UC Secure Private Branching Program and Decision Tree Evaluation

Abstract

Branching program (BP) is a DAG-based non-uniform computational model for L/poly class. It has been widely used in formal verification, logic synthesis, and data analysis. As a special BP, a decision tree is a popular machine learning classifier for its effectiveness and simplicity. In this work, we propose a UC-secure efficient 3-party computation platform for outsourced branching program and/or decision tree evaluation. We construct a constant-round protocol and a linear-round protocol. In particular, the overall (online + offline) communication cost of our linear-round protocol is <inline-formula><tex-math notation="LaTeX">$O(d(\ell + \log m+\log n))$</tex-math></inline-formula> and its round complexity is <inline-formula><tex-math notation="LaTeX">$2d-1$</tex-math></inline-formula> , where <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> is the DAG size, <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of features, <inline-formula><tex-math notation="LaTeX">$\ell$</tex-math></inline-formula> is the feature length, and <inline-formula><tex-math notation="LaTeX">$d$</tex-math></inline-formula> is the longest path length. To enable efficient oblivious hopping among the DAG nodes, we propose a lightweight 1-out-of- <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> shared OT protocol with logarithmic communication in both online and offline phase. This partial result may be of independent interest to some other cryptographic protocols. Our benchmark shows, compared with the state-of-the-arts, the proposed constant-round protocol is up to 10X faster in the WAN setting, while the proposed linear-round protocol is up to 15X faster in the LAN setting.