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Abstract
We demonstrate the efficacy of machine learning techniques in the detection of an eavesdropper in a free-space optical (FSO) communications setup. Experimentally, we use ON-OFF keying (OOK) and send strings of random bits through strong turbulence. When we apply a simulated eavesdropper to the bits in the post processing stage, a deep learning convolutional neural network (CNN) is able to successfully detect whether or not the eavesdropper is present. We vary the strength and duration of the attenuation of the simulated eavesdropper, and vary the signal-to-noise ratio (SNR) of the bit streams, and find that the strength of the eavesdropper has the greatest effect on eavesdropper detection accuracy. We are hopeful this flexible approach may be used in current and future operational FSO communications systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Free-space optical (FSO) ON-OFF keying (OOK) is one of the most widely used forms of optical communication [1–4]. FSO allows information to be sent wirelessly over long distances, allows for large bandwidths and bit rates, and has a license free spectra [1,5]. FSO OOK utilizes bits that are either on or off, to relay binary information from a sender to a receiver [5].
In this communication scheme, particularly when information must be sent over long distances, signals must be sent through the atmosphere. Disturbances and index of refraction variations in the atmosphere create turbulence, which can add non-uniform loss to the signal, thus distorting the bit streams that are demodulated at the receiver [6,7].
As the bits are sent through free space, the signal is susceptible to eavesdropper attacks where unwelcome third parties may split off some of the signal and detect it themselves [8,9]. In the quantum optics and quantum communication community, an eavesdropper manifests as a ‘man-in-the-middle’ attack, which can be physically described as a variable beamsplitter placed in the path of the light [10–12]. This sort of eavesdropping attack is also described in classical optics experiments [9]. The intended receiver would see a reduction in signal when this occurs. This provides motivation for our methods. In this paper, we limit our scope to classical OOK, where the receiver only detects the intensity of the light, and polarization does not play a role (as it would in many quantum key distribution schemes) [11,13]. Therefore, the receiver may have difficulty determining whether or not an eavesdropper is present due to changes in intensity of the signal due to atmospheric turbulence [8,14,15]. An example of bit streams under these conditions is shown in Fig. 1. Due to random fluctuations from turbulence, a fixed threshold method of eavesdropper detection may not be effective [16]. As convolutional neural networks (CNNs) have been shown to be improve optical communication [17–19], here, we use a deep learning CNN to detect the presence of an eavesdropper by differentiating between such attenuation and fluctuations due to turbulence.
Fig. 1. Illustration of the communication from sender to receiver. (a) The communication pathway with no turbulence or eavesdropper. In theory, the receiver would detect the bits exactly. (b) The communication pathway and bits with turbulence, fluctuations in the bits are introduced. (c) The communication pathway and bits with turbulence and eavesdropper. There are fluctuations due to turbulence and an eavesdropper. The receiver must be able to determine the cause of the fluctuations. In all pathways, the sender is represented by “A," the receiver is represented by “B," and the eavesdropper is represented by “E."
2. Experimental methods
Experimental data is generated with a free-space optics (FSO) setup. To generate the binary (in this case, either ‘on’ or ‘off’) bits, we pass a continuous wave, near-infrared laser through an acousto-optic modulator (AOM). The AOM is controlled by an arbitrary waveform generator (AWG), which allows for strings of random bits to be generated. The beam is then passed through a glass water tank with a submerged bubbler. The bubbler creates strong turbulence due to the large index of refraction variations that the bit stream passes through. A schematic of the setup is shown in Fig. 2. The total length of light propagation, from laser to detector, is approximately 10 m. The light diverges slightly as it propagates, such that the beam is approximately 2 cm in diameter when it reaches the detector. The entire beam is focused onto the detector. We vary the SNR of the bits by changing the intensity of the ‘on’ bit with a variable neutral density filter in the beam path. The binary bits are generated such that each bit is 7 ms long (bit frequency of $\approx 142.86$ Hz). While this is much slower than bandwidths that have been demonstrated to operate up to the terahertz range [20], the turbulence generated in the water is relatively slow, as it depends on the movement of the bubbles which are observed to move at speeds on the order of 1 m/s. This which is much slower than atmospheric air currents, which can reach 40 m/s [21]. The CNN used in the post processing stage is agnostic to the time scales, thus our methods would hold for higher frequency systems that pass through turbulence that is changing at a faster rate. Our method of turbulence generation is a low-cost alternative to transmitting a signal over a long distance. Due to the in-lab nature of our experiment, we avoid large unexpected fluctuations due to shifting weather conditions.
