# Private Information Retrieval from Coded Databases with Colluding Servers

Ragnar Freij-Hollanti, Oliver Gnilke, Camilla Hollanti, David Karpuk

Research output: Contribution to journalArticleScientificpeer-review

87 Citations (Scopus)

## Abstract

We present a general framework for private information retrieval (PIR) from arbitrary coded databases that allows one to adjust the rate of the scheme to the suspected number of colluding servers. If the storage code is a generalized Reed--Solomon code of length $n$ and dimension $k$, we design PIR schemes that achieve a PIR rate of $\frac{n-(k+t-1)}{n}$ while protecting against any $t$ colluding servers, for any $1\leq t\leq n-k$. This interpolates between the previously studied cases of $t=1$ and $k=1$ and achieves PIR capacity in both of these cases asymptotically as the number of files in the database grows.

Original language English 647–664 18 SIAM Journal on Applied Algebra and Geometry 1 1 https://doi.org/10.1137/16M1102562 Published - 2017 A1 Journal article-refereed

## Keywords

• private information retrieval
• distributed storage systems
• generalized Reed--Solomon codes