1,202 research outputs found
Private Information Retrieval Schemes With Product-Matrix MBR Codes
A private information retrieval (PIR) scheme allows a user to retrieve a file from a database without revealing any information on the file being requested. As of now, PIR schemes have been proposed for several kinds of storage systems, including replicated and MDS-coded systems. However, the problem of constructing PIR schemes on regenerating codes has been sparsely considered. A regenerating code is a storage code whose codewords are distributed among nodes, enabling efficient storage of files, as well as low-bandwidth retrieval of files and repair of nodes. Minimum-bandwidth regenerating (MBR) codes define a family of regenerating codes allowing a node repair with optimal bandwidth. Rashmi, Shah, and Kumar obtained a large family of MBR codes using the product-matrix (PM) construction. In this work, a new PIR scheme over PM-MBR codes is designed. The inherent redundancy of the PM structure is used to reduce the download communication complexity of the scheme. A lower bound on the PIR capacity of MBR-coded PIR schemes is derived, showing an interesting storage space vs. PIR rate trade-off compared to existing PIR schemes with the same reconstruction capability. The present scheme also outperforms a recent PM-MBR PIR construction of Dorkson and Ng.Peer reviewe
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
When Queueing Meets Coding: Optimal-Latency Data Retrieving Scheme in Storage Clouds
In this paper, we study the problem of reducing the delay of downloading data
from cloud storage systems by leveraging multiple parallel threads, assuming
that the data has been encoded and stored in the clouds using fixed rate
forward error correction (FEC) codes with parameters (n, k). That is, each file
is divided into k equal-sized chunks, which are then expanded into n chunks
such that any k chunks out of the n are sufficient to successfully restore the
original file. The model can be depicted as a multiple-server queue with
arrivals of data retrieving requests and a server corresponding to a thread.
However, this is not a typical queueing model because a server can terminate
its operation, depending on when other servers complete their service (due to
the redundancy that is spread across the threads). Hence, to the best of our
knowledge, the analysis of this queueing model remains quite uncharted.
Recent traces from Amazon S3 show that the time to retrieve a fixed size
chunk is random and can be approximated as a constant delay plus an i.i.d.
exponentially distributed random variable. For the tractability of the
theoretical analysis, we assume that the chunk downloading time is i.i.d.
exponentially distributed. Under this assumption, we show that any
work-conserving scheme is delay-optimal among all on-line scheduling schemes
when k = 1. When k > 1, we find that a simple greedy scheme, which allocates
all available threads to the head of line request, is delay optimal among all
on-line scheduling schemes. We also provide some numerical results that point
to the limitations of the exponential assumption, and suggest further research
directions.Comment: Original accepted by IEEE Infocom 2014, 9 pages. Some statements in
the Infocom paper are correcte
- …