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.

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