We propose novel secure multi-party protocols for decision-tree classification. Our protocols hide not only an input vector and an output class but also the structure of the tree, which incurs an exponential communication complexity in terms of the maximum depth of the tree, d_(max), for a naive construction. We tackle this problem by applying Oblivious RAM (ORAM) and obtain two efficient constructions with polynomial communication complexity (that counts the number of multiplications). The first protocol simulates ORAM in secure multiparty computation. The communication complexity of the first protocol is O(d~3_(max) log d_(max)) in the online phase and O(d~4_(max) log d_(max)) in total. We then improve this protocol by removing the position-map accesses, which is the most time-consuming parts in the ORAM. In the second protocol, we reduce the communication complexity to O(d~2_(max) log d_(max)) in the online phase and O(d~3_(max) log d_(max)) in total, and also reduce the number of rounds from O(d~2_(max)) to O(d_(max)). We implemented the proposed two constructions and the naive one, and experimentally evaluated their performance.
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