Improved User-Private Information Retrieval via Finite Geometry

TL;DR

This paper introduces a new class of User-Private Information Retrieval schemes based on finite geometry, specifically generalized quadrangles, which significantly improve privacy guarantees against collusion.

Contribution

The paper proposes a novel UPIR scheme using generalized quadrangles that enhances privacy resilience compared to previous designs based on pairwise and symmetric designs.

Findings

Privacy is maintained with high probability against collusions of up to O(n^{1/4 - ε}) users.

Previous schemes could be compromised by a single user, but the new GQ-based scheme offers stronger privacy.

The scheme leverages properties of finite geometries to improve privacy guarantees.

Abstract

In a User-Private Information Retrieval (UPIR) scheme, a set of users collaborate to retrieve files from a database without revealing to observers which participant in the scheme requested the file. Protocols have been proposed based on pairwise balanced designs and symmetric designs. Wepropose a new class of UPIR schemes based on generalised quadrangles (GQ). We prove that while the privacy of users in the previously proposed schemes could be compromised by a single user, the new GQ-UPIR schemes proposed in this paper maintain privacy with high probability even when up to $O(n^{1/4 - \epsilon})$ users collude, where $n$ is the total number of users in the scheme.