RU2566664C1 - Method for quantum cryptography using passive reflecting and redirecting elements located on spacecraft - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: invention relates to quantum cryptography and specifically to transmission of confidential information from a transmitting to a receiving ground station in the form of single-photon optical pulses through low-orbit satellites, using reflecting or redirecting devices located on said satellites. The method includes transmitting information from a transmitting to a receiving ground station in the form of single-photon optical pulses through low-orbit satellites on which there are reflecting and/or redirecting devices, which receive radiation from a transmitting ground station, reflect and/or redirect said radiation to a receiving ground station or to other satellites, followed by redirection to the receiving station, wherein a transmitter outputs single photons at a certain rate.

EFFECT: longer transmission range while maintaining absolute confidentiality.

2 cl, 2 dwg

Description

FIELD OF THE INVENTION

The invention relates to the field of quantum cryptography, namely to the transmission of secret information, from transmitting to receiving ground stations, in the form of single-photon optical pulses through low-orbit satellites using reflective or redirecting devices (mirrors, telescope systems, etc.) located on them.

State of the art

A method for encoding and transmitting cryptographic keys is known in the art, including timing the quantum states at the transmitting, receiving and converting stations by sending classical synchronizing laser pulses to the communication channel, generating a series of single-photon states in the converting station using phase transformations, and transmitting single-photon states on a quantum communication channel to a transmitting-receiving station, matching of bases on an open classical communication channel by communicating from the transmitting-receiving station to the converting station the bases for each quantum state transmission and detecting single-photon states at the receiving station by phase transformations of single-photon states (see [1] US patent No. 6529601 B1, IPC H04L 9/00, G02B 26 / 08, published on March 4, 2003). The given analogue was accepted by the expert examination as the closest analogue.

The disadvantages of the known method include the fact that the range of permissible errors in the transmitted keys at the transmitting-receiving station, in which the secrecy of the transmitted cryptographic keys is generated, is determined by the distortions of the polarization of laser and single-photon pulses caused by fluctuations in the parameters of the optical fiber elements and the quantum communication channel. Due to these disadvantages, the known method does not allow for long-term stability and to minimize the flow of errors in transmitted primary cryptographic keys.

In known methods for transmitting a secret key in quantum cryptosystems, for example, the well-known BB84 protocol is used to create a secret key in the form of a random sequence of ones and zeros (see [2] http://ru.wikipedia.org/wiki/BB84). This is only one protocol for quantum cryptography; there are others.

In quantum cryptography systems, losses and noise are essential parameters that determine the ability of the entire system to work. Unlike classical optical communication, where information is transmitted by intense optical pulses, the losses and noise in them are not as significant as for quantum cryptography systems, in which light pulses are usually single-photon and when a single photon is lost, a bit of information is lost, i.e. e. it is impossible to increase the intensity of optical signals to overcome losses and noise.

Quantum cryptography allows transmitting information with absolute secrecy, which is unattainable by other classical algorithms.

Unlike classical optical systems, where optical pulses are quite intense, i.e. one bit of information is carried by many photons; in quantum cryptography systems, for each transmitted bit, there is exactly one photon (maybe a little more, depending on the encoding scheme). Thus, photon loss determines the speed of distribution of secret keys in quantum cryptography schemes, because the loss of one photon means the loss of one transmitted bit - in classical algorithms, the loss of a photon from a powerful pulse has almost no effect on speed, because the remainder of the pulse will be recorded and the bit of information extracted. In other words, in classical optical schemes it is always possible to increase the power of transmitted pulses in order to “break through” the distribution medium, but this cannot be done in quantum schemes - this distinguishes quantum cryptography schemes from classical communication schemes.

