A Method for Identifying Tor Users Visiting Websites Based on Frequency Domain Fingerprinting of Network Traffic

Although the anonymous communication network Tor can protect the security of users’ data and privacy during their visits to the Internet, it also facilitates illegal users to access illegal websites. Website ﬁngerprinting attacks can identify the websites that users are visiting to discern whether they are performing illegal operations. Existing methods tend to manually extract the traﬃc features of users visiting websites and construct machine learning or deep learning models to classify the features. While these methods can be eﬀective in classifying unknown website traﬃc, the eﬀect of classiﬁcation in the use of defensive measures or onion service scenarios is not yet ideal. This paper proposes a method to identify Tor users visiting websites based on frequency domain ﬁngerprinting of network traﬃc (FDF). We extract the direction and length features of circuit sequences in access traﬃc and combine and transform them into the frequency domain. The classiﬁcation of access traﬃc is accomplished by using a deep learning classiﬁcation model combining CNN, FC, and Self-Attention. In this paper, the proposed FDF method is experimentally validated in common scenarios of Tor networks. The results show that FDF outperforms the existing methods for classiﬁcation in diﬀerent Tor scenarios. It can achieve 98.8% and 94.3% classiﬁcation accuracy in undefended and WTF-PAD defense scenarios, respectively. In the onion service scenario, the accuracy is improved by 4.7% over the current state-of-the-art Tik-Tok method.


Introduction
As people's awareness of protecting personal privacy continues to increase, more and more users are beginning to use anonymous communication systems to interact with the outside world. However, many criminals have also used anonymous communication systems to conduct illegal operations. Some criminals have established illegal trading websites. Users can purchase leaked database information and even network attack services through these websites. Driven by interests, a large number of network intrusions have spawned on the Internet. Tor is currently the most popular anonymous communication system, and it provides privacy to over 200 million users every day [1]. Tor protects the anonymity of user access by creating an encrypted link with three-hop relays. ese relays are randomly selected, prevented from being traced through the bridge and pluggable transmission [2], and the links are changed periodically as the client accesses the server. Although it is difficult to directly crack the Tor anonymous communication system, previous studies have shown that network traffic analysis can affect the security of Tor [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], especially website fingerprint (WF) attacks. When users visit each website, they will generate different network traffic features, such as different numbers of data packets and different traffic burst patterns. In a WF attack, the enforcer intercepts network traffic and extracts the features of the traffic packets in an encrypted connection between the monitored user and the entry node of Tor. e classifier determines whether the intercepted traffic is associated with the website of interest to the enforcer, and if the traffic matches the classifier, it indicates that the monitored user is visiting the website of interest to the enforcer. e WF attack allows the enforcer to determine whether the monitored user is browsing illegal websites, especially websites that conduct black transactions, which is of great significance for combating illegal crimes. e original intention of Tor is to provide users with anonymity during data communication. Tor should try to avoid the occurrence of WF attacks so as not to affect its security. erefore, defense measures against WF attacks are proposed. But for enforcers, due to a large number of illegal activities in Tor, it is necessary to monitor criminals and illegal websites. erefore, it is necessary to conduct further research on WF attacks on Tor that uses defensive measures. e proposed defense measures basically reduce the bursts in the original Tor traffic and confuse the traffic, which significantly reduces the efficiency of WF attacks. For measures that may be used by Tor in the future, it is important to improve their recognition accuracy. In addition, the onion service [20] is the most secure service provided by Tor, which contains a large number of illegal transactions. WF attacks on Tor networks using onion service are also of interest for research. To access the website in the onion service, users need to establish more complex links and have a more complete security verification mechanism. is makes the access traffic mixed with a lot of traffic noise generated for the purpose of authentication. Existing methods for fingerprinting Tor traffic using the onion service are not yet very effective. ese methods can detect the behavioral patterns of users visiting different websites from different features such as timing and direction of traffic. However, none of them can reduce the influence of traffic noise on fingerprint recognition.
To address the shortcomings in existing studies, this paper adopts a frequency domain transformation method to deal with Tor traffic. Unlike the existing studies, the frequency domain processing method can effectively reduce the impact of noise on fingerprint recognition when users access the server. In particular, for scenarios where defensive measures and onion services are used, the impact of noise on fingerprint recognition is greater due to the increased security mechanisms. We achieve more significant results in these environments than the existing methods. e contributions of our work are as follows: (1) We propose FDF, a fingerprint recognition method for websites based on DWT frequency domain processing. We compared several frequency domain processing methods and found that the wavelet transform works best through theoretical as well as experimental analysis. Due to the properties of the frequency domain transform, we combine for the first time the signal element sequence direction as well as length features for the input of a deep learning model.
(2) We have improved the DF [15] model. e Self-Attention module is added to the original model to support intelligent and efficient analysis of website traffic. In the closed-world scenario (we assume that the monitored user only visits the websites we are interested in. e performance of the classifier can be observed more clearly through the closed world), the classification accuracy on Undefended, WTF-PAD [21], and Onion Service [20] datasets are better than the existing models. Especially for the Onion Service [20] dataset, the accuracy of FDF has reached 70.7%, while the accuracy of the current state-of-the-art Tik-Tok [18] method is only 66.0%.
(3) We evaluated FDF in a more realistic open-world scenario (we assume that monitored users can randomly visit different websites. ese sites can be sites that we are interested in or sites that we are not interested in. rough the open world, a more realistic environment can be simulated), where we collected a dataset containing 40,000 unmonitored websites and achieved more desirable Precision and Recall in both undefended and WTF-PAD [21] environments, indicating that FDF is effective in real environments.
e remaining sections of this paper are organized as follows. e second part is the background and related work, which describes the existing approaches to the problem of website fingerprinting for the Tor system. e third part is the problem description, describing the process of fingerprint identification of the website. e fourth part introduces the FDF attack process in detail and explains the key steps of the model in principle. e fifth part introduces the experimental dataset, comparative experiments, and experimental results. e sixth part discusses the problems in the experiment of the method proposed. Finally, the seventh part is the conclusion of this paper.

