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Compressing Correlations via Secret Replication: PCFs from Symmetric Cryptography

Authors Yuval Ishai , Hugo Krawczyk , Tal Rabin

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Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic primitives
  • Theory of computation → Cryptographic protocols
Keywords
  • Pseudorandom correlation functions
  • correlated randomness
  • secure computation
  • symmetric cryptography

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Abstract

We revisit the question of securely compressing multiparty correlations using only symmetric cryptography. A linear correlation C, defined by a linear subspace C ⊆ 𝔽ⁿ, samples a secret random 𝐜 ∈ C and assigns to each party a fixed subset of the entries of 𝐜. Gilboa and Ishai (Crypto 1999) and Cramer, Damgård and Ishai (TCC 2005) provide a general technique for securely compressing many independent samples from C by replicating independent keys of a pseudorandom function (PRF) among the parties. This implies a pseudorandom correlation function (PCF) for C from any PRF, where the PCF key size scales with the number of minimal-support codewords in C.
We observe that the above generalizes to other types of useful target correlations C_T by using a secret replication pattern obtained via a random secret assignment of parties in C to parties in C_T. 
We present several corollaries of this general blueprint. These include a re-derivation of two-party PCF constructions for VOLE and subfield-VOLE over small domains (Roy, Crypto 2022) as well as new multiparty PCFs for small-domain VOLE-style correlations, including scalar-vector multiplication triples and their authenticated variants. Finally, we discuss applications to secure computation.

Cite As Get BibTex

Yuval Ishai, Hugo Krawczyk, and Tal Rabin. Compressing Correlations via Secret Replication: PCFs from Symmetric Cryptography. In 7th Conference on Information-Theoretic Cryptography (ITC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 385, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITC.2026.7

Author Details

Yuval Ishai
  • Technion, Haifa, Israel
  • Amazon Web Services, New York, NY, USA
Hugo Krawczyk
  • Amazon Web Services, New York, NY, USA
Tal Rabin
  • Amazon Web Services, New York, NY, USA

Funding

  • Ishai, Yuval: Work done while at Amazon Web Services.

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