Paper 2026/1263 Original: eprint.iacr.org/2026/1263 ↗

LCPDTE: Low-Complexity Private Decision Tree Evaluation over Homomorphic Encryption

Abstract

As machine-learning-as-a-service (MLaaS) becomes ubiquitous, protecting model queries via private inference is increasingly critical. Existing homomorphic encryption (HE)-based protocols for Private Decision Tree Evaluation (PDTE) have server complexity that scales at least as $O(2^D)$ in the tree depth $D$, so the cost of evaluating each tree grows exponentially with depth; in gradient boosted decision tree (GBDT) ensembles, where predictions aggregate the outputs of many trees, this per-tree cost is directly amplified. In this paper, we present a non-interactive HE-based PDTE protocol built on the CKKS scheme with an end-to-end complexity of $O(p\sqrt{2^D})$, where $p$ is the input bit-length. To the best of our knowledge, this is the first HE-based PDTE scheme that asymptotically improves over the $O(2^D)$ dependence on $D$ while remaining non-interactive. We address two depth-driven sources of $O(2^D)$ dependence in existing protocols: we use the One-Branch-Only (OBO) paradigm from PROBONITE for comparisons, and we design the Baby-Step Giant-Step based Branch Selection algorithm for traversal. To further exploit the structure of GBDT ensembles, we deploy the batched bootstrapping technique by applying level-major tree evaluation. Our experimental results show that, at depth $D=12$, our protocol reduces communication by $8.38\times$ and runtime by $7.74\times$ compared to FASTER, which is the fastest prior HE-based non-interactive PDTE baseline in our amortized setting, and the advantage increases as $D$ grows. These results suggest that our design provides a practical path toward depth-scalable HE-based PDTE for large boosted ensembles.