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    PIR schemes with small download complexity and low storage requirements

    Blackburn, S.R. and Etzion, T. and Paterson, Maura B. (2019) PIR schemes with small download complexity and low storage requirements. IEEE International Symposium on Information Theory , ISSN 0018-9448. (In Press)

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    Abstract

    Shah, Rashmi and Ramchandran recently considered a model for Private Information Retrieval (PIR) where a user wishes to retrieve one of several Ä-bit messages from a set of n non-colluding servers. Their security model is information-theoretic. Their paper is the first to consider a model for PIR in which the database is not necessarily replicated, so allowing distributed storage techniques to be used. Shah et al. show that at least Ä+1 bits must be downloaded from servers, and describe a scheme with linear total storage (in R) that downloads between 2R and 3R bits. For any positive e, we provide a construction with the same storage property, that requires at most (1 + e)R bits to be downloaded; moreover one variant of our scheme only requires each server to store a bounded number of bits (in the sense of being bounded by a function that is independent of R). We also provide variants of a scheme of Shah et al which downloads exactly R +1 bits and has quadratic total storage. Finally, we simplify and generalise a lower bound due to Shah et al. on the download complexity of a PIR scheme. In a natural model, we show that an n-server PIR scheme requires at least nR/(n - 1) download bits in many cases, and provide a scheme that meets this bound. This paper provides various bounds on the download complexity of a PIR scheme, generalising those of Shah et al.\ to the case when the number $n$ of servers is bounded, and providing links with classical techniques due to Chor et al. The paper also provides a range of constructions for PIR schemes that are either simpler or perform better than previously known schemes. These constructions include explicit schemes that achieve the best asymptotic download complexity of Sun and Jafar with significantly lower upload complexity, and general techniques for constructing a scheme with good worst case download complexity from a scheme with good download complexity on average.

    Metadata

    Item Type: Article
    Additional Information: Electronic ISBN: 9781509040964
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Maura Paterson
    Date Deposited: 23 Aug 2019 12:26
    Last Modified: 24 Aug 2019 11:53
    URI: http://eprints.bbk.ac.uk/id/eprint/28708

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