Opt Express. 2022 Dec 5;30(25):45862-45882. doi: 10.1364/OE.476856.
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.
从大气光学信道中提取密钥，可以生成两个通信方用来加密其传输的机密信息的公共密钥。湍流引起的光闪烁的相关时间限制了每秒提取的不相关密钥位的数量。为了打破这种限制，我们提出了一种新的方案，即使用配备随机调制的大气光学信道，在两个通信方之间共享随机数，并为这种随机数共享方案产生的公共随机源建立数学模型。我们的随机数共享方案为合法方提供了降低上述公共随机源的时间自相关的能力，即具有记忆的可控公共随机源（CCRSM），从而实现了增强的密钥提取，可以打破上述限制。合法方对 CCRSM 的观测的自相关以及两个合法方对 CCRSM 的观测的互相关都进行了理论上的公式化和检验。结果发现，执行随机调制可以使合法方使用小于由湍流引起的光闪烁的相关时间的采样间隔去解相关 CCRSM 的连续观测。从理论上处理了窃听者和合法方对 CCRSM 的观测的互相关系数，并检验了在完全公开单调制最坏窃听（FDSM-WE）场景、部分公开单调制最坏窃听（PDSM-WE）场景和双调制最坏窃听（DM-WE）场景中基于 CCRSM 的密钥提取的窃听风险。结果表明，FDSM-WE 场景具有最高的窃听风险。最后，从信息论的角度理论上制定了考虑使用 CCRSM 时的密钥容量的最低限制。从信息论的角度定量分析了随机调制对这个最低限制的影响。结果表明，随机调制不会损害从 CCRSM 的随机性组件中提取密钥的潜力，而这种随机性组件源于湍流引起的光闪烁。
