114 research outputs found
Private Computation of Systematically Encoded Data with Colluding Servers
Private Computation (PC), recently introduced by Sun and Jafar, is a
generalization of Private Information Retrieval (PIR) in which a user wishes to
privately compute an arbitrary function of data stored across several servers.
We construct a PC scheme which accounts for server collusion, coded data, and
non-linear functions. For data replicated over several possibly colluding
servers, our scheme computes arbitrary functions of the data with rate equal to
the asymptotic capacity of PIR for this setup. For systematically encoded data
stored over colluding servers, we privately compute arbitrary functions of the
columns of the data matrix and calculate the rate explicitly for polynomial
functions. The scheme is a generalization of previously studied star-product
PIR schemes.Comment: Submitted to IEEE International Symposium on Information Theory 2018.
Version 2 fixes some typos and adds some clarifying remark
An MDS-PIR Capacity-Achieving Protocol for Distributed Storage Using Non-MDS Linear Codes
We propose a private information retrieval (PIR) protocol for distributed
storage systems with noncolluding nodes where data is stored using an arbitrary
linear code. An expression for the PIR rate, i.e., the ratio of the amount of
retrieved data per unit of downloaded data, is derived, and a necessary and a
sufficient condition for codes to achieve the maximum distance separable (MDS)
PIR capacity are given. The necessary condition is based on the generalized
Hamming weights of the storage code, while the sufficient condition is based on
code automorphisms. We show that cyclic codes and Reed-Muller codes satisfy the
sufficient condition and are thus MDS-PIR capacity-achieving.Comment: To be presented at 2018 IEEE International Symposium on Information
Theory (ISIT). arXiv admin note: substantial text overlap with
arXiv:1712.0389
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
Privacy in Index Coding: Improved Bounds and Coding Schemes
It was recently observed in [1], that in index coding, learning the coding
matrix used by the server can pose privacy concerns: curious clients can
extract information about the requests and side information of other clients.
One approach to mitigate such concerns is the use of -limited-access schemes
[1], that restrict each client to learn only part of the index coding matrix,
and in particular, at most rows. These schemes transform a linear index
coding matrix of rank to an alternate one, such that each client needs to
learn at most of the coding matrix rows to decode its requested message.
This paper analyzes -limited-access schemes. First, a worst-case scenario,
where the total number of clients is is studied. For this case, a
novel construction of the coding matrix is provided and shown to be
order-optimal in the number of transmissions. Then, the case of a general
is considered and two different schemes are designed and analytically and
numerically assessed in their performance. It is shown that these schemes
perform better than the one designed for the case
Robust Private Information Retrieval on Coded Data
We consider the problem of designing PIR scheme on coded data when certain
nodes are unresponsive. We provide the construction of -robust PIR schemes
that can tolerate up to unresponsive nodes. These schemes are adaptive
and universally optimal in the sense of achieving (asymptotically) optimal
download cost for any number of unresponsive nodes up to
Private Function Retrieval
The widespread use of cloud computing services raises the question of how one
can delegate the processing tasks to the untrusted distributed parties without
breeching the privacy of its data and algorithms. Motivated by the algorithm
privacy concerns in a distributed computing system, in this paper, we introduce
the private function retrieval (PFR) problem, where a user wishes to
efficiently retrieve a linear function of messages from
non-communicating replicated servers while keeping the function hidden from
each individual server. The goal is to find a scheme with minimum communication
cost. To characterize the fundamental limits of the communication cost, we
define the capacity of PFR problem as the size of the message that can be
privately retrieved (which is the size of one file) normalized to the required
downloaded information bits. We first show that for the PFR problem with
messages, servers and a linear function with binary coefficients the
capacity is . Interestingly, this
is the capacity of retrieving one of messages from servers while
keeping the index of the requested message hidden from each individual server,
the problem known as private information retrieval (PIR). Then, we extend the
proposed achievable scheme to the case of arbitrary number of servers and
coefficients in the field with arbitrary and obtain
Private Information Retrieval Schemes for Coded Data with Arbitrary Collusion Patterns
In Private Information Retrieval (PIR), one wants to download a file from a
database without revealing to the database which file is being downloaded. Much
attention has been paid to the case of the database being encoded across
several servers, subsets of which can collude to attempt to deduce the
requested file. With the goal of studying the achievable PIR rates in realistic
scenarios, we generalize results for coded data from the case of all subsets of
servers of size colluding, to arbitrary subsets of the servers. We
investigate the effectiveness of previous strategies in this new scenario, and
present new results in the case where the servers are partitioned into disjoint
colluding groups.Comment: Updated with a corrected statement of Theorem
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