Prior work has addressed the problem of confidential inference in decision trees. Both traditional order-preserving cryptography (OPE) and order-preserving NTRU cryptography have been used to ensure data and model privacy in decision trees. Furthermore, FPGA architectures and implementations have been proposed for implementing such confidential inference algorithms on resource-limited, edge-based platforms such as low-cost FPGA boards. In this paper, we address the challenging problem of scalability of order-preserving confidential inference to random forests, which are ensembles of decision trees that are meant to improve their classification accuracy and reduce their overfitting. The paper develops a methodology and an FPGA implementation strategy for scaling up OPE to random forests. In particular, a framework is used to study the multifaceted tradeoffs that exist between the number of trees in the random forest, the strength of the encryption, the accuracy of the inferences, and the resources of the edge platform. Extensive experiments are conducted using the MNIST dataset and the Intel DE10 Standard FPGA board.

One main objective of this paper is to show how to adapt the well-known, lattice-based NTRU post-quantum encryption to the confidential inference in decision trees. Another objective is to describe a resource-efficient FPGA implementation of the adapted NTRU. The typical use case of such encryption is that of two parties where one party has proprietary ownership of the decision tree model while the other party has proprietary ownership of the data. Confidential inference in decision trees can be insured using order-preserving cryptography, which has much weaker requirements and is therefore easier to implement than fully homomorphic cryptography. Post-quantum NTRU is not order-preserving, but interestingly, it can be modified to obey the order-preserving property. We call the resulting cipher OP-NTRU. Lossless compression can be applied to the ciphertext produced by OP-NTRU to facilitate its hardware acceleration. OP-NTRU has been implemented on an FPGA with the HDL code automatically compiled from the machine learning framework. Confidential inference experiments report more than 96% compression without degrading inference accuracy in FPGA for the MNIST dataset.