**How to Correct Errors in Multi-Server PIR**

*Kaoru Kurosawa*

**Abstract: **Suppose that there exist a user and $\ell$ servers $S_1, \ldots, S_{\ell}$. Each server $S_j$ holds a copy of a database $x=(x_1, \ldots, x_n) \in \{0,1\}^n$, and the user holds a secret index $i_0 \in \{1, \ldots, n\}$. A b error correcting $\ell$ server PIR (Private Information Retrieval) scheme allows a user to retrieve $x_{i_0}$ correctly even if and $b$ or less servers return false answers while each server learns no information on $i_0$ in the information theoretic sense. Although there exists such a scheme with the total communication cost $O(n^{1/(2k-1)} \times k\ell \log{\ell})$ where $k=\ell-2b$, the decoding algorithm is very inefficient.

In this paper, we show an efficient decoding algorithm for this $b$ error correcting $\ell$ server PIR scheme. It runs in time $O(\ell^3)$.

**Category / Keywords: **Private Information Retrieval, information theoretic, error correcting

**Date: **received 13 May 2019, last revised 13 May 2019

**Contact author: **kaoru kurosawa kk at vc ibaraki ac jp

**Available format(s): **PDF | BibTeX Citation

**Version: **20190521:065321 (All versions of this report)

**Short URL: **ia.cr/2019/531

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