Evaluating Mixing Methods: Anonymity, Long-Term Information Leakage, and Cost

Mix-nets are essential tools for safeguarding user privacy in communication networks. When deploying systems, two well-known mixing methods, batch (e.g., Timed Mix) and continuous mixing (e.g., Stop-and-Go Mix), are commonly used in real-world Mix-nets. However, no comprehensive study has evaluated the impact of these methods on anonymity, long-term information leakage, and the cost associated with dummy message overhead. To address this gap, this study provides a comprehensive analysis of these mixing methods. To this end, anonymity set size and entropy metrics are used to evaluate the anonymity protection of individual messages. The applicability of the Statistical Disclosure Attack (SDA) is extended to evaluate long-term information leakage for both mixing methods, and the closed-loop control anonymity protection model is adapted to measure the cost of anonymity protection in terms of the dummy message overhead. The experimental results show that continuous mixes provide stronger anonymity protection for individual messages-yielding up to 10% higher entropy under the default experimental settings. However, both long-term information leakage and the cost of achieving the desired protection are generally higher in continuous mixes, especially under high traffic scenarios. For example, under the default experimental settings, completing the SDA requires 1.5 times more observations in batch mixing than in continuous mixing and achieves the desired protection with 49% less cost in terms of the dummy message usage. These findings highlight the importance of selecting appropriate mixing method to balance anonymity, long-term information leakage, and cost in anonymous communication systems.