Quantum cryptography systems are known in which optical signals propagate through an optical fiber. However, the secret transmission distance in modern systems is determined by the noise in the components (as a rule, the noise of single-photon detectors), which imposes restrictions on the maximum losses in the communication channel. In fiber optic channels, the minimum loss is ~ 0.2 dB / km. Modern fiber-optic systems of quantum cryptography operate at a maximum distance of ~ 200 km. The distance, in principle, can be increased with the development of new low-noise detectors, and the rate of generation of secret sequences is increased by increasing the rate of generation of single-photon sequences. However, the level of fiber loss cannot be reduced.

SUMMARY OF THE INVENTION

The problem solved by the claimed invention is to achieve smaller losses in the communication channel at large distances between the sender and the recipient.

The technical result of the invention is to increase the transmission distance, while maintaining absolute secrecy.

This technical result is ensured by the fact that the method of quantum cryptography using passive reflective and redirecting elements located on spacecraft includes the transmission of information from transmitting to receiving ground stations in the form of single-photon optical pulses via low-orbit satellites, on which reflecting and / or redirecting devices that receive radiation from a ground transmitting station, reflect and / or redirect it to the receiving azemnuyu station or to other satellites and then redirected to a receiving station, wherein the transmitter outputs the single photons with a certain speed.

Brief Description of the Drawings

Figure 1 - Space channel for quantum cryptography with

using one (a) and several satellites (b).

Figure 2 is a diagram of a quantum cryptography system with 2 satellites.

Here l _fib is the shortest distance between the sender and the receiver, laid on the surface of the Earth (minimum fiber length), L is the distance between satellites, N is the height of the orbits of the satellites above the earth's surface.

Disclosure of invention

The main factor that reduces the capacity of the space communication channel is the propagation of the optical signal from the ground station to the sender through the atmosphere to the satellite and from satellite to the receiving station to Earth. In this case, an atmospheric layer with an effective thickness of h≈20 km has the most destructive effect on the propagating optical signal: the beam is absorbed and scattered by the atmosphere; the beam becomes much wider than the diffraction limit due to turbulence. Moreover, turbulence also leads to a deviation of the center of the beam from the original (beam wander). Obviously, the atmosphere has the least effect on the signal during vertical propagation, because in this case, the length of the track is minimal. In this case, the losses due to the propagation of optical signals from the Earth to the passing satellite (unlink channel) and from the satellite to the Earth (downlink channel) will be minimal.

Consider, for example, a configuration with two low-orbit satellites simultaneously flying over the sender and receiver stations, respectively.

The orbits of such satellites (H) lie in the range of 160-2000 km. The arrangement of the main nodes of the system is shown in FIG. 2. Due to the spherical shape of the Earth, the minimum fiber length l _fib that can be laid between the sender and the receiver is the length of the corresponding arc:

$$l_{fib}=2R_{earth}\arcsin \left(\frac{L}{2\left(H+R_{earth}\right)}\right),\left(\mathrm{one}\right)$$

where R _earth is the radius of the Earth (≈6370 km), l _fib is the shortest distance between the sender and the receiver, laid on the surface of the Earth (minimum fiber length), L is the distance between satellites, H is the height of the orbits of the satellites above the earth's surface.

Let us estimate the losses due to the propagation of an optical signal from a ground station to a satellite passing over it (uplink channel).

At the initial stage of the path, an optical signal passes through an atmosphere layer with an effective thickness of h≈20 km. Destructive atmospheric effects for the optical ranges of transmitting wavelengths can be divided into 3 parts: absorption and scattering by atmospheric components and turbulence. The total coefficient of signal transmission associated with its passage through the atmosphere and airless space can be written in the form:

$${\eta }_{uplink}={\eta }_{uplink}^{ext}{\eta }_{uplink}^{atm},\left(2\right)$$

- коэффициент прохождения, связанный с поглощением и рассеянием, $${\eta }_{uplink}^{atm}$$

- коэффициент прохождения, связанный с воздействием турбулентности.Where $${\eta }_{uplink}^{ext}$$

- transmission coefficient associated with absorption and scattering, $${\eta }_{uplink}^{atm}$$

- transmission coefficient associated with the impact of turbulence.

