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原文摘要

Private decision-tree evaluation lets a server classify a client's encrypted query without learning the input. In the non-interactive, path-based setting over TFHE, the server returns a single encrypted prediction by aggregating per-path comparison outcomes, and the standard per-leaf formulation pays one programmable bootstrap (PBS) per leaf, which dominates the cost. We propose a signed dyadic path-sum encoding that nearly halves this cost: each internal node receives a signed dyadic label so that every root-to-leaf path accumulates a distinct integer sum, which lets the two children of a leaf-parent be packed into a single test polynomial and resolved by one PBS, reducing the PBS count from the number of leaves to the number of leaf-parents. We formalize the distinct-sum property and prove that the dyadic labeling is the range-minimal encoding satisfying it, and its half-symmetric signed form is magnitude-optimal, tightening the comparison-stage noise bound at fixed parameters. We derive the two conditions under which the encrypted evaluation returns the exact prediction and instantiate parameters with per-inference failure below $2^{-64}$ at 128-bit security. We show that the ring degree grows linearly with the consumed plaintext range, which confines the profitable regime to depths $\leq 4$, where our method stays faster even when each scheme runs at its own cost-optimal parameters. We further extend the encoding to gradient-boosted ensembles. On standard UCI benchmarks at depths 1-4, our method reduces single-tree latency by $1.51\times$-$1.92\times$ and ensemble latency by $2\times$, without accuracy loss, while preserving the compact, non-interactive response.