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IEEE Globecom Workshops (GC Wkshps)

Secret key generation from reciprocal spatially correlated MIMO channels

Eduard Axel Jorswieck, Anne Wolf, Sabrina Engelmann

Published Dec 1, 2013• 38 citations
Publisher

Abstract

Secret key generation from reciprocal multi-antenna channels is an interesting alternative to cryptographic key management in wireless systems without infrastructure access. In this work, we study the secret key rate for the basic source model with a MIMO channel. First, we derive an expression for the secret key rate under spatial correlation modelled by the Kronecker model and with spatial precoding at both communication nodes. Next, we analyze the result for uncorrelated antennas to understand the optimal precoding for this special case, which is equal power allocation. Then, the impact of correlation is characterized using Majorization theory. Surprisingly for small SNR, spatial correlation increases the secret key rate. For high SNR, the maximum secret key rate is achieved for uncorrelated antennas. The results indicate that a solid system design for reciprocal MIMO key generation is required to establish the secret key rate gains.

DOI
10.1109/glocomw.2013.6825164

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Secret key generation from reciprocal multi-antenna channels is an interesting alternative to cryptographic key management in wireless systems without infrastructure access. In this work, we study the secret key rate for the basic source model with a MIMO channel. First, we derive an expression for the secret key rate under spatial correlation modelled by the Kronecker model and with spatial precoding at both communication nodes. Next, we analyze the result for uncorrelated antennas to understand the optimal precoding for this special case, which is equal power allocation. Then, the impact of correlation is characterized using Majorization theory. Surprisingly for small SNR, spatial correlation increases the secret key rate. For high SNR, the maximum secret key rate is achieved for uncorrelated antennas. The results indicate that a solid system design for reciprocal MIMO key generation is required to establish the secret key rate gains.
In future wireless communication systems, more and more small low-power mobile devices will communicate without infrastructure and internet access. In order to provide a lightweight yet powerful security mechanism, physical layer parameters can be used to generate secret keys for perfect secrecy. In this paper, we study the optimal operation of a multiple antenna link with statistical channel state information at all nodes for secret key generation. The impact of spatial correlation on the achievable secret key rates is characterized. Furthermore, the optimal pilot precoding during channel estimation is computed. Numerical simulations illustrate the results for selected scenarios.
Physical-layer key generation (PKG) based on channel reciprocity has recently emerged as a new technique to establish secret keys between devices. Most works focus on pairwise communication scenarios with single or small-scale antennas. However, the fifth generation (5G) wireless communications employ massive multiple-input multiple-output (MIMO) to support multiple users simultaneously, bringing serious overhead of reciprocal channel acquisition. This paper presents a multi-user secret key generation in massive MIMO wireless networks. We provide a beam domain channel model, in which different elements represent the channel gains from different transmit directions to different receive directions. Based on this channel model, we analyze the secret key rate and derive a closed-form expression under independent channel conditions. To maximize the sum secret key rate, we provide the optimal conditions for the Kronecker product of the precoding and receiving matrices and propose an algorithm to generate these matrices with pilot reuse. The proposed optimization design can significantly reduce the pilot overhead of the reciprocal channel state information acquisition. Furthermore, we analyze the security under the channel correlation between user terminals (UTs), and propose a low overhead multi-user secret key generation with non-overlapping beams between UTs. Simulation results demonstrate the near-optimal performance of the proposed precoding and receiving matrices design and the advantages of the non-overlapping beam allocation.
Secret key generation based on channel measurements has emerged as a meaningful approach to enhance the security of wireless links. The key generation mechanism takes advantage of wireless channel reciprocity and uses the mutual information between legitimate users' channel measurements. However, the rate at which key bits are generated depends on the channel coherence time. Furthermore, eavesdroppers may obtain information to generate the secret key bits if their channels become correlated to the legitimate channels. In this paper, we propose a new approach for key generation that uses MIMO precoding and role switching by legitimate users during the key generation process in order to prevent an eavesdropper whose channel is correlated with the legitimate channel to acquire information that can be used to generate the encryption key, while also ensuring that the rate at which uncorrelated key bits are generated does not depend on the channel coherence time. The proposed approach is supported by an information theoretic analysis and is illustrated with numerical results obtained from simulations showing that, even when the legitimate and eavesdropper channels are correlated, the bit mismatch rate at the eavesdropper does not improve with increasing SNR, while that at the legitimate users improves.
Establishing secret keys from the commonly-observed randomness of reciprocal wireless propagation channels has recently received considerable attention. In this work we propose improved strategies for channel estimation between MIMO or beamforming systems for secret key generation. The amount of mutual information that can be extracted from the channel matrix estimates is determined by the quality of channel matrix estimates. By allocating increased energy to channel estimation for higher gain beamforming combinations at the expense of low-gain combinations, key establishment performance can be increased. Formalizing the notion of preferential energy allocation to the most efficient excitations is the central theme of this dissertation. For probing with beamforming systems, we formulate a theoretically optimal probing strategy that upper bounds the number of key bits that can be generated from reciprocal channel observations. Specifically, we demonstrate that the eigenvectors of the channel spatial covariance matrix should be used as beamformer weights during channel estimation and we optimize the energy allocated to channel estimation for each beamformer weight under a total energy constraint. The optimal probing strategy is not directly implementable in practice, and therefore we propose two different modifications to the optimal algorithm based on a Kronecker approximation to the spatial covariance matrix. Though these approximations are suboptimal, they each perform well relative to the upper bound. To explore how effective an array is at extracting all of the information available in the propagation environment connecting two nodes, we apply the optimal beamformer probing strategy to a vector current basis function expansion on the array volume. We prove that the resulting key rate is a key rate spatial bound that upper bounds the key rate achievable by any set of antenna arrays probing the channel with the same total energy constraint. For MIMO systems we assume the channel is separable with a Kronecker model, and then for that model we propose an improved probing strategy that iteratively optimizes the energy allocation for each node using concave maximization. The performance of this iterative approach is better than that achieved using the traditional probing strategy in many realistic probing scenarios.
We consider a wireless communication scenario where two agents aim at agreeing on a secret key, while leaving a passive eavesdropper in the darkness. All terminals are equipped with multiple antennas resulting in a multiple input multiple output (MIMO) scenario with reciprocal correlated flat Rayleigh fading channels among antenna couples. Correlation properties are known to all agents. In order to limit complexity we focus only on pilot-based secret key agreement (SKA), resulting in a source model with wiretapper, where pilot sequences are known to all agents. The contribution of the paper is twofold: a) we derive closed form expressions of lower and upper bounds of the secret key achievable rates, and b) we address the training sequence optimization taking into account the spatial channel correlation. A reduced dimensionality problem is obtained when spatial correlation follows a Kronecker model and looser bounds are discussed. Numerical results in a cellular scenario, with reference to the cellular 3GPP MIMO channel model, show significant gains by the training sequence optimization.
Secret-key generation in a wireless environment exploiting the randomness and reciprocity of the channel gains is considered. A new channel model is proposed which takes into account the effect of reflections (or re-radiations) from receive antenna elements, thus capturing an physical property of practical antennas. It turns out that the reflections have a deteriorating effect on the achievable secret-key rate between the legitimate nodes at high signal-to-noise-power-ratio (SNR). The insights provide guidelines in the design and operation of communication systems using the properties of the wireless channel to prevent eavesdropping.