Background and Related Work
For website fingerprint attacks, the data processing method of network traffic and the choice of classifier have a significant impact on its attack efficiency. e website fingerprinting methods that have performed well in recent years are shown in Table 1. In the earliest research, researchers used machine learning to classify website traffic [5][6][7][8][9][10][11][12][13]. e WF attack was first evaluated by Herrmann et al. [5] in 2009. In 2011, Panchenko et al. [6] used the Herrmann et al. dataset and employed an SVM classifier to classify Tor network traffic by various features such as packet traffic and time. e K-NN attack was proposed by Wang et al. [7] in 2014. e method employs a K-Nearest Neighbor (K-NN) classifier that uses a combination of features to evaluate the similarity between different websites through a distance metric. However, this method is not effective in reducing the impact of noise on WF attacks. In 2016, Panchenko et al. [8] proposed a novel WF attack CUMUL against Tor based on the cumulative representation of traces. e method considers the effect of real noise on WF attacks. However, the problem of overfitting occurs in the process of actual classification. In 2016, Hayes et al. [9] proposed a website fingerprinting attack K-FP based on random decision forest.
is method uses a random forest to extract fingerprints for each traffic instance, uses Hamming distance to calculate the distance between these fingerprints, and finally classifies them by k-nearest fingerprint technology.
is method shortens the classification time and reduces the impact of overfitting on the classification results. However, the noise will have a certain impact on K-FP.
In recent years, with the massive application of deep learning on WF attacks [14][15][16][17][18], the performance of WF attacks has been further improved. Sirinam et al. [15] proposed the Deep Fingerprinting (DF) attack in 2018. e highlight of DF is the design of complex convolutional neural network (CNN) structures. e deep learning model of DF can solve the WF attack problem well, and the framework of the DF model has been basically borrowed in the subsequent studies. However, DF has a long period to complete the WF attack and requires a large number of training sets to achieve better classification results. e data staleness problem also has an impact on the attack during the data collection. Sirinam et al. [16] studied a triplet fingerprint attack TF in 2019.
is attack uses a triplet network for N-shot learning [22]. is method can effectively reduce the workload of data collection and training in the implementation of WF attacks, but the accuracy of the attack needs to be improved. Rahman et al. [18] proposed the Tik-Tok attack based on packet timing information in 2020. e method uses a set of new features based on burst level features related to timing. e information contained in each of these features is mutually exclusive and improves the robustness of the classifier. e method fully considers the timing features so that it can obtain effective information and achieve a high accuracy rate of website fingerprinting under the scenario of using defense. However, due to the instability of the Tor link, it is easy to cause circuit congestion [23,24]. Circuit congestion can have an impact on the timing information, thus reducing classification accuracy.
In order to make the Tor network more secure, researchers have proposed some defensive measures [21,[25][26][27][28] to defend against WF attacks. e basic principle is to operate on packet traffic (add, delete, delay packets, etc.). In order to achieve the purpose of confusing flow features, the BuFLO [25] defense method was proposed by Dyer et al. is method achieves the effect of transmitting data packets close to a constant rate by sending data packets of a fixed length in the Tor network at a fixed time. Juarez et al. proposed WTF-PAD [21]. WTF-PAD is a probabilistic connection filling defense based on adaptive filling. It masks the features of traffic bursts by adding short-delay pseudotraffic bursts, thereby reducing the threat of WF attacks. Wang et al. proposed the Walkie-Talkie (W-T) [28] method. W-T modified the browser to communicate in half-duplex mode instead of the usual full-duplex mode. e half-duplex mode converts the cell sequence into a burst sequence, which not only saves additional overhead but also reduces the characteristics of the cell sequence, thereby leaking less information to the enforcer.

