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.

翻译：函数秘密共享（FSS）方案能够高效地共享秘密函数。针对点函数的方案（称为分布式点函数，DPF）因其在私有信息检索、匿名通信和机器学习等众多应用中的价值，成为FSS研究的核心。虽然两方DPF已实现密钥规模对数级的方案，但多方DPF的发展较为有限：现有方案的密钥规模为$O(\sqrt{N})$（其中$N$为函数定义域大小）和/或包含指数级因子。本文提出一种基于DDH的技术，能够缩减现有多方方案的密钥规模。特别地，我们构建了一个诚实多数场景下的DPF方案，其密钥规模为$O(\sqrt[3]{N})$。实验评估表明，在现实问题规模下，本方案的密钥规模比现有最优方案缩小达10倍。最后，我们将该技术扩展至支持比较函数的方案。