A survey on single server private information retrieval in a coding theory perspective

Abstract

In this paper, we present a new perspective of single server private information retrieval (PIR) schemes by using the notion of linear error-correcting codes. Many of the known single server schemes are based on taking linear combinations between database elements and the query elements. Using the theory of linear codes, we develop a generic framework that formalizes all such PIR schemes. This generic framework provides an appropriate setup to analyze the security of such PIR schemes. In fact, we describe some known PIR schemes with respect to this code-based framework, and present the weaknesses of the broken PIR schemes in a unified point of view.

Divisible Linear Rank Metric Codes

“…Since dim F q m (C) = 2, then by Theorem 2.1 the code C is MRD if and only if 2m = max{m, n}(min{m, n} − d + 1). If n ≤ m, then d = n − 1 and by (3) this is equivalent to require that U is a scattered F q -subspace. If m < n, then by (3) n | 2m and hence n = 2m, which implies that U = F 2 q m .…”

“…The maximum weight codewords seems also interesting in connection with the rank metric version of the Critical problem by Crapo and Rota (cf. [2,3] and see also [28]), and due to the connection with q-polymatroids, see [24]. Let C be a F q m -linear non-degenerate rank metric code in F n q m of dimension k and define M (C) as the number of codewords in C with weight min{m, n}.…”