Cryptanalysis of a PIR Scheme based on Linear Codes over Rings

TL;DR

This paper demonstrates a polynomial-time attack on a recent code-based PIR scheme, exploiting properties of random codes over finite rings to compromise privacy.

Contribution

It introduces a practical attack method that undermines the security assumptions of the PIR scheme based on linear codes over rings.

Findings

The server can identify the desired file index with high probability.

Random codes over finite rings are typically free, aiding the attack.

Removing rows from the query matrix reduces its dimension, revealing the target index.

Abstract

In this paper we present an attack on a recently proposed code-based Private Information Retrieval (PIR) scheme. Indeed, the server can retrieve the index of the desired file with high probability in polynomial time. The attack relies on the fact that random codes over finite rings are free with high probability and that the dimension of the rowspan of the query matrix decreases when the rows corresponding to the desired index are removed.