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IEEE Transactions on Antennas and Propagation

Nonreciprocal Radio System Calibration for Propagation-Based Key Generation

Attiya Mahmood, Michael A. Jensen

Published Jul 7, 2019• 1 citation
Publisher

Abstract

Propagation-based secret key generation (SKG) is a physical layer method for establishing encryption keys based on two radios observing a reciprocal propagation channel. However, nonreciprocal contributions to the channel introduced by the radio circuitry significantly degrade the ability to reliably generate keys using such methods, necessitating the development of calibration methods for removing the impact of channel nonreciprocity. This paper uses a total least squares (TLS) algorithm coupled with a detailed model of the multiple-input multiple-output radio frequency circuitry and propagation for the radio system to achieve such a calibration. Simulations show that the method is highly effective in removing the impact of nonreciprocal circuit contributions over a range of operational parameters.

DOI
10.1109/tap.2019.2925177

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Propagation-based secret key generation (SKG) is a physical layer method for establishing encryption keys based on two radios observing a reciprocal propagation channel. However, nonreciprocal contributions to the channel introduced by the radio circuitry significantly degrade the ability to reliably generate keys using such methods, necessitating the development of calibration methods for removing the impact of channel nonreciprocity. This paper uses a total least squares (TLS) algorithm coupled with a detailed model of the multiple-input multiple-output radio frequency circuitry and propagation for the radio system to achieve such a calibration. Simulations show that the method is highly effective in removing the impact of nonreciprocal circuit contributions over a range of operational parameters.
Propagation-based key establishment is a physical layer method for generating encryption keys based on two radios observing a reciprocal propagation channel. This work explores the impact of mutual coupling when communicating nodes are equipped with multiple antennas, multipath richness in the propagation environment, and practical limitations caused by the nonreciprocal nature of RF circuits on key establishment. First, network theory is used to formulate a model of a realistic communication system which incorporates transmit sources and receive loads, impedance matching networks, low-noise amplifiers (LNAs), mutually coupled antenna arrays, and a passive eavesdropper. Afterwards, a detailed analysis is performed to quantify the impact of coupling, type of impedance matching network, and proximity of a multi-antenna eavesdropper on key rate metrics. Next, the degradation on key establishment caused by the radiocircuitry non-reciprocal contributions to the propagation channel is analyzed. A calibration technique based on total least square algorithm is used to overcome the non-reciprocity. Results demonstrate that the method is highly effective in removing the impact of non-reciprocal circuit contributions over a range of operational parameters. Lastly, for key establishment, the propagation conditions can cause the available key rate to be significantly different from the secure key rate which takes into account the presence of a passive eavesdropper. To study this in detail, a realistic multiple-input multiple-output (MIMO) propagation environment is modeled for two communicating radios and an eavesdropper. Afterwards different propagation conditions are assumed and results demonstrate that secure key rate converges to available key rate when K-factor is small and the eavesdropper is not located very close (< 2.5 wavelength) to one of the nodes.
This work integrates electromagnetic analysis with circuit theory to explore the impact of antenna mutual coupling and radio frequency circuit design on the achievable performance of methods that establish secret encryption keys using reciprocal propagation channels. The analysis includes the impact of the impedance match between the coupled antennas and the transmit sources or receiver loads, demonstrating that an optimally-designed matching network can significantly improve the achieved performance. The model is then used to account for the fact that transceiver circuit paths differ during transmission and reception, therefore destroying the channel reciprocity required for key establishment. A total least squares method for removing the impact of the non-reciprocal contributions to the channel is then applied, with the results showing that the algorithm is able to achieve key rates similar to those obtained when the non-reciprocal contributors are known perfectly.
The physical layer secret key generation exploiting wireless channel reciprocity has attracted considerable attention in the past two decades. On-going research have demonstrated its viability in various radio frequency (RF) systems. Most of existing work rely on quantization technique to convert channel measurements into digital binaries that are suitable for secret key generation. However, non-simultaneous packet exchanges in time division duplex systems and noise effects in practice usually create random channel measurements between two users, leading to inconsistent quantization results and mismatched secret bits. While significant efforts were spent in recent research to mitigate such non-reciprocity, no efficient method has been found yet. Unlike existing quantization-based approaches, we take a different viewpoint and perform the secret key agreement by solving a bipartite graph matching problem. Specifically, an efficient dual-permutation secret key generation method, DP-SKG, is developed to match the randomly permuted channel measurements between a pair of users by minimizing their discrepancy holistically. DP-SKG allows two users to generate the same secret key based on the permutation order of channel measurements despite the non-reciprocity over wireless channels. Extensive experimental results show that DP-SKG could achieve error-free key agreement on received signal strength (RSS) with a low cost under various scenarios.
Physical Layer Security (PLS) is emerging as an innovative solution to enhance the security of wireless communications. This work analyzes the impact of a realistic indoor radio propagation on Secrecy Key Generation (SKG) in a Wi-Fi application scenario. This PLS technique is based on the extraction of raw cryptographic keys, taking advantage of the radio propagation phenomena as a source of entropy. In detail, we considered two legitimate nodes, i.e., Alice and Bob, which use the SKG to extract keys from the channel, and a malicious node, i.e., Eve, which acts as a passive eavesdropper and tries to discover the key. The reported results show that legitimate nodes key mismatch is strongly influenced by noise contribution, and the eavesdropper attack performs better with a higher Line-of-Sight (LoS) contribution. Conversely, when the power is evenly spread over all the multipath components, the eavesdropped key mismatch is maintained in the range of 30 – 50 %.
Most secret key generation (SKG) methods need channel estimation and provide insufficient performance especially in time division duplex single input single output (TDD-SISO) system and quasi-static channel scenario. This paper proposed a two-way SKG method which can completely avoid channel estimation and achieve higher SKG rate (SKGR). Firstly, the legitimate users mutually send their own random signal via the reciprocal channel. Then, the multiplication of local random signal and the received signal can be used as common randomness to generate keys. The theoretical and practical SKGRs of the three methods, namely wireless channel based, one-way randomness and two-way randomness, are derived and compared. Simulation and estimation results show that the proposed TW method acquires a better performance not only in theory but also in practice, and the practical SKGR of TW method is time-linear which provides a feasible scheme to significantly improve the SKGR for quasi-static channel scenario.