Paper 2026/1970 Original: eprint.iacr.org/2026/1970 ↗

Multi-Party Distributed Point Functions, Revisited

Abstract

In this paper, we revisit the design of multi-party distributed point functions (DPFs) and make several new contributions that advance the state of the art. We begin by revisiting security amplification, a fundamental tool underlying many DPF constructions. In particular, the recent landmark work of Goel, Wang, and Wang (CRYPTO'25) critically relies on security amplification and, for a general polynomial number of parties, gives the only known construction based on one-way functions (OWFs) that achieves sublinear dependence on the input domain size. Unfortunately, due to a known gap in the proof of the security amplification theorem of Boyle et al. (CRYPTO'22), we currently still lack a fully established security amplification theorem for DPFs. We fill this gap by providing a new proof of security amplification for DPFs with tight parameters. Equipped with this security amplification theorem as a key technical tool, we develop several new techniques that asymptotically improve the communication cost of multi-party DPFs in both the honest-majority and corrupt-majority settings. Our main results are summarized below, where $N$ denotes the input domain size, $m$ denotes the number of parties, and $t$ denotes the corruption threshold: In the all-but-one-corrupt setting, we describe a new scheme based on OWFs with $\widetilde{O}_\lambda\left(N^{\frac12 + \epsilon} \cdot \sqrt{m}\right)$ share size where $\epsilon > 0$ is an arbitrarily small constant. In comparison, the best previously known OWF-based construction due to Goel et al. incurs $\widetilde{O}_\lambda\left(N^{\frac12 + \epsilon}\cdot m^3\right)$ share size. In the honest-majority setting, assuming $m > (1+\epsilon)D t$ for some integer $D \ge 2$ and arbitrarily small constant $\epsilon > 0$, we construct a new OWF-based scheme with share size $\widetilde{O}_\lambda(N^{\frac{1+\epsilon}{2D}})$, as well as an information-theoretically secure scheme with share size $\widetilde{O}(N^{1/D})$. Both constructions achieve an exponential factor improvement in their dependence on $m$ and $t$ compared to the state-of-the-art schemes of Bunn, Kushilevitz, and Ostrovsky.