On the privacy of a code-based single-server computational PIR scheme

Abstract

We show that the single-server computational PIR protocol proposed by Holzbaur, Hollanti and Wachter-Zeh in [HHW20] is not private, in the sense that the server can recover in polynomial time the index of the desired file with very high probability. The attack relies on the following observation. Removing rows of the query matrix corresponding to the desired file yields a large decrease of the dimension over F q of the vector space spanned by the rows of this punctured matrix. Such a dimension loss only shows up with negligible probability when rows unrelated to the requested file are deleted.

On single server private information retrieval in a coding theory perspective

“…In this PIR scheme the authors consider the field extension F q m and secretly choose a partition of the basis over F q . Shortly after, this proposal has been attacked in [6], using that the removal of one row within the query matrix and checking for the dimension of the rest reveals the position of the desired file.…”

“…In the following, we describe this PIR scheme presented in [13] with respect to our code-based framework. Later, we also present the attack [6] in terms of solving the distinguishability problem.…”

“…The original PIR scheme [13] has been attacked in [6], by solving the distinguishability problem. The attack follows the second strategy mentioned in Section 3.3.…”

“…Recently, Holzbaur, Hollanti and Wachter-Zeh have proposed in [13] the first single server PIR based on coding theory. However, their proposal was attacked in [6]. The primary idea in [13] is to generate the query by hiding carefully chosen error vectors using codewords from a random linear code.…”

Storage and Retrieval Codes in PIR Schemes with Colluding Servers

“…PIR schemes with colluding servers for coded databases from general linear codes over small fields are considered in [19,20,28,30,31]. We refer to [9,18,23,25,27,29,42,43,46] for the recent related development and [45] for a nice survey of active research on private retrieval, computing and learning.…”