Paper 2026/1517 Original: eprint.iacr.org/2026/1517 ↗

ConvertInput-Free Vector Homomorphic Secret Sharing and Its Applications

Abstract

This work presents ConvertInput-Free Vector Homomorphic Secret Sharing (Vector-HSS), a novel HSS primitive based on the Decisional Composite Residuosity (DCR) assumption. Our construction enables efficient high-dimensional vector computations while avoiding the costly $\texttt{ConvertInput}$ operation. As a unified framework, Vector-HSS can be used as a building block for Private Information Retrieval (PIR), Secure Multi-Party Computation (MPC), Privacy-Preserving Machine Learning (PPML), etc. The key idea behind Vector-HSS is to introduce a vector-centric computation paradigm. Unlike traditional approaches, this design allows the server to perform natural and efficient vector computations without the $\texttt{ConvertInput}$ operation while keeping client-side overhead comparable to that of state-of-the-art solutions. To further improve efficiency, we develop a batching mechanism based on the Chinese Remainder Theorem (CRT) that enables parallel computation across multiple vectors. Building on these techniques, we further design a suite of protocol modules to securely support Euclidean/cosine distance computation, comparison, and matrix-vector multiplication in practical applications. Experiments show that our scheme achieves $280\times$ and $70\times$ speedups over prior HSS schemes (EUROCRYPT 2021 and S&P 2026, respectively) for batched inner product evaluation. When applied to privacy-preserving image retrieval, our method achieves sub-second retrieval time, outperforming state-of-the-art solutions under similar security requirements.