Guopeng Lin, Weili Han, Wenqiang Ruan et al.
Multi-party training frameworks for decision trees based on secure multi-party computation enable multiple parties to train high-performance models on distributed private data with privacy preservation. The training process essentially involves frequent dataset splitting according to the splitting criterion (e.g. Gini impurity). However, existing multi-party training frameworks for decision trees demonstrate communication inefficiency due to the following issues: (1) They suffer from huge communication overhead in securely splitting a dataset with continuous attributes. (2) They suffer from huge communication overhead due to performing almost all the computations on a large ring to accommodate the secure computations for the splitting criterion. In this paper, we are motivated to present an efficient three-party training framework, namely Ents, for decision trees by communication optimization. For the first issue, we present a series of training protocols based on the secure radix sort protocols to efficiently and securely split a dataset with continuous attributes. For the second issue, we propose an efficient share conversion protocol to convert shares between a small ring and a large ring to reduce the communication overhead incurred by performing almost all the computations on a large ring. Experimental results from eight widely used datasets show that Ents outperforms state-of-the-art frameworks by $5.5\times \sim 9.3\times$ in communication sizes and $3.9\times \sim 5.3\times$ in communication rounds. In terms of training time, Ents yields an improvement of $3.5\times \sim 6.7\times$. To demonstrate its practicality, Ents requires less than three hours to securely train a decision tree on a widely used real-world dataset (Skin Segmentation) with more than 245,000 samples in the WAN setting.