## 2 Related Works  
Anonymous communication between users is still an unsolved research topic. In order to send messages over the Internet, there must be a source IP address and a destination IP address. Encryption can be used to provide confidentiality over the content of a message, but it does not offer protection against traffic analysis attacks. [PERSON] [15] proposed mix networks as a mechanism to obtain anonymous communication. Anonymous communication may allow high latency of messages or require low latency. Examples of the first one are message-based systems such as cyberpunk remainers, anon.penet.fi, and mixminion [18; 19]. These systems do not require an immediate response,like email systems. On the other hand, low-latency anonymous systems are based on onion routing like TOR [20], as they need real-time response; web applications, instant messenger, and secure shells belong to this category. For instance, Loopix, which is a mix network architecture centered around exponential mixes that use cover traffic to prevent traffic analysis attacks, as well as Vuvuzela design [21; 22]. Anonymous communication networks aim to provide sender-unlinkability as well as other metrics of interest like unobservability, linkability, and undetectability. Most of these metrics are detailed in [23]. To guarantee sender unobservability, dummy traffic is often used. However, this overloads the communication channels, reduces throughput, and underutilizes bandwidth. [PERSON] and [PERSON] [24] proposed in 2003 to employ disjoint sets across communication observations to determine the exchange of information between users. The authors called this technique a disclosure attack. [PERSON] [25] built on this research by selecting a single user, [PERSON], and taking larger communication samples to determine the probability that other users exchange information with the first one. The authors termed this procedure a statistical disclosure attack (SDA). From here on, there are many other studies that employ SDA to help determine the exchange of information between [PERSON] and other users. In [26] the authors define the number of messages, \(n\), that [PERSON] might send with a probability \(P_{m}(n)\), while [27] assumes that all users have \(n\) friends and they send messages with uniform probability. In [28], the authors introduce the hitting set attack (HSA), which focuses on finding the number of rounds needed to determine who is sending information to [PERSON] with a set probability. [PERSON] et al. [29] use a more general user behavior model, which they call Perfect Matching SDA (PMDA), where the number of the user's friends and the distribution of sending probabilities toward them are not restricted. However, this study still uses synthetic data as input for its experiments. In a subsequent paper, [PERSON] and [PERSON] [30] introduce BT-SDA, which employed Bayesian techniques and graph theory to infer the probability of paired communication; although they assume each user has a different number of friends, the probability of sending information is the same between them. Later, the Reverse SDA (RSDA) algorithm [31] assumes that each message receives a response and uses this reverse observation to help determine the communication between users. Finally, [PERSON] and [PERSON] [32] employ least squares SDA (LSDA) to study the accuracy with which an adversary can identify the sender/receiver profile of [PERSON]. Besides seeking to identify [PERSON]'s message receivers, they also try to estimate the probability that [PERSON] sends a message to them. In [26], the authors introduce background noise, which initially should increase the difficulty to determine communication patterns between users. However, they also control users activity, which in the end helps them to obtain better predictions. In [27] the authors also include background noise to increase the difficulty of finding sending and receiving pairs; however, their data and assumptions are still far away from real scenarios. [PERSON] et. al.