The Description of Problem
Tor consists of thousands of relays that form a worldwide network of volunteer overlays to direct Internet traffic. During a user's visit to a website, the traffic is encrypted in multiple layers so that an attacker cannot know which websites the user is visiting. Many illegal websites have emerged in the onion service, where users can log in to complete transactions without being tracked. erefore, obtaining the websites that users are visiting with the knowledge of their identity is a problem worth investigating.
Although Tor can effectively protect the security and privacy of users, it is still possible to reduce the anonymity of users by means of traffic analysis. A series of associated traffic is generated when users visit a website, and the pattern of this traffic is relatively fixed within a certain period of time.
at is, users visiting the same website in the same region within a certain time frame can obtain similar packets. erefore, the user's access traffic can be analyzed to discern which website the user is visiting. As shown in Figure 1, an enforcer is deployed locally to collect the network traffic between the client and the server and identify the website that the user is visiting. is enforcer can be a router, an Internet Service Provider (ISP), an autonomous service, and so on, capable of arbitrarily collecting encrypted traffic between the client and the entry node. e enforcer cannot discard, modify, insert, and delay packets. If the traffic is tampered with during a user's visit to the site, it may result in errors or anomalies on the user's return page. is not only affects users' browsing but also alerts them to the possibility of their privacy being compromised. Especially for illegal users, it will make it more difficult to collect their incriminating evidence.
For sites of interest to the enforcer, we call them monitored sites. For other types of websites, we call them unmonitored websites. In WF attacks, the enforcer's task is to identify the monitored websites. e enforcer needs to set up a classifier, and in addition to that, he has to loop through the Tor network to the monitored website and collect the traffic during the visit. After the collection is complete, the enforcer has to manually extract the traffic features and construct a traffic matrix from all the processed traffic data for the training of the classifier. When the classifier is trained, the enforcer can passively collect the encrypted traffic during the monitored user's access to the server, process the traffic in the same way as the training set, and then use the classifier to classify the traffic to determine Table 1: Well-performing website fingerprinting methods.
K-FP [9] 95.5 Sorting time is shortened, and overfitting is reduced. Classification effect is easily affected by the noise.
DF [15] 98.3 Complex CNN model is proposed. Large datasets are needed. TF [16] 95.0 Small datasets are needed. e accuracy needs to be improved.
Tik-Tok [18] 98.4 Multiple time features are considered. Classification effect is easily affected by circuit congestion.
whether the website being visited by the monitored user is a monitored website.
In order to improve the readability of the paper, we summarize and explain the notations in our method, as shown in Table 2.

