## 4 Methodology
### General Architecture
#### 4.1.5 Information of the Multi-Path  
In the following experimental part of this paper, we successfully demonstrate the efficiency of this defense, which can greatly reduce the accuracy of WFP analysis. In addition, we further explored the reason why the multi-path transmission scheme can reduce the accuracy of the classifier and quantified it with a mathematical model. The amount of information formula \(H(X)\) proposed by [PERSON] [45] defines how much uncertainty is eliminated by the size of the amount of information contained in an event, and the calculated value is the amount of information, as shown in Equation (1). Inspired by this, we can evaluate how challenging it would be for an attacker to execute WFP attacks by calculating the amount of information contained in the multi-path transmission.  
\[H(X)=-\sum_{i=1}^{n}p(x_{i})\log p(x_{i}) \tag{1}\]  
The \(p(x_{i})\) represents the probability of the random event \(X\), which is \(x_{i}\). The splitting strategy we adopt is that each path has an equal probability of being selected and the amount of data transmitted is equal. Assuming that the number of entry relays is \(m=4\), meaning the number of circuits is four, and the attacker has the ability to monitor one of the paths, the probability of the attacker obtaining \(1/4\) of the original traffic is \(1/4\), meaning \(p(x_{i})=1/4\), where \(n=4\). Another case is that the probability that the attacker does not obtain the original traffic is \(p(x_{i})=3/4\), and the calculated amount of information contained in the traffic features obtained by the attacker from one of the paths is \(H(X)=0.811\). If the traffic only relies on single-path transmission, the probability that the attacker can obtain all the traffic features is \(p(x_{i})=0\), \(n=1\), so the calculated amount of information included is \(H(X)=0\). It can be concluded that the amount of information contained in the traffic features obtained from the multi-path is greater, and the amount of information means that any uncertainty is eliminated. For the attackers, obtaining traffic features from the multi-path will be accompanied by more uncertainty. This means the uncertainty of the WFP classification increases, which causes the accuracy of the classifier to decline. This also means that the multi-path defenses only disclose limited useful signature information to the attackers. Therefore, we prove theoretically that the multi-path can reduce the density of the statistical features of the traffic, and can productively reduce the success rate of WFP.  
This section describes the overall architecture of SMART and details how the sender and receiver work during the communication process, including the cell format and circuit creation during transmission. The Tor multi-path architecture, one of the contributions of this paper, is represented from the network layer to the transport layer to the application layer. The Tor lightweight and reliable multi-path scheme introduced in our paper effectively ensures the anonymity of Tor users and the unobservability of communication relationships. In the end, we proved that the multi-path will increase the uncertainty of WF, thereby reducing the accuracy of the classifiers. While improving the anonymity of Tor, and how to ensure the stable working of the Tor multi-path transmission, improving the reliability of data transmission is our next key research work.