31,060 research outputs found
Private Information Retrieval from MDS Coded Databases with Colluding Servers under Several Variant Models
Private information retrieval (PIR) gets renewed attentions due to its
information-theoretic reformulation and its application in distributed storage
system (DSS). The general PIR model considers a coded database containing
servers storing files. Each file is stored independently via the same
arbitrary -MDS code. A user wants to retrieve a specific file from the
database privately against an arbitrary set of colluding servers. A key
problem is to analyze the PIR capacity, defined as the maximal number of bits
privately retrieved per one downloaded bit. Several extensions for the general
model appear by bringing in various additional constraints. In this paper, we
propose a general PIR scheme for several variant PIR models including: PIR with
robust servers, PIR with Byzantine servers, the multi-file PIR model and PIR
with arbitrary collusion patterns.Comment: The current draft is extended by considering several PIR models. The
original version named "Multi-file Private Information Retrieval from MDS
Coded Databases with Colluding Servers" is abridged into a section within the
current draft. arXiv admin note: text overlap with arXiv:1704.0678
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
Secure Symmetric Private Information Retrieval from Colluding Databases with Adversaries
The problem of symmetric private information retrieval (SPIR) from replicated
databases with colluding servers and adversaries is studied. Specifically, the
database comprises files, which are replicatively stored among servers.
A user wants to retrieve one file from the database by communicating with the
servers, without revealing the identity of the desired file to any server.
Furthermore, the user shall learn nothing about the other files. Any
out of servers may collude, that is, they may communicate their
interactions with the user to guess the identity of the requested file. An
adversary in the system can tap in on or even try to corrupt the communication.
Three types of adversaries are considered: a Byzantine adversary who can
overwrite the transmission of any servers to the user; a passive
eavesdropper who can tap in on the incoming and outgoing transmissions of any
servers; and a combination of both -- an adversary who can tap in on a set
of any nodes, and overwrite the transmission of a set of any nodes. The
problems of SPIR with colluding servers and the three types of adversaries are
named T-BSPIR, T-ESPIR and T-BESPIR respectively. The capacity of the problem
is defined as the maximum number of information bits of the desired file
retrieved per downloaded bit. We show that the information-theoretical capacity
of T-BSPIR equals , if the servers share common randomness
(unavailable at the user) with amount at least times the
file size. Otherwise, the capacity equals zero. The capacity of T-ESPIR is
proved to equal , with common randomness at least
times the file size. Finally, the capacity of
T-BESPIR is proved to be , with common randomness at
least times the file size
A general private information retrieval scheme for MDS coded databases with colluding servers
The problem of private information retrieval gets renewed attentions in
recent years due to its information-theoretic reformulation and applications in
distributed storage systems. PIR capacity is the maximal number of bits
privately retrieved per one bit of downloaded bit. The capacity has been fully
solved for some degenerating cases. For a general case where the database is
both coded and colluded, the exact capacity remains unknown. We build a general
private information retrieval scheme for MDS coded databases with colluding
servers. Our scheme achieves the rate , where
. Compared to existing PIR schemes,
our scheme performs better for a certain range of parameters and is suitable
for any underlying MDS code used in the distributed storage system.Comment: Submitted to IEEE Transactions on Information Theor
Linear Symmetric Private Information Retrieval for MDS Coded Distributed Storage with Colluding Servers
The problem of symmetric private information retrieval (SPIR) from a coded
database which is distributively stored among colluding servers is studied.
Specifically, the database comprises files, which are stored among
servers using an -MDS storage code. A user wants to retrieve one file
from the database by communicating with the servers, without revealing the
identity of the desired file to any server. Furthermore, the user shall learn
nothing about the other files in the database. In the -colluding SPIR
problem (hence called TSPIR), any out of servers may collude, that is,
they may communicate their interactions with the user to guess the identity of
the requested file. We show that for linear schemes, the information-theoretic
capacity of the MDS-TSPIR problem, defined as the maximum number of information
bits of the desired file retrieved per downloaded bit, equals
, if the servers share common randomness (unavailable at the
user) with amount at least times the file size.
