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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.

The temporal characteristics of the free space optical communication (FSOC) turbulence fading channel are essential for analyzing the bit error rate (BER) performances and compiling the rationale of adaptive signal processing algorithms. However, the investigation is still limited since the majority of temporal sequence generation fails to combine the autocorrelation function (ACF) of the FSOC system parameters, and using the simplified formula results in the loss of detailed information for turbulence disturbances. In this paper, considering the ACF of engineering measurable atmospheric parameters, we propose a continuous-time FSOC channel fading sequence generation model that obeys the Gamma-Gamma (G-G) probability density function (PDF). First, under the influence of parameters such as transmission distance, optical wavelength, scintillation index, and atmospheric structural constant, the normalized channel fading models of ACF and PSD are established, and the numerical solution of the time-domain Gaussian correlation sequence is derived. Moreover, the light intensity generation model obeying the time-domain correlation with statistical distribution information is derived after employing the rank mapping, taking into account the association between the G-G PDF parameters and the large and small scales turbulence fading channels. Finally, the Monte Carlo numerical method is used to analyze the performances of the ACF, PDF, and PSD parameters, as well as the temporal characteristics of the generated sequence, and the matching relationships between these parameters and theory, under various turbulence intensities, propagation distances, and transverse wind speeds. Numerical results show that the proposed temporal sequence generation model highly restores the disturbance information in different frequency bands for the turbulence fading channels, and the agreement with the theoretical solution is 0.999. This study presents essential numerical simulation methods for analyzing and evaluating the temporal properties of modulated signals. When sophisticated algorithms are used to handle FSOC signals, our proposed temporal sequence model can provide communication signal experimental sample data generating techniques under various FSOC parameters, which is a crucial theoretical basis for evaluating algorithm performances.