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Infrared and Laser Engineering

Study on extraction of true random numbers based on propagated laser speckle in atmospheric turbulence

刘中辉 LIU Zhong-hui, 陈纯毅 Chen Chunyi, Haifeng Yao, 潘 石 Pan Shi, 向 磊 Xiang Lei, 娄 岩 Lou Yan, 倪小龙 Ni Xiaolong

Published Jan 1, 2019• 2 citations
Publisher
DOI
10.3788/irla201948.1205005

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Random numbers represent a fundamental ingredient for secure communications and numerical simulation as well as to games and in general to Information Science. Physical processes with intrinsic unpredictability may be exploited to generate genuine random numbers. The optical propagation in strong atmospheric turbulence is here taken to this purpose, by observing a laser beam after a 143 km free-space path. In addition, we developed an algorithm to extract the randomness of the beam images at the receiver without post-processing. The numbers passed very selective randomness tests for qualification as genuine random numbers. The extracting algorithm can be easily generalized to random images generated by different physical processes.
We examine the impact of the atmospheric turbulence on a recently discovered type of classical entanglement of partially coherent beams endowed with a twist phase. We derive a compact analytical expression for the Schmidt number of a bi-orthogonal decomposition of the Wigner function of a twisted Gaussian Schell-model (TGSM) beam propagating through the turbulent atmosphere. We elucidate conditions for a TGSM source to generate a strongly classically entangled paraxial field over a desired propagation distance in the turbulent atmosphere. Our results will find applications to free-space optical communications and motivate further research into classical entanglement with random light.
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.