“Functional Converses for Private Matrix-Product Retrieval under Library-Wide Decoder-Side Correlation” (2026), by Malihe Aliasgari et al. Computer Science research paper. Original abstract below, unchanged. A free PDF is available.

Functional Converses for Private Matrix-Product Retrieval under Library-Wide Decoder-Side Correlation

Malihe Aliasgari, Yousef Nejatbakhsh · November 5, 2026 · Computer Science

Abstract

We consider private retrieval of the matrix product A^top B^(θ) from replicated P_c-colluding servers when B^(ℓ)=A+N^(ℓ), with the innovations mutually independent and independent of the user-held A∈F_q^m× m. The servers store the full library, correlated with A, which changes both the communication problem and the security definition: a secrecy condition including the stored library cannot hold, as the library itself partly reveals A. We therefore measure only additional leakage and require index privacy conditioned on A; both reduce to classical notions under independence. For A of rank $k

Free PDF DOI: 10.48550/arxiv.2611.07325