450 research outputs found
The Capacity of Private Information Retrieval with Eavesdroppers
We consider the problem of private information retrieval (PIR) with colluding
servers and eavesdroppers (abbreviated as ETPIR). The ETPIR problem is
comprised of messages, servers where each server stores all
messages, a user who wants to retrieve one of the messages without
revealing the desired message index to any set of colluding servers, and an
eavesdropper who can listen to the queries and answers of any servers but
is prevented from learning any information about the messages. The information
theoretic capacity of ETPIR is defined to be the maximum number of desired
message symbols retrieved privately per information symbol downloaded. We show
that the capacity of ETPIR is
when , and when . To
achieve the capacity, the servers need to share a common random variable
(independent of the messages), and its size must be at least symbols per message symbol. Otherwise, with less amount of shared
common randomness, ETPIR is not feasible and the capacity reduces to zero.
An interesting observation is that the ETPIR capacity expression takes
different forms in two regimes. When , the capacity equals the inverse
of a sum of a geometric series with terms and decreases with ; this form
is typical for capacity expressions of PIR. When , the capacity does
not depend on , a typical form for capacity expressions of SPIR (symmetric
PIR, which further requires data-privacy, {\it i.e.,} the user learns no
information about other undesired messages); the capacity does not depend on
either. In addition, the ETPIR capacity result includes multiple previous
PIR and SPIR capacity results as special cases
Quantum Symmetric Private Information Retrieval with Secure Storage and Eavesdroppers
We consider both the classical and quantum variations of -secure,
-eavesdropped and -colluding symmetric private information retrieval
(SPIR). This is the first work to study SPIR with -security in classical or
quantum variations. We first develop a scheme for classical -secure,
-eavesdropped and -colluding SPIR (XSETSPIR) based on a modified version
of cross subspace alignment (CSA), which achieves a rate of . The modified scheme achieves the same rate as the
scheme used for -secure PIR with the extra benefit of symmetric privacy.
Next, we extend this scheme to its quantum counterpart based on the -sum box
abstraction. This is the first work to consider the presence of eavesdroppers
in quantum private information retrieval (QPIR). In the quantum variation, the
eavesdroppers have better access to information over the quantum channel
compared to the classical channel due to the over-the-air decodability. To that
end, we develop another scheme specialized to combat eavesdroppers over quantum
channels. The scheme proposed for -secure, -eavesdropped and
-colluding quantum SPIR (XSETQSPIR) in this work maintains the super-dense
coding gain from the shared entanglement between the databases, i.e., achieves
a rate of
Double Blind -Private Information Retrieval
Double blind -private information retrieval (DB-TPIR) enables two users,
each of whom specifies an index (, resp.), to efficiently
retrieve a message labeled by the two indices, from a
set of servers that store all messages , such that the two users'
indices are kept private from any set of up to colluding servers,
respectively, as well as from each other. A DB-TPIR scheme based on
cross-subspace alignment is proposed in this paper, and shown to be
capacity-achieving in the asymptotic setting of large number of messages and
bounded latency. The scheme is then extended to -way blind -secure
-private information retrieval (MB-XS-TPIR) with multiple () indices,
each belonging to a different user, arbitrary privacy levels for each index
(), and arbitrary level of security () of data
storage, so that the message can be
efficiently retrieved while the stored data is held secure against collusion
among up to colluding servers, the user's index is private against
collusion among up to servers, and each user's index is
private from all other users. The general scheme relies on a tensor-product
based extension of cross-subspace alignment and retrieves
bits of desired message per bit of download.Comment: Accepted for publication in IEEE Journal on Selected Areas in
Information Theory (JSAIT
The Asymptotic Capacity of -Secure -Private Linear Computation with Graph Based Replicated Storage
The problem of -secure -private linear computation with graph based
replicated storage (GXSTPLC) is to enable the user to retrieve a linear
combination of messages privately from a set of distributed servers where
every message is only allowed to store among a subset of servers subject to an
-security constraint, i.e., any groups of up to colluding servers must
reveal nothing about the messages. Besides, any groups of up to servers
cannot learn anything about the coefficients of the linear combination
retrieved by the user. In this work, we completely characterize the asymptotic
capacity of GXSTPLC, i.e., the supremum of average number of desired symbols
retrieved per downloaded symbol, in the limit as the number of messages
approaches infinity. Specifically, it is shown that a prior linear programming
based upper bound on the asymptotic capacity of GXSTPLC due to Jia and Jafar is
tight by constructing achievability schemes. Notably, our achievability scheme
also settles the exact capacity (i.e., for finite ) of -secure linear
combination with graph based replicated storage (GXSLC). Our achievability
proof builds upon an achievability scheme for a closely related problem named
asymmetric -secure -private linear computation with
graph based replicated storage (Asymm-GXSTPLC) that guarantees non-uniform
security and privacy levels across messages and coefficients. In particular, by
carefully designing Asymm-GXSTPLC settings for GXSTPLC problems, the
corresponding Asymm-GXSTPLC schemes can be reduced to asymptotic capacity
achieving schemes for GXSTPLC. In regard to the achievability scheme for
Asymm-GXSTPLC, interesting aspects of our construction include a novel query
and answer design which makes use of a Vandermonde decomposition of Cauchy
matrices, and a trade-off among message replication, security and privacy
thresholds.Comment: 39 pages, 2 figure
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