Optical key distribution system using atmospheric turbulence as the randomness generating function: classical optical protocol for information assurance
Marvin D. Drake, Christophe F. Bas, David R. Gervais, Priscilla F. Renda, Daniel Townsend, Joseph J. Rushanan, Joe Francoeur, Nick Donnangelo, Michael D. Stenner
We describe an experimental laboratory system that generates and distributes random binary sequence bit streams between two optical terminals (labeled Alice and Bob). The random binary sequence is generated through probing the optical channel of a turbulent atmosphere between the two terminals with coincident laser beams. The two laser beams experience differential phase delays while propagating through the atmospheric optical channel. The differential phase delays are detected and sampled at each terminal to yield raw random bit streams. The random bit streams are processed to remove bit errors and, through privacy amplification, to yield a bit stream known only to Alice and Bob. The same chaotic physical mechanism that provides randomness also provides confidentiality. The laboratory system yielded secret key bit rates of a few bits/second . For external optical channels over longer channel lengths with atmospheric turbulence levels, secret bit rates of 10 s of bits/second are predicted.
We describe an experimental laboratory system that generates and distributes random binary sequence bit streams between two optical terminals (labeled Alice and Bob). The random binary sequence is generated through probing the optical channel of a turbulent atmosphere between the two terminals with coincident laser beams. The two laser beams experience differential phase delays while propagating through the atmospheric optical channel. The differential phase delays are detected and sampled at each terminal to yield raw random bit streams. The random bit streams are processed to remove bit errors and, through privacy amplification, to yield a bit stream known only to Alice and Bob. The same chaotic physical mechanism that provides randomness also provides confidentiality. The laboratory system yielded secret key bit rates of a few bits/second . For external optical channels over longer channel lengths with atmospheric turbulence levels, secret bit rates of 10 s of bits/second are predicted.
This paper investigates the extent to which atmospheric turbulence can be exploited as a random bit generator. Atmospheric turbulence is considered an inherently random process due to the complex inhomogeneous system composition and its sensitivity to changes in pressure, temperature, humidity, and wind conditions. A self-calibrating Mach-Zehnder interferometer was used to collect phase fluctuations in the temporal domain introduced to an optical beam propagating through the atmosphere. The recorded phase fluctuations were converted into bit streams that were further analyzed in order to search for evidence of randomness. Empirical data and results that characterize the degree of randomness produced in the temporal phase component of an optical wave propagating through the atmosphere are presented.
In our recent paper, we proposed the secret-key generation (SKG) scheme leveraging both atmospheric turbulence and background radiation as sources of randomness, which provides high secret-key rates and is compatible with state-of-the-art optical communications. Unfortunately, its application is limited to the symmetric line-of-sight free-space optical (FSO) links. In this paper, we propose two SKG schemes suitable for asymmetric and non-line-of-sight (NLOS) communications over FSO links. The proposed schemes employ turbulence, solar background radiation, and post-quantum cryptography-based randomly generated Alice and Bob's PSK sequences. To reduce the system cost, an unmodulated carrier is transmitted alongside the modulated PSK signal. On the receiver side, the coherent detection is performed by beating the unmodulated carrier with the received modulated signal on the PIN-photodetector (or the avalanche photodiode), followed by the DC blocker to remove undesired DC components. The proposed SKG schemes are applicable to both physical-layer security (PLS) cryptosystems and protocols similar to the quantum key distribution (QKD). The proposed SKG schemes show excellent tolerance to the atmospheric turbulence effects compared to the traditional PLS schemes. Experimental results indicate that the secret-key capacity of the NLOS SKG scheme is significantly higher than the corresponding traditional PLS counterpart.
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.
To overcome the limitations of QKD, post-quantum cryptography, and computational security-based cryptography protocols in this paper, an atmospheric turbulence-controlled cryptosystem is proposed. The proposed encryption scheme employs the traditional scheme to utilize the atmospheric turbulence as the common source of randomness only in the initialization stage to determine the common parameters to be used in the proposed encryption scheme. To overcome low secret-key rates of traditional scheme, dictated by the long coherence time Tc of turbulence channel, the proposed encryption scheme updates the parameters of gamma-gamma distribution, used to generate irradiance samples for cumulative distribution function-based determination of the key, every Tc seconds and as such the final key is shaped by the atmospheric turbulence channel. We also describe a scheme that randomly selects one of several available paths in which the simultaneously measured irradiance samples, after interleaving, are used to generate the raw key. The secret-key rates of the proposed schemes are orders of magnitude higher compared to corresponding traditional QKD and source type physical-layer security schemes and are comparable with the state-of-the-art optical communication data rates.
Abstract Much scientific work has focused on the generation of random numbers as well as the distribution of said random numbers for use as a cryptographic key. However, emphasis is often placed on one of the two to the exclusion of the other, but both are often simultaneously important. Here we present a simple hybrid free-space link scheme for both the generation and secure distribution of (pseudo-)random numbers between two remote parties, drawing the randomness from the stochastic nature of atmospheric turbulence. The atmosphere is simulated using digital micro-mirror devices for efficient, all-digital control. After outlining one potential algorithm for extracting random numbers based on finding the centre-of-mass (COM) of turbulent beam intensity profiles, the statistics of our experimental COM measurements is studied and found to agree well with the literature. After implementing the scheme in the laboratory, Alice and Bob are able to establish a string of correlated random bits with an 84% fidelity. Finally, we make a simple modification to the original setup in an attempt to thwart the hacking attempts of an eavesdropper, Eve, who has access to the free-space portion of the link. We find that the fidelity between Eve’s key and that of Alice/Bob is 54%, only slightly above the theoretical minimum. Atmospheric turbulence could hence be leveraged as an added security measure, rather than being seen as a drawback.
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.