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Limits on the Power of Private Constrained PRFs

Authors Mengda Bi , Yaohua Ma , Chenxin Dai

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LIPIcs.ITC.2026.2.pdf
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ACM Subject Classification
  • Theory of computation → Cryptographic primitives
Keywords
  • Black-box Separations
  • Private Constrained PRFs
  • Key Agreement

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Abstract

Private constrained PRFs are constrained PRFs where the constrained key hides information about the predicate circuit. Although there are many constructions and applications of PCPRF, its relationship to basic cryptographic primitives, such as one-way functions and public-key encryptions, has been unclear. For example, we don't know whether one-way functions imply PCPRFs for general predicates, nor do we know whether 1-key secure PCPRF for all polynomial-sized predicates imply public-key primitives such as public-key encryption and secret-key agreement.
In this work, we prove the black-box separation between a 1-key secure PCPRF for any predicate and a secret-key agreement, which is the first black-box separation result about PCPRF. Specifically, we prove that there exists an oracle relative to which 1-key secure PCPRFs exist while secret-key agreement does not. Our proof is based on the simulation-based technique proposed by Impagliazzo and Rudich (STOC 89). The main technical challenge in generalizing the simulation-based technique to PCPRF is the issue of unfaithfulness of Eve’s simulation to the real world because our oracle is more complicated than a random oracle. We introduce a new technique which we call the "weighting" technique and show how to leverage it to circumvent the issue of unfaithfulness in the proof framework of Impagliazzo and Rudich.

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Mengda Bi, Yaohua Ma, and Chenxin Dai. Limits on the Power of Private Constrained PRFs. In 7th Conference on Information-Theoretic Cryptography (ITC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 385, pp. 2:1-2:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITC.2026.2

Author Details

Mengda Bi
  • Tsinghua University, Beijing, China
Yaohua Ma
  • Tsinghua University, Beijing, China
Chenxin Dai
  • Tsinghua University, Beijing, China

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