Fig. 2. Experimental setup. Note that some of the light split off before it passes through the turbulence and detected in Det. 1. This light is used to determine the actual bit pattern for used in bit error enhancement. The light detected by Det. 2 is used for our analysis. Abbreviations: ND = neutral density, Det. = detector, BS = beamsplitter, AOM = acousto-optic modulator.
When the light passes through bubbles in the tank, it is shown to obey intensity fluctuations consistent with that of log-normal atmospheric turbulence [24], as shown in Fig. 3. Log-normal turbulence, a function of intensity, $I$, is modeled by the equation
Fig. 3. Experimental data of light passing through air bubbles in water is shown to obey a log-normal distribution with the normalization constant of $0.305 \pm 0.009$, normalized mean intensity of $0.398 \pm 0.002$ V, and scintillation index of $0.051 \pm 0.002$. This scintillation index is consistent with that of weak atmospheric turbulence [22,23].
3. Post-processing
The bit streams are detected after the beam has passed through the turbulence by a biased photodetector. A measurement is taken every .02 ms, corresponding to each bit being 35 points long. We take the average value of each set of 35 data points to be the voltage value of one bit. We generate 32568 bits for each of the six different SNRs.
In theory, with an OOK scheme the ‘off’ bit would result in the receiver producing no voltage. However, ambient light from the room provides an offset, resulting in the ‘off’ bits having a nonzero voltage. Therefore, for ‘off’ bits, there is still the ability to be attenuated by the simulated eavesdropper.
3.1 Eavesdropper simulation
For each SNR, we have a bit stream that is 32568 bits long. We slice this bit stream into 501 smaller bits streams, such that each contains 65 consecutive bits (with 3 extra bits leftover, which are not used). We apply a simulated eavesdropper to all 501 bit streams, with a given length and attenuation intensity, beginning at a random point with the condition that the eavesdropper attenuates a continuous group of bits. We also take the same 501 bit streams and do not apply an eavesdropper to them. Therefore, we have 1002 bit streams, half of which have a simulated eavesdropper and half of which do not. We then randomly split the 1002 bit streams into a training set of 500 bit streams (exactly 250 with an eavesdropper and 250 without an eavesdropper) and a testing set of 502 bit streams (exactly 251 with an eavesdropper and 251 without an eavesdropper). We repeat this process for each desired attenuation intensity and number of bits attenuated. Then this whole process is repeated for all six SNRs.
The eavesdropper is simulated by subtracting a set percentage of the detected voltage for a bit that is being eavesdropped on. This is analogous to the light passing through a beamsplitter in which small percentage of the light it split off after it passes through the turbulence [7]. The detected voltage is not dependant on the shape of the beam; an eavesdropper that measures light from a portion of the beam results in the same detected voltage by the receiver as light that was uniformly attenuated by an eavesdropper. In our setup, we assume the receiver collects all of the light from the beam, thus an eavesdropper cannot collect light from behind the receiver, which would clearly not be detectable by our CNN approach. While we recognize an eavesdropper may manifest itself in a variety of ways, we suppose an attack where the eavesdropper passively intercepts some of the beam in this work.
3.2 Convolutional neural network (CNN)
The CNN used consists of two convolutional and max-pooling units, followed by three fully-connected-dense layers. The output layer, where the decisions are made, is provided with the softmax function. Cross-entropy loss at the output layer is minimized with the ada-grad optimizer package of Tensorflow. A schematic of the CNN architecture is shown in Fig. 4. First, the input of 65 bits in length is converted into a 2D array of size (13, 5, 1), which is later convoluted to (12, 4, 25) with a kernel of size of (2, 2), stride of 1, ReLU activation, and 25 filters. After that a max-pooling layer with a stride of 2, and a ’valid’ padding reduces the dimension of the convoluted input to (6, 2, 25), which is again followed by another convolutional layer with the same parameters as described earlier, but with the same padding. In order to decrease an overall computational cost for the training, we again implement the max-pooling layer that further reduces the dimension to (3, 1, 25). After this, we use a flatten operation to have a layer with 75 neurons, which is then fully-connected to a dense layer consisting of 150 neurons with the ReLU activation function. In order to regularize the training, after the first fully connected dense layer we apply a dropout with the rate of 50$\%$, which forwards the data to the next dense layer of size of 75 with the ReLU function. This leads to the final fully-connected output layer of size of 2, where predictions are made. We set the hyperparameters at: learning rate of 0.05, batch size of 10, and 200 epochs. Note that we manually optimize the hyperparameters of the networks.