e Principle Framework and Main Steps of the Method.
In the existing website fingerprint identification methods, the main factor affecting the classification of Tor traffic fingerprints is the noise in the traffic. ese noises can effectively confuse the features of the original Tor traffic and reduce its classification accuracy. In response to this problem, we found that frequency domain transformation can reduce the impact of noise on classification and proposed a DWT-based website fingerprint recognition method. e complete fingerprint identification process is shown in Figure 2.
is method is divided into two stages: data preprocessing and classifier classification. Data preprocessing is mainly to extract features from the collected data packets and transform the extracted sequences into the frequency domain to form circuit frequency domain feature sequences. e method of frequency domain transformation can increase the difference of traffic patterns of different websites and can obtain better classification results. Classifier classification focuses on identifying and classifying the preprocessed data using deep learning techniques. Before classifying the unknown traffic, the classifier is trained. is process requires collecting a large number of circuit frequency domain feature sequences and corresponding the sequences to their site labels one by one to generate a training sequence matrix and a training label matrix. After the training is completed, the traffic to be tested is converted into a test sequence matrix for classifier classification. is method uses a deep learning classification model combining CNN, FC, and Self-Attention and uses various regularization techniques in the model to prevent overfitting in the website recognition process.
Step 1. Capture the traffic packets of users visiting the website. Capture the background traffic during the user's visit to the website and generate the raw traffic packets.
Step 2. Extract the feature sequence of the circuit. Extract the direction and length information of the sequence of circuits in the raw network traffic packets, and combine them to form the feature sequence of circuits.
Step 3. Generate the frequency domain feature sequence of the circuit. e feature sequence of the circuit is transformed into the frequency domain feature sequence of the circuit by DWT transformation, and the low-frequency sequence generated after DWT transformation is retained.
Step 4. Store the data into the database. Store the frequency domain feature sequences of the circuits and their corresponding site labels into the database.
Step 5. Generate training set. e frequency domain feature sequences of the circuits and the site labels are extracted from the database according to the model training requirements, and the training sequence matrix and the training label matrix are generated.
Step 6. Construction of the model framework. A suitable neural network framework is selected according to the data type and features of the traffic, and a series of overfitting prevention methods are used to improve the accuracy of the model classification.
Step 7. Model training. e deep learning model is trained using the above matrix. e appropriate hyperparameters are selected through training.
Step 8. Generate the test set. Extract the frequency domain feature sequence of the circuit to be tested from the database and generate the test sequence matrix.  Step 9. Model classification. Use the model to predict the test sequence matrix and obtain the website labels corresponding to the frequency domain feature sequences of the circuit to be tested. Complete the identification of the unknown traffic and correspond the traffic to the website.

Data Preprocessing
4.2.1. Extract the Feature Sequence of the Circuit. By capturing the packets during a user's visit to a website, we can obtain the circuit sequence of the packets of this website. By analyzing this sequence, we can extract various features, including the direction, length, timing, and burst of the circuit sequence. We select the direction and length of the sequence as the key features to be extracted.
Direction. e sequence of the original circuit is mapped into the value domain of [+1, −1], and the enforcer is usually monitored before the entry relay. Specify the direction of data inflow into the enforcer as "+1" and the direction of data outflow from the enforcer as "−1." By this method, the direction sequence of the circuit Seq dir is formed.
Length. Each packet in the sequence of the circuit is packaged by the protocol before transmission. Clients and servers interact with each other through TCP protocol, so packets that do not contain TCP protocol are to be filtered  Security and Communication Networks 5 out. Next, the length of the TCP protocol layer circuit is extracted to compose the length sequence of the circuit Seq len . e length sequence and direction sequence of the circuit are combined, and a new feature sequence Seq mix is constructed by multiplying the terms of these two sequences.
Seq mix � Seq dir × Seq len . (1) In a previous study [15], researchers have verified through experimental arguments that the length of the circuit sequence does not significantly improve the accuracy of the attack. A good attack can be achieved by using only the direction of the circuit sequence. However, in our approach, the length of the circuit sequence is necessary. Any time sequence can be seen as an infinite superposition of sine waves of different frequencies and formed. Amplitude is the most basic characteristic of a sine wave. If only the direction of the circuit sequence is used, the full information of the sine wave cannot be reflected. erefore, we consider combining the length and direction of the circuit sequence to be able to achieve better results in the frequency domain transformation.

