An efficient cross-domain few-shot website fingerprinting attack with Brownian distance covariance

Website fingerprinting (WF) attacks can infer the specific websites from Tor encrypted traffic. However, most existing WF attacks require a large number of training samples (e.g., hundreds) per website to achieve the desirable accuracy. To lessen the training data scale, the low-data WF (LDWF) attacks are proposed. Whereas existing LDWF attacks generally require gathering an auxiliary dataset, which increases the bootstrap time to launch a WF attack. To address this limitation, we present the cross-domain LDWF attack problem and put forward the first cross-domain LDWF attack, namely WFBDC (WF with Brownian Distance Covariance), which can use a historical gathered dataset to be the auxiliary dataset. The primary advantage of WFBDC is the introduction of the BDC metric to measure the similarity between two samples. The key to BDC lies in that it defines the similarity by measuring the discrepancy between joint characteristic functions of embedded features and the product of the marginals. To mitigate the domain deviation, the transfer learning and multi-similarity loss techniques are also adopted. We conduct 10 experiments based on 15 datasets to evaluate the performance and efficiency of WFBDC. Evaluation results show that WFBDC can improve the performance of the state-of-the art LDWF attacks by up to 9% and 19% in the closed-world and open-world scenarios, respectively. Meanwhile, WFBDC can significantly reduce the pre-training time of existing LDWF attacks.