The results are classified in four different ways: true positive (eavesdropper is present and is detected), false negative (eavesdropper is present and is not detected), true negative (eavesdropper is not present and is not detected), and false positive (eavesdropper is not present and is detected). We seek to maximize the true positive and true negative situations.
3.3 Support Vector Machine (SVM)
We implement the SVM method to compare the efficacy of a CNN with respect to another shallow, kernel-based machine learning technique. The SVM algorithm searches for a hyperplane in a higher-dimensional space that distinctly classifies the input data points. In order to detect an eavesdropper, we use the Support Vector Classification (SVC) module with a kernel of ‘poly’ from the scikit-learn library [26]. Additionally, we construct a pipeline with the ‘StandardScalar’ pre-processing unit and SVC as the final estimator. The training and testing sets are prepared as previously described. After this we fit the SVC model for the training sets and save the trained model locally. Finally, we use the saved model to detect an eavesdropper.
4. Results
The accuracy of the CNN while varying several parameters is shown in Fig. 5: 5(a) intensity of attenuation, 5(b) SNR of the bits, and 5(c) number of bits being attenuated.
Fig. 5. (a) Plot of the accuracy of the CNN as the strength of the eavesdropper is varied. The number of bits being attenuated is held constant at 8 bits and the SNR of the bits is held constant at −1.641 dB. (b) Plot of the accuracy of the CNN as the SNR of the bit strings is varied. The number of bits being attenuated is held constant at 8 bits and the intensity of the attenuation is held constant at .12. (c) Plot of the accuracy of the CNN as the number of bits being attenuated is varied. The SNR of the bits is held constant at 1.057 dB and the intensity of the attenuation is held constant at .1. The inset on each plot shows the accuracy of the CNN as a function of epoch, with sample bit strings shown to the right, after an average of 5 trials, with error bars shown for the average accuracy. Points are connected to aid the eye.
As expected, a more intense eavesdropper results in a higher detection accuracy. We observe an accuracy rate greater than 90% when the attenuation due to the eavesdropper is greater than .08 of the beam intensity. There is a large increase in network accuracy when the eavesdropper attenuation goes from .06 to .08, suggesting that the effect of the eavesdropper intensity has a greater impact than that of the SNR of the bits. The CNN also has slightly increased accuracy as the number of bits being attenuated increases, although the accuracy is relatively high with a small number of bits attenuated. This parameter seems to have a larger effect than the that of the SNR of the bits, but appears to be less significant than the strength of the eavesdropper. There does not appear to be a strong correlation of the accuracy of the CNN with respect to the SNR of the bits. We do not see a well defined trend for accuracy as SNR is varied. While the accuracy appears to decrease as SNR increases, once the SNR surpasses 1 dB, we see an increase in accuracy. We suspect this may be a result of the amplitude of the bits approaching the magnitude of the attenuation due to the eavesdropper, which creates a challenge for the CNN to distinguish between the ‘off’ bits and the eavesdropper. All data points on the plots indicate the accuracy of the CNN after 200 epochs.
We now turn to comparing the accuracy of simulated eavesdropper detection using the CNN with the accuracy of simulated eavesdropper detection using a simple threshold algorithm and a SVM with polynomial kernel (a non-deep) learning technique.
To check for an eavesdropper in a given string of 65 bits, the average value of the detected voltages is taken, and values below a given threshold are checked for, where the threshold is some multiple of the standard deviation (SD) away from the mean. The same original bit strings are used, but the location at which the eavesdropper attenuated the bits may not be the same. This should not make a difference in the detection accuracy, as the location at which the eavesdropper is applied is chosen at random for all trials.