Generate the Frequency Domain Feature Sequence of the Circuit.
e circuit sequence of a packet based on timing can be understood as the result of the variation of the signal over time. e analysis of the circuit sequence in the frequency domain allows us to obtain more useful information. It is possible to analyze the composition of the sequence frequency, more precisely to decompose the sequence into several subsequences. In this way, the internal connection of each packet in the circuit sequence is reflected, and it is convenient to achieve better results in the subsequent neural network training process.
DWT (Discrete Wavelet Transformation) can discretize the scales and translations of the fundamental wavelets. It can analyze the frequency domain features of local timedomain processes and is more suitable for the analysis of nonsmooth processes. e discrete wavelet transform uses a bandpass filter to decompose the circuit sequence into multiple frequency domain components, which greatly reduces the interference of noise and makes the presentation more intuitive. e architecture of the discrete wavelet transform decomposition process for discrete sequences is shown in Figure 3. L(n) and H(n) represent the low-pass filter and highpass filter, and their correspondence is shown in relation (2). ↓Q denotes the Q-fold downsampling filter. e sequences decomposed at layer α in the architecture can be represented according to the relations (3) and (4). e high-frequency components are extracted in each layer, while the low-frequency components are deployed to the next layer to continue the decomposition. Since Q-fold downsampling is performed at each layer, if the length of the input circuit sequence is N, then the length of both x α,L (n) and x α,H (n) in the α th layer is N/Q α .
x α,L (n) � x α,L (n) � In our model, we perform a one-layer architectural decomposition of the circuit sequence and set the multiplier of the downsampling filter to 2. us, we are able to obtain the sequence decomposition method as shown in relations (5) and (6).
e circuit sequence is processed in the frequency domain using the relation (5) after the feature processing. e frequency domain processing results in a low-frequency sequence x 1,L (n) and a high-frequency sequence x 1,H (n). x 1,L (n) contains the slowly changing part of the circuit sequence. It is the basic frame of the sequence and belongs to the approximate information of the sequence. x 1,H (n) contains the rapidly changing part of the circuit sequence. It belongs to the detailed information of the sequence, which contains the noise. We use the low-frequency part x 1,L (n), which can represent the contour features of the sequence, for the training of the model. It can reduce the interference of noise in the sequence for fingerprint recognition.
In our method, both L(n) and H(n) are of constant length, independent of the length N of the circuit sequence. We only need the low-frequency part of the wavelet transform. e convolution of the circuit sequence and the filter requires O(N) time complexity. After each layer of convolution, a branch of length N/2 is formed. erefore, the time complexity required for the entire frequency domain transformation process is O(N).

Construction of the Model Framework.
Website fingerprinting on Tor is a supervised classification problem. Starting from DF [15], deep learning techniques have achieved good results on the website fingerprinting problem. We have borrowed from these models and made improvements. In DF, two convolutional layers were used before each Max Pooling. e researchers believe that adding more convolutional layers to each Base Model can obtain a deeper network and extract features more efficiently. In our model, each Max Pooling layer is preceded by only one convolutional layer, which can effectively reduce the complexity of the neural network. After the Base Model, we add a Self-Attention layer. e reason for this is that CNN only considers the information in the receptive field and only acts on a local scale. Self-Attention, on the other hand, considers the information on the entire circuit sequence. It contains a much wider range. erefore, we consider extracting the local features in the circuit sequence by CNN first and then extracting the global features by Self-Attention, so as to form a complete model. is approach not only reduces the complexity of the neural network but also does not affect the extraction of features. e neural network classification model is shown in Figure 4.
Since neural networks have a fixed input size requirement, for one-dimensional circuit sequences, different lengths of circuit sequences need to be fixed to the same length. After data preprocessing, the circuit sequence length needs to be set to a fixed threshold. Sequences with length less than the threshold are filled with 0, and those with length greater than the threshold are truncated. All circuit sequences are combined to form the input matrix.
To address the selection of hyperparameters in different modules, we empirically assign a range of values to these hyperparameters. For hyperparameters with a small range of values, the hyperparameters are taken iteratively. For hyperparameters with a large range of values, the hyperparameters are taken using the dichotomous method. In the process of model construction, we filtered the hyperparameters module by module and finally obtained the best combination of hyperparameters.
In Tor, many useless data packets are generated when users visit websites due to network congestion, identity verification, and other reasons. is may cause the same user to make multiple visits to the same website in the near time to generate quite different traffic. ese noisy data packets can cause overfitting problems during neural network training. For the overfitting problem, we use regularization techniques such as Dropout, Batch Normalization (BN), and Label Smoothing methods. Dropout reduces the interaction between hidden nodes and makes the model more generalizable by making a certain neuron probabilistically stop working. BN normalizes the output results so that the output obeys the standard normal distribution and reduces the internal covariance shift (ICS), which not only helps the network fit faster but also reduces the overfitting problem. Due to the small number of parameters in the convolutional layer, Dropout is rarely used after the convolutional layer, and BN is usually used. In our model, BN is connected immediately after each CNN, and Dropout is used after Max Pooling to prevent overfitting. ere are many parameters in the FC and Prediction process, so BN and Dropout can be used together.
In order to approximate the predicted probability distribution to the true distribution during neural network prediction, a common practice is to encode the true labels using the one-hot method.
is encoding approach can make the model lack adaptability and be overconfident in its predictions, which can lead to overfitting problems. Label Smoothing smoothes the empirical distribution of the gap between the maximum prediction and the mean of the other categories by adding a smoothing factor. e essence of Label Smoothing is to drive the classification probability results after the activation of the Softmax activation function in the neural network closer to the correct classification, so it is placed in the last part of the model.

