13 research outputs found
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
Private Database Queries Using Quantum States with Limited Coherence Times
We describe a method for private database queries using exchange of quantum
states with bits encoded in mutually incompatible bases. For technology with
limited coherence time, the database vendor can announce the encoding after a
suitable delay to allow the user to privately learn one of two items in the
database without the ability to also definitely infer the second item. This
quantum approach also allows the user to choose to learn other functions of the
items, such as the exclusive-or of their bits, but not to gain more information
than equivalent to learning one item, on average. This method is especially
useful for items consisting of a few bits by avoiding the substantial overhead
of conventional cryptographic approaches.Comment: extended to generalized (POVM) measurement
Shortest Path Computation with No Information Leakage
Shortest path computation is one of the most common queries in location-based
services (LBSs). Although particularly useful, such queries raise serious
privacy concerns. Exposing to a (potentially untrusted) LBS the client's
position and her destination may reveal personal information, such as social
habits, health condition, shopping preferences, lifestyle choices, etc. The
only existing method for privacy-preserving shortest path computation follows
the obfuscation paradigm; it prevents the LBS from inferring the source and
destination of the query with a probability higher than a threshold. This
implies, however, that the LBS still deduces some information (albeit not
exact) about the client's location and her destination. In this paper we aim at
strong privacy, where the adversary learns nothing about the shortest path
query. We achieve this via established private information retrieval
techniques, which we treat as black-box building blocks. Experiments on real,
large-scale road networks assess the practicality of our schemes.Comment: VLDB201
Reed-Muller codes for random erasures and errors
This paper studies the parameters for which Reed-Muller (RM) codes over
can correct random erasures and random errors with high probability,
and in particular when can they achieve capacity for these two classical
channels. Necessarily, the paper also studies properties of evaluations of
multi-variate polynomials on random sets of inputs.
For erasures, we prove that RM codes achieve capacity both for very high rate
and very low rate regimes. For errors, we prove that RM codes achieve capacity
for very low rate regimes, and for very high rates, we show that they can
uniquely decode at about square root of the number of errors at capacity.
The proofs of these four results are based on different techniques, which we
find interesting in their own right. In particular, we study the following
questions about , the matrix whose rows are truth tables of all
monomials of degree in variables. What is the most (resp. least)
number of random columns in that define a submatrix having full column
rank (resp. full row rank) with high probability? We obtain tight bounds for
very small (resp. very large) degrees , which we use to show that RM codes
achieve capacity for erasures in these regimes.
Our decoding from random errors follows from the following novel reduction.
For every linear code of sufficiently high rate we construct a new code
, also of very high rate, such that for every subset of coordinates, if
can recover from erasures in , then can recover from errors in .
Specializing this to RM codes and using our results for erasures imply our
result on unique decoding of RM codes at high rate.
Finally, two of our capacity achieving results require tight bounds on the
weight distribution of RM codes. We obtain such bounds extending the recent
\cite{KLP} bounds from constant degree to linear degree polynomials
Refuting Learning Revisited
We consider, within the framework of inductive inference, the concept of refuting learning as introduced by Mukouchi and Arikawa, where the learner is not only required to learn all concepts in a given class but also has to explicitly refute concepts outside the class