DDH-based schemes for multi-party Function Secret Sharing

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.