Absorption and scattering reduce the amplitude of the transmitted optical signal, i.e. during the propagation of a single-photon pulse, the probability of its passage and, accordingly, the probability of detection are reduced. The level of such losses is quite stable over time - it changes slowly with weather and cloud cover. Thus, losses during vertical propagation through an atmosphere of thickness h can be written as

$${\eta }_{uplink}^{ext}=\exp \left(-{\displaystyle \underset{0}{\overset{h}{\int }}\alpha \left(z\text{'}\text{'}\right)dz\text{'}\text{'}}\right),\left(3\right)$$

- коэффициент экстинкции (поглощение + рассеяние), зависящий, вообще говоря, еще и от длины волны передающегося сигнала. Заметим, что здесь подразумевается, что передающая станция находится на уровне моря. Теоретический расчет коэффициента α не представляется оправданным из-за сложной зависимости от длины волны - целесообразно пользоваться таблицами с коэффициентами потерь. С помощью аккуратного выбора несущей длины волны передаваемых сигналов можно добиться малого поглощения (~3 дБ). В свою очередь, рассеяние, обусловленное наличием в атмосфере дымки, тумана, облаков, дождя и т.д. сильно зависит от местности, времени суток и погоды. Рассеяние может приводить к потерям в диапазоне от ~2 дБ для самого благоприятного случая до очень больших значений (тысячи дБ) для дождливой и облачной погоды. Таким образом, потери за счет экстинкции начинается от 5 дБ, т.е. минимальный коэффициент потерь $${\eta }_{uplink}^{ext}={10}^{-5дБ/10дБ}\approx 0.3$$

.Where $$\alpha {\left(z\right)}_{ab{s}_{scat}}$$

- extinction coefficient (absorption + scattering), depending, generally speaking, also on the wavelength of the transmitted signal. Note that this implies that the transmitting station is at sea level. The theoretical calculation of the coefficient α does not seem justified due to the complex dependence on the wavelength - it is advisable to use tables with loss coefficients. By careful selection of the carrier wavelength of the transmitted signals, a low absorption (~ 3 dB) can be achieved. In turn, the scattering due to the presence in the atmosphere of haze, fog, clouds, rain, etc. highly dependent on terrain, time of day and weather. Scattering can lead to losses ranging from ~ 2 dB for the most favorable case to very large values (thousands of dB) for rainy and cloudy weather. Thus, extinction loss starts at 5 dB, i.e. minimum loss ratio $${\eta }_{uplink}^{ext}={10}^{-5dB/10dB}\approx 0.3$$

.

Let us estimate the losses due to the propagation of an optical signal from a passing satellite to a ground station (downlink channel).

, радиус телескопа приемника R_r=0,5 м, ошибка в наведении пучка на телескоп Δθ=1 мкрад, оценка для минимальных потерь ≈15 дБ. С учетом минимальных потерь за счет поглощения и рассеяния в атмосфере (5 дБ), минимальные потери в downlink-канале - 20 дБ.The loss coefficient when sending an optical signal from a satellite to a receiving ground station is determined by diffraction beam divergence, beam broadening by turbulence and extinction (absorption + scattering) of the atmosphere. Unlike the uplink channel, the beam wandering effect can be neglected here, since a thin layer of the atmosphere (20 km versus H ~ 1000 km) affects the signal before detection and the beam does not have time to significantly drift apart. In this case, the broadening of the beam can also be neglected, since it is small: hθ _turb << Hθ _diffraction . Assuming the radius of the transmitting region of satellite C2 $$R_t^{S2}=0.25m$$

, the radius of the receiver telescope R _r = 0.5 m, the error in pointing the beam at the telescope Δθ = 1 mrad, the estimate for the minimum loss is ≈15 dB. Given the minimum loss due to absorption and scattering in the atmosphere (5 dB), the minimum loss in the downlink channel is 20 dB.

The minimum loss in the downlink channel can be estimated based on the loss analysis for the uplink channel.

