# Non-Interactive Decision Trees and Applications with Multi-Bit TFHE
## 7 Conclusions and Future Work  
This paper introduced a new non-interactive integer comparison protocol using TFHE with programmable bootstrapping. This protocol was tested with 128-bit security and scaled linearly with the input bit length. As an application, we developed an efficient protocol for the private evaluation of decision trees. The evaluation is done in a non-interactive manner, where there is no interaction between the client and server. The model owner can delegate the evaluation to a third-party evaluator, and the client can be offline after sending the feature vector to the evaluator. We experimented with widely used real datasets from the UCI machine learning repository and compared them with the existing protocols. The protocol can be extended to perform more complex inferences using random forest classification.  
An important future extension to the protocol is to support ensemble and gradient boosting methods. This extension is possible if we can extend the protocol with homomorphic operations, such as division on encrypted numbers. Our solution evaluates the tree encrypted with the client's public key. Therefore, it requires a key distribution mechanism to share the client's public key with the model owner. An exciting direction for future work is to use multi-key homomorphic encryption [28; 29] to encrypt the tree and the feature vector with different keys. This technique eliminates the need for key distribution between the client and the model owner.  
J.P.: Conceptualization, Methodology, Software, Validation, Writing--Original Draft; B.H.M.T.: Conceptualization, Methodology, Writing--Review and Editing; B.V.: Supervision, Writing--Review and Editing; K.M.M.A.: Supervision, Resources, Funding Acquisition. All authors have read and agreed to the published version of the manuscript.  
[PERSON], [PERSON] and [PERSON] are supported by A*STAR under its RIE2020 Advanced Manufacturing and Engineering (AME) Programmatic Programme (Award A19E3b0099).  
**Data Availability Statement:** The dataset used for this study is publicly available at UCI Machine Learning Repository [5].  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{\(n\)} & \multirow{2}{*}{\(d\)} & \multirow{2}{*}{\(m\)} & \multicolumn{5}{c}{**The Evaluation Time (s)**} \\  & & & & & **This Work** & **XCMP [6]** & **[PERSON] et al. [21]** \\  & & & & **32-bit** & **64-bit** & **13-bit** & **64-bit** \\ \hline Heart-disease & 13 & 3 & 5 & 24.29 & 47.52 & 0.59 & 0.25 \\ Credit-screening & 15 & 4 & 5 & 24.29 & 47.52 & – & 0.27 \\ Breast-cancer & 9 & 8 & 12 & 58.30 & 114.04 & – & 0.34 \\ Housing & 13 & 13 & 92 & 446.98 & 874.29 & 10.27 & 1.98 \\ Spambase & 57 & 17 & 58 & 281.79 & 551.19 & 6.88 & 1.80 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance of secure evaluation on real datasets from UCI repository.