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The Asymptotic Capacity of Private Search

12 January 2018
Zhen Chen
Zhiying Wang
S. Jafar
    FedML
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Abstract

The private search problem is introduced, where a dataset comprised of LLL i.i.d. records is replicated across NNN non-colluding servers, each record takes values uniformly from an alphabet of size KKK, and a user wishes to search for all records that match a privately chosen value, without revealing any information about the chosen value to any individual server. The capacity of private search is the maximum number of bits of desired information that can be retrieved per bit of download. The asymptotic (large KKK) capacity of private search is shown to be 1−1/N1-1/N1−1/N, even as the scope of private search is further generalized to allow approximate (OR) search over a number of realizations that grows with KKK. The results are based on the asymptotic behavior of a new converse bound for private information retrieval with arbitrarily dependent messages.

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