11,625 research outputs found
On Quantum Advantage in Information Theoretic Single-Server PIR
In (single-server) Private Information Retrieval (PIR), a server holds a
large database of size , and a client holds an index and
wishes to retrieve without revealing to the server. It is well
known that information theoretic privacy even against an `honest but curious'
server requires communication complexity. This is true even if
quantum communication is allowed and is due to the ability of such an
adversarial server to execute the protocol on a superposition of databases
instead of on a specific database (`input purification attack'). Nevertheless,
there have been some proposals of protocols that achieve sub-linear
communication and appear to provide some notion of privacy. Most notably, a
protocol due to Le Gall (ToC 2012) with communication complexity ,
and a protocol by Kerenidis et al. (QIC 2016) with communication complexity
, and shared entanglement.
We show that, in a sense, input purification is the only potent adversarial
strategy, and protocols such as the two protocols above are secure in a
restricted variant of the quantum honest but curious (a.k.a specious) model.
More explicitly, we propose a restricted privacy notion called \emph{anchored
privacy}, where the adversary is forced to execute on a classical database
(i.e. the execution is anchored to a classical database). We show that for
measurement-free protocols, anchored security against honest adversarial
servers implies anchored privacy even against specious adversaries.
Finally, we prove that even with (unlimited) pre-shared entanglement it is
impossible to achieve security in the standard specious model with sub-linear
communication, thus further substantiating the necessity of our relaxation.
This lower bound may be of independent interest (in particular recalling that
PIR is a special case of Fully Homomorphic Encryption)
2-Server PIR with sub-polynomial communication
A 2-server Private Information Retrieval (PIR) scheme allows a user to
retrieve the th bit of an -bit database replicated among two servers
(which do not communicate) while not revealing any information about to
either server. In this work we construct a 1-round 2-server PIR with total
communication cost . This improves over the
currently known 2-server protocols which require communication and
matches the communication cost of known 3-server PIR schemes. Our improvement
comes from reducing the number of servers in existing protocols, based on
Matching Vector Codes, from 3 or 4 servers to 2. This is achieved by viewing
these protocols in an algebraic way (using polynomial interpolation) and
extending them using partial derivatives
A Storage-Efficient and Robust Private Information Retrieval Scheme Allowing Few Servers
Since the concept of locally decodable codes was introduced by Katz and
Trevisan in 2000, it is well-known that information the-oretically secure
private information retrieval schemes can be built using locally decodable
codes. In this paper, we construct a Byzantine ro-bust PIR scheme using the
multiplicity codes introduced by Kopparty et al. Our main contributions are on
the one hand to avoid full replica-tion of the database on each server; this
significantly reduces the global redundancy. On the other hand, to have a much
lower locality in the PIR context than in the LDC context. This shows that
there exists two different notions: LDC-locality and PIR-locality. This is made
possible by exploiting geometric properties of multiplicity codes
Some Applications of Coding Theory in Computational Complexity
Error-correcting codes and related combinatorial constructs play an important
role in several recent (and old) results in computational complexity theory. In
this paper we survey results on locally-testable and locally-decodable
error-correcting codes, and their applications to complexity theory and to
cryptography.
Locally decodable codes are error-correcting codes with sub-linear time
error-correcting algorithms. They are related to private information retrieval
(a type of cryptographic protocol), and they are used in average-case
complexity and to construct ``hard-core predicates'' for one-way permutations.
Locally testable codes are error-correcting codes with sub-linear time
error-detection algorithms, and they are the combinatorial core of
probabilistically checkable proofs
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