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 \(\mathbf {x}=(x_1, \ldots , x_n) \in \{0,1\}^n\), 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 \(O(\ell ^3)\).
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Notes
- 1.
I.e., the total number of bits communicated between the user and the servers.
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Kurosawa, K. (2019). How to Correct Errors in Multi-server PIR. In: Galbraith, S., Moriai, S. (eds) Advances in Cryptology – ASIACRYPT 2019. ASIACRYPT 2019. Lecture Notes in Computer Science(), vol 11922. Springer, Cham. https://doi.org/10.1007/978-3-030-34621-8_20
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