Communication Cost of Two-Database Symmetric Private Information Retrieval: A Conditional Disclosure of Multiple Secrets Perspective

TL;DR

This paper explores the communication cost of two-database symmetric private information retrieval (SPIR) by linking it to a new concept called conditional disclosure of multiple secrets (CDMS), and provides cost-efficient schemes and exact cost calculations.

Contribution

It introduces the concept of CDMS as an extension of CDS, establishes its equivalence to two-database SPIR, and designs schemes that minimize communication costs.

Findings

Exact minimum total communication cost for 2-database SPIR with 3 messages determined.

Proposed bipartite graph-based schemes improve communication efficiency.

Established theoretical connection between SPIR and CDMS.

Abstract

We consider the total (upload plus download) communication cost of two-database symmetric private information retrieval (SPIR) through its relationship to conditional disclosure of secrets (CDS). In SPIR, a user wishes to retrieve a message out of $K$ messages from $N$ non-colluding and replicated databases without learning anything beyond the retrieved message, while no individual database learns the retrieved message index. In CDS, two parties each holding an individual input and sharing a common secret wish to disclose this secret to an external party in an efficient manner if and only if their inputs satisfy a public deterministic function. As a natural extension of CDS, we introduce conditional disclosure of multiple secrets (CDMS) where two parties share multiple i.i.d.~common secrets rather than a single common secret as in CDS. We show that a special configuration of CDMS is equivalent to two-database SPIR. Inspired by this equivalence, we design download cost efficient SPIR schemes using bipartite graph representation of CDS and CDMS, and determine the exact minimum total communication cost of $N=2$ database SPIR for $K=3$ messages.