Let us estimate the losses for the channel between satellites. Optical signals between spacecraft are transmitted through an airless environment. The main losses here are introduced by the diffraction divergence of the beam and the inaccuracy of the beam direction from the transmitting satellite (C1) to the receiving (C2); the latter also includes a decrease in directional efficiency due to “jitter” of the equipment on the transmitting satellite. With these effects in mind, the transmittance can be written as:

$${\eta }_{SS}={\left(\frac{2\pi R_t^{S\mathrm{one}}}{\lambda }\right)}^2{\left(\frac{2\pi R_r^{S2}}{\lambda }\right)}^2{\left(\frac{\lambda }{\mathrm{four}L\pi }\right)}^2\exp \left(-\frac{\Delta {\theta }^2}{{\theta }_{0^2}}\right),\left(\mathrm{four}\right)$$

, $$R_r^{S2}$$

- радиус передающей (или эффективный радиус отражающей плоскости в направлении спутника C2) и принимающей оптических антенн, θ₀ - расходимость пучка на выходе из передающей антенны, Δθ - угол, описывающий отклонение от идеального направления центра пучка на принимающий спутник, который зависит от использующейся системы стабилизации (неточность направления, «дрожание» передающей оптики). В качестве минимальной оценки для угла θ₀ возьмем угловую расходимость гауссова пучка $${\theta }_0=\frac{\lambda }{\pi D_T}$$

. Такие пучки обладают минимальным расхождением.Where $$R_t^{S\mathrm{one}}$$

, $$R_r^{S2}$$

is the radius of the transmitting (or effective radius of the reflecting plane in the direction of satellite C2) and receiving optical antennas, θ ₀ is the beam divergence at the exit of the transmitting antenna, Δθ is the angle describing the deviation from the ideal direction of the center of the beam to the receiving satellite, which depends on the system used stabilization (inaccuracy of direction, “jitter” of transmitting optics). As a minimum estimate for the angle θ _0, we take the angular divergence of the Gaussian beam $${\theta }_0=\frac{\lambda }{\pi D_T}$$

. Such bundles have a minimum discrepancy.

Expression (3) can be written as follows:

, λ>0,8 мкм, θ₀≈0.5 мкрад. Оценку для реальных значений Δθ возьмем, например, из статьи по классической космической коммуникации: Δθ=1 мкрад. В итоге имеет следующее значение для коэффициента пропускания оптического канала спутник-спутник: η_SS=1,1·10⁹ м²/L² для L=5000 км, η_SS=4·10^-5≈-40 dBFor evaluation, we take the following parameters: $$R_t^{S\mathrm{one}}=R_r^{S2}=0.25m$$

, λ> 0.8 μm, θ ₀ ≈0.5 mrad. We take an estimate for real Δθ values, for example, from an article on classical space communication: Δθ = 1 mrad. As a result, it has the following value for the transmittance of the optical satellite-to-satellite channel: η _SS = 1.1 · 10 ⁹ m ² / L ² for L = 5000 km, η _SS = 4 · 10 ^-5 ≈ -40 dB

Let us estimate the losses in turbulence. Unlike extinction, turbulence does not change the signal amplitude - it randomly changes the phase front of the optical wave. This effect is associated with temperature fluctuations, which lead to fluctuations in the refractive index. The pattern of fluctuations in the refractive index is in the form of turbulent vortices. The characteristic dimensions of the vortex inhomogeneities are distributed in the range from millimeters to hundreds of meters. Small inhomogeneities of the refractive index effectively broadens the beam width, while the effect of inhomogeneities larger than the diameter of the beam reduces to a deviation of the beam propagation direction (beam wander). As a result, at the observation point, the optical beam has a diameter substantially wider than the size of diffraction spreading, and the center of the beam wanders.

The parameters of atmospheric fluctuations depend on the geographical area, the signal propagation path and weather conditions. There is no rigorous analytic theory working for a wide range of atmospheric parameters. As a rule, analytical results are obtained for a weak turbulence regime.

