# Binary-Tree-Fed Mixnet: An Efficient Symmetric Encryption Solution
## 6 Conclusions  
This section offers an overview of this work. The main contributions are reviewed, the advantages and limitations of this new scheme are highlighted, and future lines of research are discussed. In the context prior to this article, ESEBM was the fastest mixnet to date. It represented a qualitative leap over previous schemes by reducing the computing time in the nodes by two orders of magnitude. Its greatest merit is perhaps to have demonstrated that it is possible to do without asymmetric encryption. However, ESEBM has certain weaknesses and needs to use long message headers. The challenge driving this work was to further improve performance by leveraging the pure symmetric encryption approach. The solution comes from two simple ideas: fragmenting the keys to hide them from the nodes (stage 1) and using labels to enable free permutation in stage 2. The former originated the key sending method of the binary graph, and the latter enables the nodes to reduce the operations to be performed to a minimum (stage 3), thus maximizing their performance. Among the contributions, the new technique of sending keys through a binary graph from stage 1 stands out. Through this, a set of entities can establish a symmetric key with another anonymously, all this using only XOR operations and permutations. Although it has been applied to mixnets, it could be used in other environments. For example, a group of authorized users could establish label-key pairs in this way with a server. They could then contact it using any anonymous channel [1]. By identifying themselves only with the tag and demonstrating knowledge of the key, the server would know that they belong to the authorized group but would not be able to identify any user in particular. From here, users could interact anonymously and securely with the server. This technique would be similar to blind signature but with the advantage of requiring less computational cost and without the weakness inherent to any asymmetric key cryptosystem. The main contribution is BTFM. It is a new mixnet scheme inside a very rare category, symmetric encryption mixnets, which includes only two more: SEBM and ESEBM. While these types of mixnets lack robustness, fault tolerance, and verifiability, they instead offer a qualitative leap in performance, reducing delay. In this respect, BTFM shows better rates  
Figure 7: Excedance of an ESEBM batch over BTFM. than ESEBM (4 times faster). The reason is that BTFM minimizes the processing of each node. As far as we know, there is no mixnet faster than BTFM. This new scheme can be used in any scenario where a mixnet is the solution. Nevertheless, the requisite of a complex starting phase leads to environments where the same users send messages continuously, like in forums or meetings. In this context, using the same key multiple times could be a weakness when just an XOR operation is performed. However, the same scheme is valid with other symmetric encryption algorithms like AES (Advanced Encryption Standard) in the production phase. Other applications appropriate for BTFM are those requiring high throughput, such as elections or nationwide surveys. Another contribution of this article has been the revelation of ESEBM vulnerabilities. A comparison with BTFM yields a tougher constraint on adversaries being successful. Therefore, BTFM improves ESEBM in speed and security. The drawback is that BTFM must be applied to batches of users acting at the same time. ESEBM can better deal with an asynchronous demand. For both, it remains an open question to provide verifiability and robustness to overcome traditional schemes. In this sense, it would be interesting as a line of research to study the combination with asymmetric encryption techniques only for verifiability, trying to maintain the same performance when all nodes are honest. Another challenge for future work is to increase the minimum threshold of adversaries to break anonymity. Conceptualization, D.A.L.-G.; Methodology, D.A.L.-G.; Literature review, D.A.L.-G., J.P.T., D.V.