Quantifying Mix Network Privacy Erosion with Generative Models

Abstract

Modern mix networks improve over Tor and provide stronger privacy guarantees by robustly obfuscating metadata. As long as a message is routed through at least one honest mixnode, the privacy of the users involved is safeguarded. However, the complexity of the mixing mechanisms makes it difficult to estimate the cumulative privacy erosion occurring over time. This work uses a generative model trained on mixnet traffic to estimate the loss of privacy when users communicate persistently over a period of time. We train our large-language model from scratch on our specialized network traffic ``language'' and then use it to measure the sender-message unlinkability in various settings (e.g. mixing strategies, security parameters, observation window). Our findings reveal notable differences in privacy levels among mix strategies, even when they have similar mean latencies. In comparison, we demonstrate the limitations of traditional privacy metrics, such as entropy and log-likelihood, in fully capturing an adversary's potential to synthesize information from multiple observations. Finally, we show that larger models exhibit greater sample efficiency and superior capabilities implying that further advancements in transformers will consequently enhance the accuracy of model-based privacy estimates.