The main parameter describing turbulence is the structural constant C _n . Typical C _n values range from 10 ^-9 to 10 ^-7 for weak and strong turbulence. Another parameter of turbulence is the Fried radius ρ ₀ , which determines the correlation of the wavefront distorted by turbulence. The following formula is valid for the Fried radius:

where integration is carried out along the propagation path, here k = 2π / λ is the wave vector of the optical signal.

The divergence angle of an optical beam in a turbulent medium without taking into account the walk of the center of the beam (beam wander) can be written as

$${\theta }_{turb}\approx \sqrt{{\theta }_0^2+{\left(\frac{\lambda }{{\rho }_0}\right)}^2},\left(7\right)$$

Here θ ₀ ≈λ / πR _t is the diffraction divergence angle of the Gaussian beam (without turbulence), R _t is the aperture radius of the optical telescope of the transmitting station. A typical value for the Fried radius is ~ 0.1 m. The radius R _t determines the diffraction divergence of the beam. Usually use transmitting telescopes with R _t ~ ρ ₀ . Then, for example, for λ = 0.8 μm, the typical value of the divergence angle in the turbulent atmosphere is θ _turb = 8.4 mrad. In this case, the radius of the beam that has passed the distance R _beam = Hθ _turb . For estimation, we put H = 1000 km, then R _beam = 8.4 m.

Let us evaluate the effect of beam wandering caused by large-scale fluctuations in the refractive index. The probability of deviation of the beam center by a distance r in a turbulent atmosphere is given by the probability distribution function

where for the uplink channel dispersion can be obtained:

. Эта оценка находится в соответствии с численным моделированием распространения пучка от наземного передатчика до низкоорбитального спутника.For the selected typical value ρ ₀ and the radius of the transmitting telescope (R _t ) $${\sigma }_r^2\approx \mathrm{eleven}{m}^2$$

. This estimate is consistent with numerical modeling of beam propagation from a ground-based transmitter to a low-orbit satellite.

Non-ideal beam guidance. Another factor that causes losses is the non-ideal beam direction from the transmitter to the satellite. We assume that the inaccuracy is associated with the “jitter” Δθ of the transmitter equipment. We take an estimate for real Δθ values, for example, from an article on classical space communication: Δθ = 1 mrad.

.Thus, taking into account the diffraction divergence of the beam, broadening of the beam by turbulence, wandering of the center of the beam caused by turbulence, and imperfect pointing of the beam to the satellite, estimate of the time-averaged radius of the beam incident on the satellite for the selected parameters $$R=\sqrt{\Delta {\theta }^2{H}^2+R_{beam}^2+{\sigma }_{turb}^2}\approx 9.1m$$

.

, тогда $${\eta }_{uplink}^{atm}=\left({R_r^{S1}/R}^2\right)=2.7\cdot {10}^{-4}$$

. Общий коэффициент пропускания для uplink-канала:We take the aperture radius of the receiving satellite lens C1 $$R_r^{S\mathrm{one}}=0.15m$$

then $${\eta }_{uplink}^{atm}=\left({R_r^{S\mathrm{one}}/R}^2\right)=2.7\cdot {10}^{-\mathrm{four}}$$

. Total transmittance for uplink channel:

η _uplink = 0.3 · 2.7 · 10 ^-4 = 8.1 · 10 ⁵ or -10 · log ₁₀ η _uplink ≈41 dB.

In the presence of haze, fog, clouds, rain, high temperature drops, atmospheric losses increase significantly.

General losses in a space channel with optical reflectors.

For the configuration of the space channel shown in Figure 1 with the indicated parameters, the minimum losses without taking into account the imperfect detection efficiency, redirection of radiation by satellites, establishment and removal of radiation from telescopes can be from 41 dB (uplink) + 20 dB (downlink) + 10 log ₁₀ L ² -90 dB (intersatellite). For example, for L = 5000 km, the minimum loss is ≈100 dB. In accordance with formula (1), the length of the optical fiber is 4410 km, and the corresponding minimum loss is 882 dB. Thus, the use of the space channel in quantum cryptography is justified for large transmission distances.

