15,669 research outputs found
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 Polynomial Computation from Lagrange Encoding
Private computation is a generalization of private information retrieval, in
which a user is able to compute a function on a distributed dataset without
revealing the identity of that function to the servers. In this paper it is
shown that Lagrange encoding, a powerful technique for encoding Reed-Solomon
codes, enables private computation in many cases of interest. In particular, we
present a scheme that enables private computation of polynomials of any degree
on Lagrange encoded data, while being robust to Byzantine and straggling
servers, and to servers colluding to attempt to deduce the identities of the
functions to be evaluated. Moreover, incorporating ideas from the well-known
Shamir secret sharing scheme allows the data itself to be concealed from the
servers as well. Our results extend private computation to high degree
polynomials and to data-privacy, and reveal a tight connection between private
computation and coded computation.Comment: To appear in Transactions on Information Forensics and Securit
Private Polynomial Computation from Lagrange Encoding
Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers. In this paper, it is shown that Lagrange encoding, a powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers colluding to attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to high degree polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation
Private Polynomial Computation from Lagrange Encoding
Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers that store the dataset. In this paper it is shown that Lagrange encoding, a recently suggested powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers that collude in attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to non-linear polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation
The Capacity of Multi-round Private Information Retrieval from Byzantine Databases
In this work, we investigate the capacity of private information retrieval
(PIR) from replicated databases, where a subset of the databases are
untrustworthy (byzantine) in their answers to the query of the user. We allow
for multi-round queries and demonstrate that the identities of the byzantine
databases can be determined with a small additional download cost. As a result,
the capacity of the multi-round PIR with byzantine databases (BPIR) reaches
that of the robust PIR problem when the number of byzantine databases is less
than the number of trustworthy databases.Comment: 8 pages, 2 figure
Private Polynomial Computation from Lagrange Encoding
Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers that store the dataset. In this paper it is shown that Lagrange encoding, a recently suggested powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers that collude in attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to non-linear polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation
The Capacity of Private Information Retrieval from Byzantine and Colluding Databases
We consider the problem of single-round private information retrieval (PIR)
from replicated databases. We consider the case when databases are
outdated (unsynchronized), or even worse, adversarial (Byzantine), and
therefore, can return incorrect answers. In the PIR problem with Byzantine
databases (BPIR), a user wishes to retrieve a specific message from a set of
messages with zero-error, irrespective of the actions performed by the
Byzantine databases. We consider the -privacy constraint in this paper,
where any databases can collude, and exchange the queries submitted by the
user. We derive the information-theoretic capacity of this problem, which is
the maximum number of \emph{correct symbols} that can be retrieved privately
(under the -privacy constraint) for every symbol of the downloaded data. We
determine the exact BPIR capacity to be
, if . This capacity expression shows that the effect of Byzantine databases on
the retrieval rate is equivalent to removing databases from the system,
with a penalty factor of , which signifies that even though the
number of databases needed for PIR is effectively , the user still needs
to access the entire databases. The result shows that for the
unsynchronized PIR problem, if the user does not have any knowledge about the
fraction of the messages that are mis-synchronized, the single-round capacity
is the same as the BPIR capacity. Our achievable scheme extends the optimal
achievable scheme for the robust PIR (RPIR) problem to correct the
\emph{errors} introduced by the Byzantine databases as opposed to
\emph{erasures} in the RPIR problem. Our converse proof uses the idea of the
cut-set bound in the network coding problem against adversarial nodes.Comment: Submitted to IEEE Transactions on Information Theory, June 201
The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases
We consider private information retrieval (PIR) of a single file out of
files from non-colluding databases with heterogeneous storage constraints
. The aim of this work is to jointly design the
content placement phase and the information retrieval phase in order to
minimize the download cost in the PIR phase. We characterize the optimal PIR
download cost as a linear program. By analyzing the structure of the optimal
solution of this linear program, we show that, surprisingly, the optimal
download cost in our heterogeneous case matches its homogeneous counterpart
where all databases have the same average storage constraint . Thus, we show that there is no loss in the PIR capacity
due to heterogeneity of storage spaces of the databases. We provide the optimum
content placement explicitly for .Comment: Submitted for publication, February 201
PIR with Low Storage Overhead: Coding instead of Replication
Private information retrieval (PIR) protocols allow a user to retrieve a data
item from a database without revealing any information about the identity of
the item being retrieved. Specifically, in information-theoretic -server
PIR, the database is replicated among non-communicating servers, and each
server learns nothing about the item retrieved by the user. The cost of PIR
protocols is usually measured in terms of their communication complexity, which
is the total number of bits exchanged between the user and the servers, and
storage overhead, which is the ratio between the total number of bits stored on
all the servers and the number of bits in the database. Since single-server
information-theoretic PIR is impossible, the storage overhead of all existing
PIR protocols is at least .
In this work, we show that information-theoretic PIR can be achieved with
storage overhead arbitrarily close to the optimal value of , without
sacrificing the communication complexity. Specifically, we prove that all known
-server PIR protocols can be efficiently emulated, while preserving both
privacy and communication complexity but significantly reducing the storage
overhead. To this end, we distribute the bits of the database among
servers, each storing coded bits (rather than replicas). For every fixed
, the resulting storage overhead approaches as grows;
explicitly we have . Moreover, in the special case , the storage overhead is only . In order to achieve these
results, we introduce and study a new kind of binary linear codes, called here
-server PIR codes. We then show how such codes can be constructed, and we
establish several bounds on the parameters of -server PIR codes. Finally, we
briefly discuss extensions of our results to nonbinary alphabets, to robust
PIR, and to -private PIR
Private Information Retrieval from Storage Constrained Databases -- Coded Caching meets PIR
Private information retrieval (PIR) allows a user to retrieve a desired
message out of possible messages from databases without revealing the
identity of the desired message. Majority of existing works on PIR assume the
presence of replicated databases, each storing all the messages. In this
work, we consider the problem of PIR from storage constrained databases. Each
database has a storage capacity of bits, where is the number of
messages, is the size of each message in bits, and is
the normalized storage. In the storage constrained PIR problem, there are two
key design questions: a) how to store content across each database under
storage constraints; and b) construction of schemes that allow efficient PIR
through storage constrained databases. The main contribution of this work is a
general achievable scheme for PIR from storage constrained databases for any
value of storage. In particular, for any , with normalized storage , where the parameter can take integer values , we show that our proposed PIR scheme achieves a download cost of
. The
extreme case when (i.e., ) corresponds to the setting of
replicated databases with full storage. For this extremal setting, our scheme
recovers the information-theoretically optimal download cost characterized by
Sun and Jafar as . For
the other extreme, when (i.e., ), the proposed scheme achieves
a download cost of . The interesting aspect of the result is that for
intermediate values of storage, i.e., , the proposed scheme can
strictly outperform memory-sharing between extreme values of storage
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