Figure 6 compares the results of varying threshold detection methods with those of the CNN. In most cases the CNN performs better than the threshold method. In this ‘threshold method’, the threshold is set between 2 and 3 standard deviations below the mean. It outperforms the CNN when the intensity of the eavesdropper is relatively weak. However, as the eavesdropper increases in strength, the CNN surpasses the threshold method. As shown in Fig. 6, some thresholds perform much worse than the CNN under various eavesdropper conditions. As such, the CNN should be more effective if the receiver does not have knowledge of the nature of the eavesdropper, or of the SNR of the bits. CNNs are also able to better adapt to varying conditions [27,28], whereas the threshold method is less adaptable to changing eavesdropper conditions over time.
Fig. 6. CNN (black) eavesdropper detection compared to average accuracy of various threshold detection methods (green, cyan, red, blue, and yellow), average of 10 trials with errorbars. (a) Eavesdropper detection accuracy as the intensity of the attenuation is varied. The black line shows the average detection accuracy of the CNN. (b) Eavesdropper detection accuracy as the SNR of the bits is varied. The black line shows the average detection accuracy of the CNN. (c) Eavesdropper detection accuracy as the number of bits being attenuated is varied. For all, the black line shows the average detection accuracy of the CNN with each set of respective parameters. Points are connected to aid the eye.
Figure 7 shows a comparison in accuracy of the SVM with the CNN and the optimal threshold method (2.5 SD threshold) when the intensity of the eavesdropper is attenuated. Both machine learning techniques outperform the threshold method in most cases, where we see the CNN provides the highest accuracy for all attenuation intensities. Due to the rather small training sets, the accuracy of the SVM technique is comparable to that of the deep learning CNN [29] under some conditions.
Fig. 7. Eavesdropper detection accuracy as the intensity of the attenuation is varied. The purple line indicates the accuracy of the SVM.
5. Discussion
A realistic optical communication systems contains bits at a high SNR, with a relatively weak eavesdropper that is attenuating an unknown percentage of the bits being sent [7]. This scenario is demonstrated in Fig. 5(c). The accuracy of the network increases as the number of bits being attenuated increases, and remains relatively accurate even down to only attenuating 8 bits at a time. Therefore, the present CNN detection method could be applied to a realistic communication scheme where some arbitrary number of bits are attenuated.
Jamming attacks, which can occur when a third party adds to the signal (rather than attenuates the signal as an eavesdropper would), produce another threat to FSO communication [30–33]. While we do not examine jamming here, we suspect CNNs could be beneficial in jamming detection, as we have shown CNNs are capable of detecting fluctuations in signal intensity.
The current approach is an inexpensive and effective method to create experimental optical communications systems with varying strengths of turbulence in a lab. In the past, spatial light modulators (SLMs) have been used to simulate turbulence [34,35], where the current method allows for truly random atmospheric turbulence in real time.
We also note that we examine one environmental condition. We anticipate that the neural network may need to be retrained given transmission through different types of experimental conditions. However, if a given atmospheric condition results in a similar intensity distribution as created in our experiment, our CNN should also be effective, as it does not consider the mechanics behind the generation of the fluctuations, only the nature of the fluctuations themselves. Given a large change in environmental conditions, we suspect the neural network would need to be retrained.
We expect future work to extend the present approach to quantum communications systems, such as quantum key distribution [11], single photon detection [36,37], and quantum state estimation [38]. While we may need to adjust the mechanics of the neural network, we believe our general approach will translate to other amplitude modulation FSO communication schemes. CNNs have the ability to work in tandem with other detection and encryption methods to produce enhanced security. When the eavesdropper is very weak, the CNN detection rates drop. The CNN alone may not be viable in detecting very weak eavesdroppers. However, coupling a CNN with other physical and computation methods, along with larger training set sizes, may increase detection rates of very weak attenuation. Additionally, other properties of communications systems, such as the wavelength of light used and the nature of the turbulence [39], which have been shown to affect the bit-error rate of FSO communications, can also be explored for their effects on eavesdropper detection.
Funding
Office of Naval Research (N000141912374).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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