107 research outputs found
Recommended from our members
Breaking the MDS-PIR Capacity Barrier via Joint Storage Coding
Paper explores the possibility of the capacity of private information retrieval (PIR) from databases coded using maximum distance separable (MDS) codes to be broken through joint encoding and storage of messages
Private Information Retrieval Schemes for Coded Data with Arbitrary Collusion Patterns
In Private Information Retrieval (PIR), one wants to download a file from a
database without revealing to the database which file is being downloaded. Much
attention has been paid to the case of the database being encoded across
several servers, subsets of which can collude to attempt to deduce the
requested file. With the goal of studying the achievable PIR rates in realistic
scenarios, we generalize results for coded data from the case of all subsets of
servers of size colluding, to arbitrary subsets of the servers. We
investigate the effectiveness of previous strategies in this new scenario, and
present new results in the case where the servers are partitioned into disjoint
colluding groups.Comment: Updated with a corrected statement of Theorem
MDS Variable Generation and Secure Summation with User Selection
A collection of random variables are called -MDS if any of the
variables are independent and determine all remaining variables. In the MDS
variable generation problem, users wish to generate variables that are
-MDS using a randomness variable owned by each user. We show that to
generate bit of -MDS variables for each ,
the minimum size of the randomness variable at each user is bits.
An intimately related problem is secure summation with user selection, where
a server may select an arbitrary subset of users and securely compute the
sum of the inputs of the selected users. We show that to compute bit of an
arbitrarily chosen sum securely, the minimum size of the key held by each user
is bits, whose achievability uses the generation
of -MDS variables for
On the Download Rate of Homomorphic Secret Sharing
A homomorphic secret sharing (HSS) scheme is a secret sharing scheme that
supports evaluating functions on shared secrets by means of a local mapping
from input shares to output shares. We initiate the study of the download rate
of HSS, namely, the achievable ratio between the length of the output shares
and the output length when amortized over function evaluations. We
obtain the following results.
* In the case of linear information-theoretic HSS schemes for degree-
multivariate polynomials, we characterize the optimal download rate in terms of
the optimal minimal distance of a linear code with related parameters. We
further show that for sufficiently large (polynomial in all problem
parameters), the optimal rate can be realized using Shamir's scheme, even with
secrets over .
* We present a general rate-amplification technique for HSS that improves the
download rate at the cost of requiring more shares. As a corollary, we get
high-rate variants of computationally secure HSS schemes and efficient private
information retrieval protocols from the literature.
* We show that, in some cases, one can beat the best download rate of linear
HSS by allowing nonlinear output reconstruction and error
probability
- β¦