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This paper introduces a new construction for Information-Theoretic Distributed Point Functions (ITDPFs) that leverages a recent private information retrieval (PIR) scheme. The construction achieves perfect security in a 1-private setting with output group Z_p for any prime p. The key result is an ITDPF with asymptotically shorter secret keys compared to existing perfectly secure ITDPFs for the same output group, improving efficiency.
Asymptotically shorter secret keys in Information-Theoretic Distributed Point Functions are now possible, thanks to a novel construction leveraging private information retrieval.
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.
