Paper 2026/1942

Improved Multi-Party Distributed Point Functions from Oblivious Tensor Evaluation

Abstract

A multi-party distributed point function (DPF) compresses a point function instance $f_{\alpha,\beta}$, i.e., $f$ evaluates to $\beta$ at $\alpha$ and to $0$ otherwise, into short keys that are distributed to $N$ parties. Each key allows a party to locally derive an additive share of the point function evaluation. DPFs have become a widespread building block for cryptographic protocols and sometimes rely on a distributed setup. In this work, we present an $N$-party, full-threshold DPF for full-domain evaluation making black-box use of oblivious tensor evaluation. Let $L$ denote the domain size of the point function and $\lambda$ the security parameter. Instantiated with the non-interactive oblivious tensor evaluation primitive (NIOTE) by Abram et al. (STOC '25) based on learning with errors (LWE), we obtain $N$-party DPFs with (i) key-size $\mathcal{O}(N \cdot \mathsf{poly}(\lambda) \cdot \log^2 L)$ with a $\log L$-round distributed setup protocol, or (ii) similar key-size with almost $(\log \log L)$-rounds (asymptotically $\Theta(\log L)$ but for relevant values of $L$ in practice equal to $\log \log L$), or (iii) key-size $\mathcal{O}(N \cdot \mathsf{poly}(\lambda) \cdot \log L \cdot \sqrt{L})$ with $(\log \log L)$-round distributed setup (also asymptotically). Our construction improves over most of the state of the art either in terms of key-size or in the setup round complexity.