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

“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.

- Authors: Malihe Aliasgari, Yousef Nejatbakhsh
- Published: November 5, 2026
- Field: Computer Science
- DOI: https://doi.org/10.48550/arxiv.2611.07325
- Free PDF: https://arxiv.org/pdf/2611.07325

## 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

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