A t-private n-server Information-Theoretic Distributed Point Function ((t,n)-ITDPF) allows one to convert any point function f_{alpha,beta}(x): [N] -> G into n shares (secret keys), such that each server can compute an additive share of f_{alpha,beta}(x) with a key while any <= t servers learn absolutely no information about the function. This paper constructs a novel share conversion based on the private information retrieval (PIR) of Ghasemi, Kopparty, and Sudan (STOC 2025) and proposes a perfectly secure 1-private ITDPF with output group G = Z_p, where p can be any prime. Compared with the existing perfectly secure ITDPFs for the same output group, the proposed ITDPF is more efficient with asymptotically shorter secret keys.

翻译：一个t-私密的n-服务器信息论分布式点函数（(t,n)-ITDPF）允许将任意点函数f_{alpha,beta}(x): [N] -> G转换为n个份额（密钥），使得每个服务器可使用密钥计算f_{alpha,beta}(x)的一个加法份额，同时任意不超过t个服务器对函数信息一无所知。本文基于Ghasemi、Kopparty和Sudan（STOC 2025）的私有信息检索（PIR）构造了一种新颖的份额转换，并提出了一种输出群G = Z_p（p可为任意素数）的完全安全1-私密ITDPF。与针对相同输出群的现有完全安全ITDPF相比，所提出的ITDPF具有渐近更短的密钥，因而效率更高。