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.
Buhrman, Patro, and Speelman presented a framework of conjectures that together form a quantum analogue of the strong exponential-time hypothesis and its variants. They called it the QSETH framework. In this paper, using a notion of quantum natural proofs (built from natural proofs introduced by Razborov and Rudich), we show how part of the QSETH conjecture that requires properties to be `compression oblivious' can in many cases be replaced by assuming the existence of quantum-secure pseudorandom functions, a standard hardness assumption. Combined with techniques from Fourier analysis of Boolean functions, we show that properties such as PARITY and MAJORITY are compression oblivious for certain circuit class
Λ if subexponentially secure quantum pseudorandom functions exist in
Λ, answering an open question in [Buhrman-Patro-Speelman 2021].