12,317 research outputs found
The capacity of symmetric Private information retrieval
Private information retrieval (PIR) is the problem of retrieving as efficiently as possible, one out of K messages from N non-communicating replicated databases (each holds all K messages) while keeping the identity of the desired message index a secret from each individual database. Symmetric PIR (SPIR) is a generalization of PIR to include the requirement that beyond the desired message, the user learns nothing about the other K - 1 messages. The information theoretic capacity of SPIR (equivalently, the reciprocal of minimum download cost) is the maximum number of bits of desired information that can be privately retrieved per bit of downloaded information. We show that the capacity of SPIR is 1-1/N regardless of the number of messages K, if the databases have access to common randomness (not available to the user) that is independent of the messages, in the amount that is at least 1/(N - 1) bits per desired message bit, and zero otherwise
Asymmetry Helps: Improved Private Information Retrieval Protocols for Distributed Storage
We consider private information retrieval (PIR) for distributed storage
systems (DSSs) with noncolluding nodes where data is stored using a non maximum
distance separable (MDS) linear code. It was recently shown that if data is
stored using a particular class of non-MDS linear codes, the MDS-PIR capacity,
i.e., the maximum possible PIR rate for MDS-coded DSSs, can be achieved. For
this class of codes, we prove that the PIR capacity is indeed equal to the
MDS-PIR capacity, giving the first family of non-MDS codes for which the PIR
capacity is known. For other codes, we provide asymmetric PIR protocols that
achieve a strictly larger PIR rate compared to existing symmetric PIR
protocols.Comment: To be presented at 2018 IEEE Information Theory Workshop (ITW'18).
See arXiv:1808.09018 for its extended versio
Cross Subspace Alignment and the Asymptotic Capacity of -Secure -Private Information Retrieval
-secure and -private information retrieval (XSTPIR) is a form of
private information retrieval where data security is guaranteed against
collusion among up to servers and the user's privacy is guaranteed against
collusion among up to servers. The capacity of XSTPIR is characterized for
arbitrary number of servers , and arbitrary security and privacy thresholds
and , in the limit as the number of messages .
Capacity is also characterized for any number of messages if either or if . Insights are drawn from these results, about aligning
versus decoding noise, dependence of PIR rate on field size, and robustness to
symmetric security constraints. In particular, the idea of cross subspace
alignment, i.e., introducing a subspace dependence between Reed-Solomon code
parameters, emerges as the optimal way to align undesired terms while keeping
desired terms resolvable
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