152 research outputs found
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outdated (unsynchronized), or even worse, adversarial (Byzantine), and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
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 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
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
Towards the Capacity of Private Information Retrieval from Coded and Colluding Servers
In this work, two practical concepts related to private information retrieval
(PIR) are introduced and coined full support-rank PIR and strongly linear PIR.
Being of full support-rank is a technical, yet natural condition required to
prove a converse result for a capacity expression and satisfied by almost all
currently known capacity-achieving schemes, while strong linearity is a
practical requirement enabling implementation over small finite fields with low
subpacketization degree. Then, the capacity of MDS-coded, linear, full
support-rank PIR in the presence of colluding servers is derived, as well as
the capacity of symmetric, linear PIR with colluding, adversarial, and
nonresponsive servers for the recently introduced concept of matched
randomness. This positively settles the capacity conjectures stated by
Freij-Hollanti et al. and Tajeddine et al. in the presented cases. It is also
shown that, further restricting to strongly-linear PIR schemes with
deterministic linear interference cancellation, the so-called star product
scheme proposed by Freij-Hollanti et al. is essentially optimal and induces no
capacity loss
Privacy-Preserving Smart Parking System Using Blockchain and Private Information Retrieval
Searching for available parking spaces is a major problem for drivers
especially in big crowded cities, causing traffic congestion and air pollution,
and wasting drivers' time. Smart parking systems are a novel solution to enable
drivers to have real-time parking information for pre-booking. However, current
smart parking requires drivers to disclose their private information, such as
desired destinations. Moreover, the existing schemes are centralized and
vulnerable to the bottleneck of the single point of failure and data breaches.
In this paper, we propose a distributed privacy-preserving smart parking system
using blockchain. A consortium blockchain created by different parking lot
owners to ensure security, transparency, and availability is proposed to store
their parking offers on the blockchain. To preserve drivers' location privacy,
we adopt a private information retrieval (PIR) technique to enable drivers to
retrieve parking offers from blockchain nodes privately, without revealing
which parking offers are retrieved. Furthermore, a short randomizable signature
is used to enable drivers to reserve available parking slots in an anonymous
manner. Besides, we introduce an anonymous payment system that cannot link
drivers' to specific parking locations. Finally, our performance evaluations
demonstrate that the proposed scheme can preserve drivers' privacy with low
communication and computation overhead
The Capacity of Cache Aided Private Information Retrieval
The problem of cache enabled private information retrieval (PIR) is
considered in which a user wishes to privately retrieve one out of
messages, each of size bits from distributed databases. The user has a
local cache of storage bits which can be used to store any function of the
messages. The main contribution of this work is the exact characterization
of the capacity of cache aided PIR as a function of the storage parameter .
In particular, for a given cache storage parameter , the
information-theoretically optimal download cost (or the inverse of
capacity) is shown to be equal to . Special cases of this result correspond to the
settings when , for which the optimal download cost was shown by Sun and
Jafar to be , and the
case when , i.e., cache size is large enough to store all messages
locally, for which the optimal download cost is . The intermediate points
can be readily achieved through a simple memory-sharing based PIR
scheme. The key technical contribution of this work is the converse, i.e., a
lower bound on the download cost as a function of storage which shows that
memory sharing is information-theoretically optimal
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
The -error Capacity of Symmetric PIR with Byzantine Adversaries
The capacity of symmetric private information retrieval with messages,
servers (out of which any may collude), and an omniscient Byzantine
adversary (who can corrupt any answers) is shown to be
[1], under the requirement of zero probability of error. In this work, we show
that by weakening the adversary slightly (either providing secret low rate
channels between the servers and the user, or limiting the observation of the
adversary), and allowing vanishing probability of error, the capacity increases
to .Comment: Part of this paper will be presented in 2018 IEEE Information Theory
Workshop (ITW
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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