer GSK generation extract randomness from a subset of their wireless channels, referred as the common source of randomness (CSR). Unlike two-user key generation, in GSK generation, some nodes must act as facilitators by broadcasting quantized versions of the linear combinations of the channel realizations, so as to assist all the nodes to observe a CSR. However, we note that broadcasting linear combination of channel realizations incurs non-zero leakage of the CSR to an eavesdropper, and moreover, quantizing the linear combination also reduces the overall key-rate. Identifying these issues, we propose a practical GSK generation protocol, referred to as Algebraic Symmetrically Quantized GSK (A-SQGSK) protocol, in a network of three nodes, wherein due to quantization of symbols at the facilitator, the other two nodes also quantize their channel realizations, and use them appropriately over algebraic rings to generate the keys. First, we prove that the A-SQGSK protocol incurs zero leakage to an eavesdropper. Subsequently, on the CSR provided by the A-SQGSK protocol, we propose a consensus algorithm among the three nodes, called the Entropy-Maximization Error-Minimization (EM-EM) algorithm, which maximizes the entropy of the secret-key subject to an upper-bound on the mismatch-rate. We use extensive analysis and simulation results to lay out guidelines to jointly choose the parameters of the A-SQGSK protocol and the EM-EM algorithm.
In physical-layer Group Secret-Key (GSK) generation, multiple nodes of a wireless network synthesize symmetric keys by observing a subset of their channel realizations, referred to as the common source of randomness (CSR). Unlike the case of two-user key generation, exchanging pilot symbols within the coherence-block is not sufficient to arrive at a CSR. In addition, some nodes must act as facilitators by broadcasting linear combinations of the channel realizations within the coherence-block, thereby giving rise to low-latency requirement for sharing the CSR. To assist the latency constraint, practical radio devices are forced to quantize the linear combination of channel realizations directly to finite complex constellations before broadcasting them to the other nodes. First, we show that this direct quantization at the facilitator results in asymmetric noise levels at the nodes, which in turn impacts the overall key-rate.Identifying the above issue, we propose a practical GSK generation protocol, referred to as Algebraic Symmetrically Quantized GSK (A-SQGSK) protocol, in a network of three nodes. In the proposed protocol, due to quantization of symbols at the facilitator, the other two nodes also quantize their channel realizations, and use them appropriately over algebraic rings to generate the keys. Under special conditions, we analytically show that the A-SQGSK protocol provides higher key-rate than the baselines, and also prove that the proposed protocol incurs zero leakage to an external eavesdropper. We also use extensive simulation results to demonstrate the benefits of the proposed protocol at different regimes of signal-to-noise-ratios.
It is well known that physical-layer Group Secret-Key (GSK) generation techniques allow multiple nodes of a wireless network to synthesize a common secret-key, which can be subsequently used to keep their group messages confidential. As one of its salient features, the wireless nodes involved in physical-layer GSK generation extract randomness from a subset of their wireless channels, referred as the common source of randomness (CSR). Unlike two-user key generation, in GSK generation, some nodes must act as facilitators by broadcasting quantized versions of the linear combinations of the channel realizations, so as to assist all the nodes to observe a CSR. However, we note that broadcasting linear combination of channel realizations incurs non-zero leakage of the CSR to an eavesdropper, and moreover, quantizing the linear combination also reduces the overall key-rate. Identifying these issues, we propose a practical GSK generation protocol, referred to as Algebraic Symmetrically Quantized GSK (A-SQGSK) protocol, in a network of three nodes, wherein due to quantization of symbols at the facilitator, the other two nodes also quantize their channel realizations, and use them appropriately over algebraic rings to generate the keys. First, we prove that the A-SQGSK protocol incurs zero leakage to an eavesdropper. Subsequently, on the CSR provided by the A-SQGSK protocol, we propose a consensus algorithm among the three nodes, called the Entropy-Maximization Error-Minimization (EM-EM) algorithm, which maximizes the entropy of the secret-key subject to an upper-bound on the mismatch-rate. We use extensive analysis and simulation results to lay out guidelines to jointly choose the parameters of the A-SQGSK protocol and the EM-EM algorithm.
It is well known that physical-layer key generation methods enable wireless devices to harvest symmetric keys by accessing the randomness offered by the wireless channels. Although two-user key generation is well understood, group secret-key (GSK) generation, wherein more than two nodes in a network generate secret-keys, still poses open problems. Recently, Manish Rao et al., have proposed the Algebraic Symmetrically Quantized GSK (A-SQGSK) protocol for a network of three nodes wherein the nodes share quantized versions of the channel realizations over algebraic rings, and then harvest a GSK. Although A-SQGSK protocol guarantees confidentiality of common randomness to an eavesdropper, we observe that the key-rate of the protocol is poor since only one channel in the network is used to harvest GSK. Identifying this limitation, in this paper, we propose an opportunistic selection method wherein more than one wireless channel is used to harvest GSKs without compromising the confidentiality feature, thereby resulting in remarkable improvements in the key-rate. Furthermore, we also propose a log-likelihood ratio (LLR) generation method for the common randomness observed at various nodes, so that the soft-values are applied to execute LDPC codes based reconciliation to reduce the bit mismatches among the nodes.
Physical-layer group secret-key (GSK) generation is an effective way of generating secret keys in wireless networks, wherein the nodes exploit inherent randomness in the wireless channels to generate group keys, which are subsequently applied to secure messages while broadcasting, relaying, and other network-level communications. While existing GSK protocols focus on securing the common source of randomness from external eavesdroppers, they assume that the legitimate nodes of the group are trusted. In this paper, we address insider attacks from the legitimate participants of the wireless network during the key generation process. Instead of addressing conspicuous attacks such as switching-off communication, injecting noise, or denying consensus on group keys, we introduce stealth attacks that can go undetected against state-of- the-art GSK schemes. We propose two forms of attacks, namely: (i) different-key attacks, wherein an insider attempts to generate different keys at different nodes, especially across nodes that are out of range so that they fail to recover group messages despite possessing the group key, and (ii) low-rate key attacks, wherein an insider alters the common source of randomness so as to reduce the key-rate. We also discuss various detection techniques, which are based on detecting anomalies and inconsistencies on the channel measurements at the legitimate nodes. Through simulations we show that GSK generation schemes are vulnerable to insider-threats, especially on topologies that cannot support additional secure links between neighbouring nodes to verify the attacks.