Otherwise, the capacity equals zero. We conjecture that our capacity holds also
for general MDS-TSPIR schemes.Comment: arXiv admin note: text overlap with arXiv:1707.0215
Secure Private Information Retrieval from Colluding Databases with Eavesdroppers
The problem of private information retrieval (PIR) is to retrieve one message
out of messages replicated at databases, without revealing the identity
of the desired message to the databases. We consider the problem of PIR with
colluding servers and eavesdroppers, named T-EPIR. Specifically, any out of
databases may collude, i.e. they may communicate their interactions with
the user to guess the identity of the requested message. An eavesdropper is
curious to know the database and can tap in on the incoming and outgoing
transmissions of any databases. The databases share some common randomness
unknown to the eavesdropper and the user, and use the common randomness to
generate the answers, such that the eavesdropper can learn no information about
the messages. Define as the optimal ratio of the number of the
desired message information bits to the number of total downloaded bits, and
to be the optimal ratio of the information bits of the shared common
randomness to the information bits of the desired file. In our previous work,
we found that when , the optimal ratio that can be achieved equals
. In this work, we focus on the case when . We derive
an outer bound . We also obtain a lower bound of
. For the achievability, we propose a scheme which
achieves the rate (inner bound)
. The amount of shared
common randomness used in the achievable scheme is
times the file size. The gap between the derived inner and outer bounds
vanishes as the number of messages tends to infinity
Private Information Retrieval Through Wiretap Channel II: Privacy Meets Security
We consider the problem of private information retrieval through wiretap
channel II (PIR-WTC-II). In PIR-WTC-II, a user wants to retrieve a single
message (file) privately out of messages, which are stored in
replicated and non-communicating databases. An external eavesdropper observes a
fraction (of its choice) of the traffic exchanged between the th
database and the user. In addition to the privacy constraint, the databases
should encode the returned answer strings such that the eavesdropper learns
absolutely nothing about the \emph{contents} of the databases. We aim at
characterizing the capacity of the PIR-WTC-II under the combined privacy and
security constraints. We obtain a general upper bound for the problem in the
form of a max-min optimization problem, which extends the converse proof of the
PIR problem under asymmetric traffic constraints. We propose an achievability
scheme that satisfies the security constraint by encoding a secret key, which
is generated securely at each database, into an artificial noise vector using
an MDS code. The user and the databases operate at one of the corner points of
the achievable scheme for the PIR under asymmetric traffic constraints such
that the retrieval rate is maximized under the imposed security constraint. The
upper bound and the lower bound match for the case of and messages,
for any , and any .Comment: Submitted to IEEE Transactions on Information Theory, January 201
Cache-Aided Private Information Retrieval with Partially Known Uncoded Prefetching: Fundamental Limits
We consider the problem of private information retrieval (PIR) from
non-colluding and replicated databases, when the user is equipped with a cache
that holds an uncoded fraction of the symbols from each of the stored
messages in the databases. This model operates in a two-phase scheme, namely,
the prefetching phase where the user acquires side information and the
retrieval phase where the user privately downloads the desired message. In the
prefetching phase, the user receives uncoded fraction of each
message from the th database. This side information is known only to the
th database and unknown to the remaining databases, i.e., the user possesses
\emph{partially known} side information. We investigate the optimal normalized
download cost in the retrieval phase as a function of , , .
We develop lower and upper bounds for the optimal download cost. The bounds
match in general for the cases of very low caching ratio () and very high caching ratio (). We fully characterize the optimal download cost
caching ratio tradeoff for . For general , , and , we show that
the largest gap between the achievability and the converse bounds is
.Comment: Submitted for publication, December 2017. arXiv admin note:
substantial text overlap with arXiv:1709.0105
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 with Partially Known Private Side Information
We consider the problem of private information retrieval (PIR) of a single
message out of messages from replicated and non-colluding databases
where a cache-enabled user (retriever) of cache-size possesses side
information in the form of full messages that are partially known to the
databases. In this model, the user and the databases engage in a two-phase
scheme, namely, the prefetching phase where the user acquires side information
and the retrieval phase where the user downloads desired information. In the
prefetching phase, the user receives full messages from the th
database, under the cache memory size constraint . In
the retrieval phase, the user wishes to retrieve a message such that no
individual database learns anything about the identity of the desired message.
In addition, the identities of the side information messages that the user did
not prefetch from a database must remain private against that database. Since
the side information provided by each database in the prefetching phase is
known by the providing database and the side information must be kept private
against the remaining databases, we coin this model as \textit{partially known
private side information}. We characterize the capacity of the PIR with
partially known private side information to be
.
Interestingly, this result is the same if none of the databases knows any of
the prefetched side information, i.e., when the side information is obtained
externally, a problem posed by Kadhe et al. and settled by Chen-Wang-Jafar
recently. Thus, our result implies that there is no loss in using the same
databases for both prefetching and retrieval phases.Comment: Submitted to IEEE Transactions on Information Theory, November 201
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