Model Training.
e selection process of the hyperparameters in the model is shown in Table 3, containing the range of values for each hyperparameter and the value that achieves the best results. We conducted experiments on tuning parameters using the collected Undefended Closed-World dataset and validated them using other datasets, all with good results.

Experiments and Results Analysis
To validate the performance of the proposed FDF method, we conducted a series of experiments based on the Undefended, WTF-PAD [21], and Onion Sites [20] datasets.

e Closed-World Dataset.
We performed a recursive crawl of the homepages of the top 100 websites ranked by Alexa [31] through the Tor network, with a total of 1000 crawls per site. We deployed the work on LXD containers on ten VPS servers in different countries.

e Open-World Dataset.
Since it is not realistic to visit all Internet sites, we selected some of them for simulating the open-world experiment. We visited the top 40,000 websites in Alexa ranking in order. Because these sites are unmonitored sites, they cannot contain the 100 monitored sites collected in the closed-world experiment. We deployed the work in the same ten VPS servers. e Onion Service Dataset. A collection of onion domains was conducted by Overdorf et al. [19], and the sites were fingerprinted. ey published the dataset used for their experiments to the Internet in the form of tshark logs, which we chose to use for our experiments. Since collecting a large number of onion domains is a difficult task, we chose to use this dataset for experiments.

e Defense Dataset.
We performed evaluation tests on the WTF-PAD [15] defense approach. For the WTF-PAD [21] defense, we adapted the raw traffic we collected using a script code posted by the researchers in GitHub. It is used to simulate the traffic generated during access in a real environment according to the defense protocol populated.
A total of five datasets were used in our experiments. In the closed-world scenario, data were collected for undefended, WTF-PAD [21] defense, and onion services, generating the Undefended (CW), WTF-PAD (CW), and Onion Sites (CW) datasets. In the open-world scenario, data collection was performed for both undefended and WTF-PAD [21] defense methods to generate Undefended (OW) and WTF-PAD (OW) datasets. Table 4 shows the website classes and the number of visited website instances in each dataset. We randomly divided each dataset into three parts: training set, validation set, and test set. Due to the large size of the dataset, we divided it according to the ratio of 8 : 1 : 1.

