XXVIII Международный симпозиум «Оптика атмосферы и океана. Физика атмосферы»
Coherence of counter-propagating beams in a confidential communication system based on generation of cryptographic keys at the expense of atmospheric turbulence
V. P. Aksenov, Vadim V. Dudorov, В. В. Колосов, Cheslav E. Pogutsa
Analytical equations for mutual spatial coherence functions of counter-propagating laser beams in integrated transmit/receive optical systems are derived. These equations being fourfold integrals allow estimating the diffraction parameters of transceivers and turbulent propagation conditions, under which a cryptographic key can be generated based on the principle of reciprocity. For particular cases, the degree of coherence of counter-propagating beams and the degree of coherence averaged over the receiver aperture are calculated as functions of generalized parameters describing the turbulence intensity and diffraction at the apertures.
Analytical equations for mutual spatial coherence functions of counter-propagating laser beams in integrated transmit/receive optical systems are derived. These equations being fourfold integrals allow estimating the diffraction parameters of transceivers and turbulent propagation conditions, under which a cryptographic key can be generated based on the principle of reciprocity. For particular cases, the degree of coherence of counter-propagating beams and the degree of coherence averaged over the receiver aperture are calculated as functions of generalized parameters describing the turbulence intensity and diffraction at the apertures.
Abstract The potentials for and limitations to the use of intensity fluctuations of laser beams propagating through a turbulent atmosphere for generating random data when keying in confidential optical communication systems are analyzed. The technique is based on the reciprocity theorem for optical fields. Light propagation in a system of two transceivers directed at each other, the signals from which are distorted by an atmospheric channel, is numerically simulated. An experimental setup is created; the generation of random correlated signals in this system is experimentally studied. A need for low-pass filtration of signals received is experimentally ascertained. The efficiency of this filtration is estimated. The dependences of the correlation coefficient on the geometrical parameters of the system and turbulent conditions along the propagation path are derived from the numerical simulation in a wide range of distances, aperture radii, and turbulence strength values. Theoretical results are shown to be in a good agreement with the results of laboratory experiments.
The security of transmission and retrieval depends on the encryption of information sent over public networks. At present, approaches to data protection based on cryptography methods using one-way mathematical functions are widely used. Symmetric and asymmetric methods of key transmission over open communication channels have been developed. The stability of information protection methods using one-way mathematical functions is based on the algorithmic complexity of their hacking for modern computers. The emergence of quantum computers of sufficient power will radically change the situation. Therefore, at present, the question of developing methods for distributing cryptographic keys based on new principles is acute. Such methods include quantum cryptography and cryptography based on stochastic physical processes. In this work, a brief review of the key generation methods based on the principles of quantum physics is carried out, and then the possibility of using fluctuations of the received radiation power caused by atmospheric turbulence to generate keys is investigated. Numerical and experimental modeling of the process of wave propagation in a system of two coupled transceivers operating in a turbulent medium (atmosphere) has been performed. For this purpose, appropriate algorithms for numerical simulation of the characteristics of optical fields distorted by the atmospheric propagation channel have been developed. An experimental setup has been developed and a model experimental study of the formation of correlated random signals in transmit-receive laser systems has been carried out. The need to use low-frequency filtering of the received signals was found. The efficiency of this filtration has been studied. The results of the work allow us to conclude that the use of atmospheric turbulence as a random signal generator makes it possible to form an almost identical cryptographic key in two communication channels directed towards each other.
Abstract Quantum Key Distribution (QKD) has been widely applied due to its theoretical one-time pad encryption. Typically employing laser beam as carrier, quantum states are transmitted through optical fibers or free-space channels, with the latter being more commonly adopted. However, compared to optical fibers, free-space links are more susceptible to external environmental factors, particularly atmospheric conditions. Beam propagation through the atmosphere experiences diffraction, refraction, and intensity attenuation, which can degrade key distribution efficiency and even prevent key generation at the receiver. The atmospheric turbulence poses the most significant challenge in all influencing factors, especially for the commonly encountered moderate-to-strong turbulence regimes. Therefore, in this work, we develop a phase screen model and turbulence-dominated transmittance model to comprehensively investigate the impact of various key parameters on optical beam propagation through turbulent atmospheres. Furthermore, we derive the key rate for the CV-QKD protocol using a TMSV (two-mode squeezed vacuum) state and perform numerical simulations.
Physical layer security of a free-space optical (FSO) communication link is investigated for certain eavesdropping scenarios in which the eavesdropper exploits the divergence of the transmitted laser beam, which is subject to atmospheric turbulence, to compromise the security of the transmission link. A solution for physical layer security in which the legitimate receiver is positioned to receive only the coherent component of the transmitted laser beam is proposed. The irradiance fluctuations are modeled with separate distributions for the coherent and non-coherent components of the transmitted beam, corresponding to the main channel and the eavesdropper’s channel, respectively. Complete secrecy analysis of this setup is presented, and closed form expressions of the probability of strictly positive secrecy capacity, average secrecy capacity, and secrecy outage probability are derived. The analytical results are verified by Monte-Carlo simulations. Secrecy performance for worst-case scenarios corresponding to an adversary with powerful resources to capture all of the leaked information is explored. Results are analyzed for different turbulence regimes, and it was found that secure communication is possible even in the region of strong turbulence.
This paper investigates the physical layer security (PLS) of multi-aperture coherent free-space optical (FSO) systems with heterodyne detection over atmospheric turbulence-induced fading channels, while accounting for residual phase distortions after Zernike polynomial-based modal compensation. Unlike prior work focused primarily on intensity modulation/direct detection (IM/DD)-based FSO systems, this study considers coherent multi-aperture reception. Based on a Rician approximation of the turbulence-induced fading envelope, we derive an analytical approximation for the secrecy outage probability (SOP), a tractable semi-closed-form expression for the SOP lower bound, and a closed-form approximation for the strictly positive achievable secrecy rate probability. Moreover, high-SNR and low-SNR asymptotic analyses are presented to characterize the asymptotic secrecy behavior. The results show that the secrecy diversity order equals the number of receive apertures at the legitimate receiver, whereas, in the high-SNR regime at the legitimate receiver, the eavesdropper’s channel parameters affect the leading-order coefficient but not the decay exponent. Numerical results validate the proposed analytical approximations and asymptotic expressions and demonstrate that increasing the number of receive apertures at the legitimate receiver improves secrecy performance under various turbulence conditions.
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.