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Optics Express

Shared secret key generation from signal fading in a turbulent optical wireless channel using common-transverse-spatial-mode coupling

Chunyi Chen, Huamin Yang

Published Jun 13, 2018• 24 citations
Publisher

Abstract

Common randomness arising from turbulence-induced signal fading in reciprocal optical wireless channels is a beneficial resource that can be used to generate secret keys shared by two legitimate parties. The concept of optical wireless channels using common-transverse-spatial-mode coupling (CTSMC) that can maintain perfect fading reciprocity in atmospheric turbulence is first developed in a general manner. Subsequently, by performing Monte Carlo simulations, the Johnson SB probability distribution is demonstrated to be appropriate for statistical description of turbulence-induced signal fading in an optical wireless channel constructed by use of two identical CTSMC transceivers, and the nature of correlation between signal fadings detected by two contiguous reception spatial modes is further quantitatively characterized, revealing that rapid spatial decorrelation between signal fadings observed by a legitimate party and an eavesdropper holds for scenarios of practical interest. Finally, the information theoretic capacity for generating secret keys from CTSMC-based optical wireless channels is theoretically formulated and quantitatively examined under different conditions, manifesting that the turbulence strength and average electrical signal-to-noise ratio have a noticeable combined impact on the secret key capacity, especially in the far-field case.

