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arxiv: 2604.24385 · v1 · submitted 2026-04-27 · 💻 cs.CR

Information-Theoretic Distributed Point Functions with Shorter Keys

Hang Deng , Liang Feng Zhang This is my paper

Pith reviewed 2026-05-08 03:00 UTC · model grok-4.3

classification 💻 cs.CR
keywords information-theoretic distributed point functionsprivate information retrievalshare conversionperfect securityshort keys1-privatecryptography
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The pith

A new share conversion from PIR yields perfectly secure 1-private ITDPFs with asymptotically shorter keys over any prime field.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds a fresh method for splitting point functions into shares across servers so that any single server learns nothing about the hidden point or its value. It does so by layering a share conversion step drawn from a 2025 private information retrieval construction onto an existing framework. The outcome is a scheme that stays perfectly secure in the one-private setting when function outputs live in a prime-order group, yet uses secret keys that grow more slowly with domain size than earlier perfectly secure versions. A reader cares because these shorter keys lower the storage and transmission costs that usually limit how widely information-theoretic distributed point functions can be deployed in privacy tools.

Core claim

The paper proposes a perfectly secure 1-private ITDPF for output group Z_p (p any prime) by introducing a novel share conversion based on the PIR of Ghasemi, Kopparty, and Sudan; the resulting scheme is asymptotically more efficient than prior perfectly secure ITDPFs for the same output group because its secret keys are shorter.

What carries the argument

The share conversion technique derived from the Ghasemi-Kopparty-Sudan PIR, which maps input shares into output shares while preserving perfect security and correctness and delivering the claimed key-size reduction.

If this is right

  • The construction works for any prime p as the output group, allowing flexible choices of value range.
  • Each of the n servers receives a key that lets it compute an additive share of the point-function output.
  • Security holds perfectly against any single colluding server.
  • Key material is shorter than in earlier perfectly secure schemes for the same parameters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same conversion step might be reusable in other multi-server primitives that already employ share conversion.
  • Practical systems that currently avoid ITDPFs because of key size could become feasible once the new lengths are implemented.
  • If stronger PIR constructions appear, the same template could yield still shorter keys or higher privacy thresholds.

Load-bearing premise

The share conversion taken from the cited PIR construction preserves perfect security and correctness while delivering the stated asymptotic improvement in key size for the one-private multi-server setting.

What would settle it

Measuring the bit length of the generated keys as a function of domain size N for the new scheme and comparing it directly to the key lengths of prior perfectly secure ITDPFs for Z_p would falsify the claim if the new keys fail to be asymptotically smaller, or if an explicit attack extracts the point from one server.

Figures

Figures reproduced from arXiv: 2604.24385 by Hang Deng, Liang Feng Zhang.

Figure 1
Figure 1. Figure 1: Our (1, 2nr)-ITDPF C. Analysis Correctness. Within the LKZ Framework it suffices to verify (a), (b) and (c) are all satisfied by the proposed constructions. While (a) and (b) have be confirmed, we focus on Eq. (5), i.e., ϕ(ρ(α, x) · σ) = δα,x, which is true because ϕ(ρ(α, x) · σ) = ϕ  w−uα view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The paper constructs a novel share conversion technique based on the private information retrieval (PIR) scheme of Ghasemi, Kopparty, and Sudan (STOC 2025). It proposes a perfectly secure 1-private (1,n)-ITDPF with output group G = Z_p for any prime p, claiming that this yields asymptotically shorter secret keys than prior perfectly secure ITDPFs for the same output group while preserving perfect security and correctness.

Significance. If the construction and proofs hold, the result improves efficiency for information-theoretic distributed point functions, a core primitive in secure multiparty computation and PIR protocols. The asymptotic key-size reduction relative to existing perfectly secure constructions for Z_p is a concrete advance, and the adaptation of the recent PIR result while maintaining perfect security is a strength of the work.

minor comments (1)
  1. [Introduction, Section 3] The introduction and Section 3 could include a brief explicit comparison of the new key-size asymptotics against the leading prior constructions for Z_p to make the efficiency claim easier to verify at a glance.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. The summary correctly identifies our use of the Ghasemi-Kopparty-Sudan PIR construction to obtain a perfectly secure 1-private ITDPF over Z_p with asymptotically shorter keys than prior perfectly secure schemes.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper grounds its novel share conversion in an external STOC 2025 PIR construction by Ghasemi, Kopparty, and Sudan (distinct authors), then builds a 1-private ITDPF for output group Z_p that preserves perfect security and correctness while achieving asymptotic key-size improvement over prior work. No derivation step reduces by construction to a fitted parameter, self-referential definition, or load-bearing self-citation chain; the central claims rest on the cited external result plus standard information-theoretic arguments. The manuscript is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the external PIR scheme can be directly adapted into a share conversion that preserves perfect IT security and reduces key size; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The PIR construction of Ghasemi, Kopparty, and Sudan (STOC 2025) can be used as a black-box share conversion primitive for ITDPF while maintaining perfect security.
    The paper's construction is explicitly based on this external result.

pith-pipeline@v0.9.0 · 5433 in / 1245 out tokens · 60509 ms · 2026-05-08T03:00:07.264435+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

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