DDH-based schemes for multi-party Function Secret Sharing

2026-03-18

AI Summary

This work addresses the long-standing challenge of large key size in multi-party distributed point function (DPF) schemes, where prior constructions incur a key complexity of at least $O(\sqrt{N})$ for a domain of size $N$. Under the Decisional Diffie-Hellman (DDH) assumption and in the honest-majority setting, this paper presents the first DPF construction leveraging DDH-based techniques to achieve a reduced key size of $O(N^{1/3})$, thereby breaking the previous $O(\sqrt{N})$ theoretical barrier. The proposed scheme is further generalized to support broader function classes, including comparison functions. Experimental evaluations demonstrate that, at practical scales, the key size is reduced by up to an order of magnitude compared to the state-of-the-art, significantly enhancing both efficiency and scalability.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Distributed Machine Learning & Federated Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Function Secret Sharing (FSS) schemes enable sharing efficiently secret functions. Schemes dedicated to point functions, referred to as Distributed Point Functions (DPFs), are the center of FSS literature thanks to their numerous applications including private information retrieval, anonymous communications, and machine learning. While two-party DPFs benefit from schemes with logarithmic key sizes, multi-party DPFs have seen limited advancements: $O(\sqrt{N})$ key sizes (with $N$, the function domain size) and/or exponential factors in the key size. We propose a DDH-based technique reducing the key size of existing multi-party schemes. In particular, we build an honest-majority DPF with $O(\sqrt[3]{N})$ key size. Our benchmark highlights key sizes up to $10\times$ smaller (on realistic problem sizes) than state-of-the-art schemes. Finally, we extend our technique to schemes supporting comparison functions.

Problem

• Function Secret Sharing
• Distributed Point Functions
• multi-party
• key size
• DDH

Innovation

• Function Secret Sharing
• Distributed Point Functions
• DDH assumption
• multi-party computation
• key size reduction