Website Fingerprinting Experiments on the Closed-World
Dataset.
e core of the FDF method is to process the circuit sequence in the frequency domain before performing the deep learning fingerprint recognition on the circuit sequence. In addition to DWT, Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT) are also mainstream frequency domain processing methods, which have good applications in the direction of image processing. We compared the above three frequency domain processing methods in the closed-world environment. FFT is an efficient and fast algorithm of DFT that can reduce the operation time. erefore, we use FFT instead of DFT for our experiments. Table 5 shows the accuracy results of fingerprint recognition on different datasets after processing by three frequency domain processing methods. It can be found that the accuracy rates of the two methods, DCT and FFT, are relatively close to each other. Meanwhile, DWT is significantly better than the other two methods on all three different datasets.
is is because circuit sequences are nonstationary signals, and DWT has better results for nonstationary signals, while FFT is more suitable for handling stationary signals.
To show the good attack effect of FDF, we compared it with K-NN [7], K-FP [9], CUMUL [8], DF [15], and Tik-Tok [18] attacks.    Table 6 shows the accuracy results of different attack methods in the closed-world scenario for the three environments. It can be found that FDF outperforms the other attacks on the Undefended, WTF-PAD [21], and Onion datasets. Each attack method does not perform very well on the Onion dataset, which we believe is related to the dataset.
e Onion dataset has 539 categories with only 77 traffic data per category, which is much less data than other datasets and therefore reduces the accuracy rate. For open-world scenarios, Precision and Recall were suggested in literature [9,21] for the evaluation of classifiers. Because the difference between the limited set of monitored sites and the limited set of unmonitored sites may be too large, True Positive Rate (TPR) and False Positive Rate (FPR) can be wrong in the interpretation of the model attack performance.

Website Fingerprinting Experiments on the Open-World
For the performance evaluation process, we used the standard model proposed in DF Attack [15]. In the openworld scenario, for the dataset of monitored websites, they are trained in the same way as in the closed world. For the dataset of unmonitored websites, it is trained as an additional class. We evaluated undefended and WTF-PAD [21] in the open-world scenario by tuning the attack for Precision and Recall. Precision and Recall are shown in relations (7) and (8).
Tables 7 and 8 show the results of different methods to tune the attacks for Precision and Recall, respectively, for the two datasets in the open-world scenario. Figure 5

Discussion
In this section, we discuss the data preprocessing method before the feature frequency domain processing and the number of DWT decomposition layers for the feature frequency domain processing.
Input for feature frequency domain processing: e most important feature of packets in WF attacks is the direction of the circuit sequence. In DF [15], researchers have also compared packet processing methods and found that the best results can be achieved using only the direction of the circuit sequence. But for frequency domain transformation, not only the direction of the cell sequence but the amplitude of the cell sequence is also very important. If only the direction of the circuit sequence is used and its amplitude is ignored, a lot of information of the original sequence will be leaked during the frequency domain transformation. us, the effect of frequency domain processing of the signal cannot be achieved, and the result is degraded. erefore, we choose to use the direction and length of the signal element sequence as the input for the feature frequency domain processing. e number of decomposition layers of DWT: in other applications of DWT, multiple layers of wavelet decomposition are often required to achieve better results. Each DWT decomposition results in two components, a highfrequency component, and a low-frequency component.
ese two components are of the same length. In our method, we use the decomposed low-frequency components every time. In other words, for each layer of DWT decomposition, the length of the circuit sequence is halved. For example, if the input length of the circuit sequence in the FDF model is 5000, a two-layer DWT would require an original circuit sequence length of 20000. We found through statistical analysis that all the original circuit sequences are less than 10,000 in length, so a lot of padding is needed for the circuit sequences. is will have a great impact on the original sequences and lead to a decrease in the accuracy of the classification results. In summary, we choose to perform one layer of DWT decomposition for the feature frequency domain processing. We believe that future additions to the website content and updates to the security mechanisms will result in longer circuit sequences during visits to the website. On this basis, WF attacks using multilayer DWT are expected to achieve a better result.

Conclusion
In this study, we propose an efficient DWT-based WF attack method FDF. We construct key features for traffic analysis by performing DWT on the length and directional features of circuit sequences. After that, we use neural networks to complete the learning and classification of the traffic frequency domain features. Overall, our results show that transforming circuit sequences to the frequency domain for deep learning can achieve good results. However, a large number of training sets are required for data support during the training process. is leads to longer data collection time and increases the difficulty of WF attacks. In the future, we should work to shorten the time to complete the fingerprint identification of the website. One possibility is to learn from the idea of the big data framework [32]. e fingerprint identification process of the website should be layered, especially the data collection process. Collect data through a distributed architecture and reasonably arrange the modules to add new data and delete old data. Ultimately, our methods can effectively respond to urgent tasks [33].

Data Availability
Previously reported Onion Service datasets were used to support this study and are available at DOI:10.1145/ 3133956.3134005. ese prior studies (and datasets) are cited at relevant places within the text as references [12]. e closed-world datasets used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.