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IEEE International Conference on Wireless Information Technology and Systems

Bit error rate and efficiency analysis of wireless reciprocal channel key generation

R. K. Sharma, Jon W. Wallace

Published Aug 1, 2010• 3 citations
Publisher

Abstract

This paper has computed the bit error rate (BER) performance of two practical key generation methods CQG and CQA considering Gray coded mapping. An improved efficiency metric was also presented that gives a more realistic indication of key generation performance.
DOI
10.1109/icwits.2010.5612262

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Physical layer secret key can be extracted from wireless fading channels based on channel quantization with guardband (CQG). In this paper, we analyze the key generation efficiency of the CQG protocol. Analytical closed-form expressions of bit error rate (BER) and key generation efficiency are derived for the CQG protocol. In order to further improve the key generation efficiency, we concatenate the CQG protocol with reconciliation. And then, we present a upper bound of key generation efficiency, which can be maximized by careful selecting the guardband region and LDPC codes. The key generation efficiency is also analyzed by considering the attacks in the case of an unauthenticated wireless channel.
Due to non-ideal conditions in the measurements of the wireless channel, high initial bit error rate (BER) in the preliminary key is resulted, which reduces the final secret key generation rate and even causes the secret key generation process fail. Aiming to resolve this problem, we first present and verify an optimal information reconciliation protocol; the validation experiment shows that not only the BER comes down more quickly, but also a higher information rate is achieved. Then, to address the problem of very high initial BER and further improve the efficiency of the secret key generation, we introduce the idea of pre-distillation into the secret key generation system, and present a pre-distillation method, which makes the initial BER comes down quickly, and ensures the subsequent information reconciliation be easily performed; hence the total key generation rate is improved. Experimental results demonstrate that the pre-distillation method has excellent ability of reducing the initial BER, especially in the case of very high initial BER. The combination of our proposed pre-distillation and our optimal information reconciliation is the most efficient one when the initial BER is larger than 0.15, and the information rate is improved by more than forty-nine times when the initial BER is 0.3
Information theoretic limits for random key generation in multiple-input multiple-output (MIMO) wireless systems exhibiting a reciprocal channel response are investigated experimentally with a new three-node MIMO measurement campaign. As background, simple expressions are presented for the number of available key bits, as well as the number of bits that are secure from a close eavesdropper. Two methods for generating secret keys are analyzed in the context of MIMO channels and their mismatch rate and efficiency are derived. A new wideband indoor MIMO measurement campaign in the 2.51- to 2.59-GHz band is presented, whose purpose is to study the number of available key bits in both line-of-sight and nonline-of-sight environments. Application of the key generation methods to measured propagation channels indicates key generation rates that can be obtained in practice for four-element arrays.
Methods of symmetric key establishment using reciprocal quantization of channel parameters in wireless Rayleigh and Rician fading channels are considered. Two important aspects are addressed through generic analysis: impact of a proximity attack by a passive eavesdropper and achievable key establishing rates. The analysis makes use of the National Institute of Standards and Technology statistical test suite applied to the channel quantization bits as the outputs of a random number generator. For proximity attacks, a passive mobile eavesdropper with an ability to approach one of the communicating parties and a possible signal-to-noise ratio advantage is assumed. The minimal required distance from the eavesdropper in order to maintain perfect secrecy during key establishment is evaluated as a function of the Rician factor and quantization depth. For key establishing rates, the maximal rates are evaluated while ensuring that the generated secret key bits pass the entire statistical test suite. The generic analysis is applied to channel-phase quantization and performance in practical systems is considered as well.
As an alternative and appealing approach to providing information security in wireless communication systems, secret key generation at physical layer has demonstrated its potential in terms of efficiency and reliability over traditional cryptographic methods. Without the necessity of a management centre for key distribution or reliance on computational complexity, physical layer key generation protocols enable two wireless entities to extract identical and dynamic keys from the randomness of the wireless channels associated with them.\nIn this thesis, the reliability of secret key generation at the physical layer is examined in practical wireless channels with imperfect channel state information (CSI). Theoretical analyses are provided to relate key match rate with channel's signal-to-noise ratio (SNR), degrees of channel reciprocity, and iterations of information reconciliation.\nIn order to increase key match rate of physical layer secret key generation, improved schemes in the steps of channel estimation and sample quantization are proposed respectively. In the channel estimation step, multiple observations of the wireless channels are integrated with a linear processor to provide a synthesized and more accurate estimation of the wireless channel. In the sample quantization step, a magnitude based quantization method with two thresholds is proposed to quantize partial samples, where specific quantization areas are selected to reduce cross-over errors. Significant improvements in key match rate are proven for both schemes in theoretical analysis and numerical simulations. Key match rate can even achieve 100% in both schemes with the assistance of information reconciliation process.\nIn the end, a practical application of physical layer secret key generation is presented, where dynamic keys extracted from the wireless channels are utilized for securing secret data transmission and providing efficient access control.
The basis of generating secret key from the common wireless channel at two communication parties is reciprocity. However, due to non-simultaneous measurements and unavoidable estimation error, bias always exists and key disagreement occurs. In this paper, performance analysis and improvements for key generation exploiting imperfect channel statement information (CSI) is studied. Firstly, the closed-form expression for key disagreement rate (KDR) is derived to evaluate the key mismatch caused by time delay and estimation error. Secondly, the energy efficiency involving power allocation between key generation and private data transmission is presented. After that, a neural network based prediction (NNBP) algorithm is proposed to improve the key consistency. Simulation results verify the theoretical analysis and show that NNBP achieves significant improvements. And it's interesting to find that NNBP algorithm achieves a higher performance gain in low signal-to-noise ration (SNR) and high delay condition, which is different from other methods, like guard band based quantizer (GBBQ).