An essential sign is that the transmitter should emit single photons at a certain speed. Most of these photons are lost in the communication channel, but the part that reaches the receiver is used to generate the keys. It is appropriate to talk here not about the power of the transmitter, but about the speed of generation of single-photon pulses. If, for example, the source produces 1 photon per second (1 Hz), then the probability that it will reach the receiver is ≈10 ^-10 , i.e. in 10 billion seconds only 1 photon will reach. If the source generates 10 ¹⁰ photons per second (10 GHz), then, accordingly, on average every second the detector will detect one incoming photon.

The mirrors placed on the spacecraft have such a shape that the optical beam incident on it from a ground station or from a nearby spacecraft (SC) is reflected in the direction of the receiving station or in the direction of the mirror of a nearby SC. In this case, for minimal losses, it is necessary that the radius of the beam that reaches the receiving station or the mirror of a nearby spacecraft be minimal. The surface shape of the mirrors must have a special shape (http://en.wikipedia.org/wiki/%D0%97%D0%B5%D1%80%D0%BA%D0%B0%D0%BB%D1%8C%D0 % BD% D0% B0% D1% 8F_% D0% B0% D0% BD% D1% 82% D0% B5% D0% BD% D0% BD% D0% B0), which depends on the specific parameters of the system (distance between the spacecraft , tilt angles of beams sent from the sender station to the spacecraft and from the spacecraft to the ground station).

Telescope systems serving as analogs of mirrors are pairs of telescopes on each spacecraft — receiving and transmitting, between which optical signals are transmitted through a waveguide channel or through free space with a system of internal reflectors. Telescope lens systems satisfy the same requirements described above for mirrors: collecting and redirecting an optical signal to a nearby spacecraft or to a ground station with maximum accuracy and focusing the redirected optical signal to a minimum radius on a telescope or mirror of a nearby spacecraft.

The implementation of the invention

Single-photon light pulses are generated at the sender’s ground station, in which information is encoded, for example, into polarization (protocol BB84) or another variable. Using a telescope aimed at a passing spacecraft, these pulses are fed to the mirror / receiver of this spacecraft. The spacecraft mirror / telescope system is configured so that it reflects the incident optical signal towards the ground station of the receiver, if the system is based on one spacecraft, or to a nearby spacecraft from the spacecraft group. After that, the reflected signal from the spacecraft flying over the receiver’s ground station enters the receiver’s receiving telescope and enters the detection system. The distribution of optical signals continues as many times as necessary. Further actions of the participants of the transmission are the same as in the well-known methods of quantum cryptography: matching information on an open communication channel, implementing algorithms for correcting errors and increasing secrecy on an open communication channel.

The use of the space communication channel described in the proposed method can significantly reduce losses during the propagation of optical signals between two ground stations in clear weather (in the absence of fog, clouds, rain and other factors). As a result of the use of such a channel in favorable weather in quantum cryptography schemes, it becomes possible to significantly increase the maximum secret transmission distance.

Claims (2)

1. A method of transmitting quantum cryptographic information using passive reflective and redirecting elements located on spacecraft, including the transmission of cryptographic information from transmitting to receiving ground stations in the form of single-photon optical pulses with a minimum beam radius reaching the receiving station or a mirror of a nearby spacecraft through low-orbit satellites on which reflecting and / or redirection devices having the form are located, isyaschuyu on system parameters, which receive the radiation from terrestrial transmitting station, reflect and / or redirect it to a receiving ground station or to other satellites and then redirected to a receiving station, wherein the transmitter outputs the single photons with a certain speed. 2. The method according to claim 1, characterized in that mirrors and / or telescope systems are used as reflective and / or redirecting devices.

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