DOI
10.1364/oe.26.016422

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Common randomness arising from turbulence-induced signal fading in reciprocal optical wireless channels is a beneficial resource that can be used to generate secret keys shared by two legitimate parties. The concept of optical wireless channels using common-transverse-spatial-mode coupling (CTSMC) that can maintain perfect fading reciprocity in atmospheric turbulence is first developed in a general manner. Subsequently, by performing Monte Carlo simulations, the Johnson SB probability distribution is demonstrated to be appropriate for statistical description of turbulence-induced signal fading in an optical wireless channel constructed by use of two identical CTSMC transceivers, and the nature of correlation between signal fadings detected by two contiguous reception spatial modes is further quantitatively characterized, revealing that rapid spatial decorrelation between signal fadings observed by a legitimate party and an eavesdropper holds for scenarios of practical interest. Finally, the information theoretic capacity for generating secret keys from CTSMC-based optical wireless channels is theoretically formulated and quantitatively examined under different conditions, manifesting that the turbulence strength and average electrical signal-to-noise ratio have a noticeable combined impact on the secret key capacity, especially in the far-field case.
Secret-key distribution leveraging the fading characteristics of wireless optical channels has attracted significant attention. To address the challenges of high-frequency sampling over slowly varying channels, a turbulence-induced fading scrambling-assisted key distribution scheme is proposed to enhance the randomness of shared keys. Combined with random modulation, the scheme enables legitimate parties to obtain more decorrelated wireless signal sequences. Additionally, a specialized interleave quantization (IQ) method is introduced to improve the statistical properties of the generated keys. The entire observation sequence is processed using IQ to mitigate the impact of large-scale slow channel variations. Simulation and experimental results demonstrate that the proposed scheme generates highly random original key sequences at high sampling frequencies without increasing the key disagreement rate (KDR). The final key sequence, incorporating random modulation and interleaving, is evaluated using the NIST test suite, yielding p-values greater than 0.01. These results confirm the effectiveness of the proposed scheme in generating statistically random shared secret keys under slowly varying wireless optical channels.
Secret-key extraction from atmospheric optical channels can generate common keys used by two communicating parties to encrypt their transmitted confidential information. The correlation time of turbulence-induced optical fluctuations imposes a restriction on the number of extracted uncorrelated key bits per second. To break this restriction, we propose a novel randomness sharing scheme between two communicating parties using an atmospheric optical channel equipped with random modulation and develop mathematical models for the common randomness source created by such a randomness-sharing scheme. Our randomness-sharing scheme provides the legitimate parties with the ability to decrease the temporal autocorrelation of the said common randomness source, which is called controllable common randomness source with memory (CCRSM), thereby enabling an enhanced secret-key extraction that can break the aforementioned restriction. Both the autocorrelation of the legitimate parties' observations of the CCRSM and the cross-correlation of the two legitimate parties' observations of the CCRSM are formulated and examined theoretically. It is found that the performing random modulation can decorrelate consecutive observations of the CCRSM obtained by the legitimate parties using a sampling interval smaller than the correlation time of turbulence-induced optical fluctuations. The cross-correlation coefficient of the eavesdropper's and legitimate parties' observations of the CCRSM is dealt with theoretically and the eavesdropping risk in the CCRSM-based key extraction is inspected for the fully-disclosed-single-modulation worst eavesdropping (FDSM-WE) scenario, partially-disclosed-single-modulation worst eavesdropping (PDSM-WE) scenario and double-modulation worst eavesdropping (DM-WE) scenario. It is shown that the FDSM-WE scenario has the highest degree of eavesdropping risk. Finally, the lowest limit of the secret-key capacity in consideration of using the CCRSM is theoretically formulated. The effects of random modulation on such the lowest limit are quantitatively analyzed from an information-theoretic perspective. It is manifested that random modulation does not harm the potential of extracting secret keys from the CCRSM's randomness component stemming from turbulence-induced optical fluctuations.
Utilizing reciprocal atmospheric turbulence as a physical entropy source for extracting random secret key is an effective means to achieve physical layer security in wireless channels. To study the impact of turbulence intensity on secret key extraction rate in atmospheric optical channels, this paper conducted a bi-directional synchronous atmospheric channel laser transmission experiment, analyzed the experimental data from three different time periods, and tested the KolmogorovSmirnov (KS) fitting efficiency values for five types of probability distribution normalized received signals. Comparative analysis shows that Johnson SB and Log-Normal distributions have the most ideal fitting effects on data. Based on these distribution parameters, a theoretical model of key capacity was constructed. The Monte Carlo method was used to simulate the secret key extraction rates under different turbulence intensities and different probability distribution models. The analysis results show that under weak turbulence conditions, using Johnson SB distribution yields about 87% higher average maximum secret key extraction rate than using Log-Normal distribution; under medium turbulence conditions, there is no significant difference in secret key extraction rates between the two distribution models. Compared with Log-Normal distribution, Johnson SB distribution is more suitable for secret key extraction under medium to weak turbulence intensities.
Wireless channel reciprocity can be successfully exploited as a common source of randomness for the generation of a secret key by two legitimate users willing to achieve confidential communications over a public channel. This paper presents an analytical framework to investigate the theoretical limits of secret-key generation when wireless multi-dimensional Gaussian channels are used as source of randomness. The intrinsic secrecy content of wide-sense stationary wireless channels in frequency, time and spatial domains is derived through asymptotic analysis as the number of observations in a given domain tends to infinity. Some significant case studies are presented where single and multiple antenna eavesdroppers are considered. In the numerical results, the role of signal-to-noise ratio, spatial correlation, frequency and time selectivity is investigated.
Fundamental limits of secret-key agreement over reciprocal wireless channels are investigated. We consider a two-way block-fading channel where the channel gains in the forward and reverse links between the legitimate terminals are correlated. The channel gains between the legitimate terminals are not revealed to any terminal, whereas the channel gains of the eavesdropper are revealed to the eavesdropper. We propose a two-phase transmission scheme, that reserves a certain portion of each coherence block for channel estimation, and the remainder of the coherence block for correlated source generation. The resulting secret-key involves contributions of both channel sequences and source sequences, with the contribution of the latter becoming dominant as the coherence period increases. We also establish an upper bound on the secret-key capacity, which has a form structurally similar to the lower bound. Our upper and lower bounds coincide in the limit of high signal-to-noise-ratio (SNR) and large coherence period, thus establishing the secret-key agreement capacity in this asymptotic regime. Numerical results indicate that the proposed scheme achieves significant gains over training-only schemes, even for moderate SNR and small coherence periods, thus implying the necessity of randomness-sharing in practical secret-key generation systems.
This paper presents a practical key generation algorithm based on the reciprocity of wireless fading channels. A broadband chaotic signal is employed for transmission so that the fading is frequency selective. In this case, signal components in the frequency domain spaced greater than the coherence bandwidth of the channel can be considered uncorrelated. The proposed algorithm exploits this property to generate a unique shared key between two parties. The nonperiodicity of the chaotic signal provides a unique signal for key generation, which can be used even with static fading channels. The proposed approach is robust to timing differences between the parties because the frequency spectrum of the signals is employed. A technique for information reconciliation is presented which does not reveal any information about the values used to generate the key. The randomness of the key is confirmed, and the effects of additive white Gaussian noise and timing differences on the performance of the algorithm are examined.