Distributed Point Functions and Function Secret Sharing

arXiv:2607.27696 · cs.CR · Submitted 2026-07-30 · Read on arXiv

Elette Boyle, Niv Gilboa, Yuval Ishai, Peter Scholl

cs.CR

Submitted: 2026-07-30

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

The gist: A distributed point function (DPF) is a cryptographic primitive that enables compressed additive sharing of a secret weight-1 vector (equivalently, a point function) across two or more parties.

Terminology

Oblivious Transfer — 7× in this paper
Distributed Multi-Point Functions — 6× in this paper
Generalization — 6× in this paper · explained in 13 episodes
Aggregation — 5× in this paper · explained in 1 episode
Distributed Comparison Function — 5× in this paper
Security and Privacy — 5× in this paper
Consistency — 3× in this paper · explained in 3 episodes
Core — 3× in this paper · explained in 2 episodes
Foundations of Computer Science — 3× in this paper
Abstraction — 2× in this paper · explained in 1 episode
Activation Function — 2× in this paper · explained in 1 episode
Aggregation Function — 2× in this paper · explained in 1 episode
Israeli Science Foundation — 2× in this paper
Verification — 2× in this paper · explained in 2 episodes
Computational overhead — 1× in this paper · explained in 2 episodes
Cryptography and Information Security — 1× in this paper
Decisional Composite Residuosity — 1× in this paper
Decode — 1× in this paper · explained in 2 episodes
International Association of Cryptologic Research — 1× in this paper
Israeli Ministry of Science and Technology — 1× in this paper
Learning With Errors — 1× in this paper
Robustness — 1× in this paper · explained in 5 episodes
Sparsity — 1× in this paper · explained in 4 episodes
THE L EARNING PARITY WITH N OISE — 1× in this paper
Verifiability — 1× in this paper · explained in 2 episodes

Abstract

A distributed point function (DPF) is a cryptographic primitive that enables compressed additive sharing of a secret weight-1 vector (equivalently, a point function) across two or more parties. The appealing lightweight structure of DPF constructions has enabled a wide range of applications. These include private information retrieval, anonymous messaging, secure computation with preprocessing, and pseudorandom correlation generators for expanding small correlated seeds into large pseudorandom instances of cryptographic correlations. In this article, we survey definitions, constructions, and applications of DPFs. We also discuss the extension of DPF to function secret sharing (FSS), which generalizes point functions to support richer function classes. Efficient FSS schemes yield a similar generalization for most of the applications of DPFs.

Terminology

Abstract

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