## 4 Methodology
### Redundant Slicing
\[E_{n,1}=EM_{n,k}*M_{k,1} \tag{4}\]  
R means twice the amount of original data because the amount of initial data processed by the redundant encoding will double. After the encoding operation, the value of the post-redundancy R is obtained as 2*K, according to Equation (5). The data will be encrypted layer by layer by the session keys of the entry and the middle OR after the redundancy encoding operation. The fragments will be transmitted via subcircuits. \[R=\left\{ \begin{array}{ll}r+2*K&(r=0,\text{Default })\\ r+K&(r\in(0,K],\text{Defined })\end{array} \right. \tag{5}\]  
**Decoding operation:** The decoding operation starts when the receiver (middle OR) receives the minimum recovery number of redundant slices. The decoding operation should meet the following requirements for successful decoding:  
* **The minimum recovery amount K:** This requires receiving a sufficient number of slices to recover the original data, where K is the number of minimum recoverable slices. The initial slice number, for instance, is K. After the redundant encoding procedure, the data slice number reaches 2K. When performing redundant decoding, the middle OR must receive at least K redundant slices to recover the original data; \begin{table}
\begin{tabular}{c c} \hline
**Symbol** & **Description** \\ \hline K & The number of initial packets \\ r & Redundant parameters \\ IM & Independent matrix \\ EM & Coding coefficient matrix \\ CM & Circulant matrix \\ M & Initial data matrix \\ E & Packet matrix after coding \\ RM & Matrix of received data \\ DM & Decoding matrix \\ \hline \end{tabular}
\end{table} 
Table 2: Redundant symbol description. * **Linear independence principle:** This requirement has been satisfied during the experiment. The coding coefficient matrix we applied satisfies the linear independence principle. In the decoding process, as shown in Equation (6), the received packet data is first integrated into a corresponding square matrix, and its inverse matrix should be deduced later. The square matrix and the inverse matrix are used for matrix operations to finally obtain the original matrix M. \[DM_{k,k}*RM_{k,1}=M_{k,1}\] (6) In order to make the reader understand the decoding process more clearly, we show the slice redundancy process in Figure 4. After the coding operation is completed, the traffic is transmitted over multiple Tor subcircuits, and the traffic pattern is observed by the attacker at the entry OR, and the website fingerprinting afterward is basically inconsistent, completely changing the original pipelined single path model, and the experimental results prove that this effectiveness against WFP attacks is significantly improved. The problem of unrecoverable data slice loss is also solved. If \(\mathbf{m}_{1}\), \(\mathbf{m}_{3}\), and \(\mathbf{r}_{1}\) are lost during transmission (\(\mathbf{m}_{1}\) and \(\mathbf{r}_{1}\) represent the packet and redundant slice on the first subcircuit), the receiver will select the matching row vectors, which, in the encoding coefficient matrix, are made up of the slices received, compose the square matrix and perform the inverse operation to obtain the DM (decoding matrix), and then use RM to perform the decoding operation to successfully recover the initial content, which ensures the reliability of communication.