Single Server Private Information Retrieval Protocols With Codes Over Rings

TL;DR

This paper introduces a single-server Private Information Retrieval protocol utilizing codes over rings, enhancing security against linear algebra attacks and relying solely on modular arithmetic.

Contribution

It presents a novel PIR protocol based on two types of codes over different rings, improving security and efficiency compared to previous coding-based PIR schemes.

Findings

Provides computational security against linear algebra attacks

Uses modular arithmetic at server and recovery stages

Employs inner and outer codes over different rings

Abstract

A Private Information Retrieval (PIR) protocol based on coding theory for a single server is proposed. It provides computational security against linear algebra attacks, addressing the main drawback of previous PIR proposals based on coding theory. The approach involves two types of codes each one over a different ring, an inner non-free linear code that will be used as a distinguisher of some elements added to the query matrix, and an outer code that will be used for generating the query matrix. Moreover, it only uses modular arithmetic at the server level and the recovering stage if the base ring chosen for the inner code is $\mathbb Z_m$.