Random forest evaluation using multi-key homomorphic encryption and lookup tables

In recent years, machine learning (ML) has become increasingly popular in various fields of activity. Cloud platforms have also grown in popularity, as they offer services that are more secure and accessible worldwide. In this context, cloud-based technologies emerged to support ML, giving rise to the machine learning as a service (MLaaS) concept. However, the clients accessing ML services in order to obtain classification results on private data may be reluctant to upload sensitive information to cloud. The model owners may also prefer not to outsource their models in order to prevent model inversion attacks and to protect intellectual property. The privacy-preserving evaluation of ML models is possible through multi-key homomorphic encryption (MKHE), that allows both the client data and the model to be encrypted under different keys. In this paper, we propose an MKHE evaluation method for decision trees and we extend the proposed method for random forests. Each decision tree is evaluated as a single lookup table, and voting is performed at the level of groups of decision trees in the random forest. We provide both theoretical and experimental evaluations for the proposed method. The aim is to minimize the performance degradation introduced by the encrypted model compared to a plaintext model while also obtaining practical classification times. In our experiments with the proposed MKHE random forest evaluation method, we obtained minimal (less than 0.6%) impact on the main ML performance metrics considered for each scenario, while also achieving reasonable classification times (of the order of seconds).