78,235 research outputs found
The Capacity of Private Computation
We introduce the problem of private computation, comprised of distributed
and non-colluding servers, independent datasets, and a user who wants to
compute a function of the datasets privately, i.e., without revealing which
function he wants to compute, to any individual server. This private
computation problem is a strict generalization of the private information
retrieval (PIR) problem, obtained by expanding the PIR message set (which
consists of only independent messages) to also include functions of those
messages. The capacity of private computation, , is defined as the maximum
number of bits of the desired function that can be retrieved per bit of total
download from all servers. We characterize the capacity of private computation,
for servers and independent datasets that are replicated at each
server, when the functions to be computed are arbitrary linear combinations of
the datasets. Surprisingly, the capacity,
, matches the capacity of PIR with
servers and messages. Thus, allowing arbitrary linear computations does
not reduce the communication rate compared to pure dataset retrieval. The same
insight is shown to hold even for arbitrary non-linear computations when the
number of datasets
Private Outsourcing of Polynomial Evaluation and Matrix Multiplication using Multilinear Maps
{\em Verifiable computation} (VC) allows a computationally weak client to
outsource the evaluation of a function on many inputs to a powerful but
untrusted server. The client invests a large amount of off-line computation and
gives an encoding of its function to the server. The server returns both an
evaluation of the function on the client's input and a proof such that the
client can verify the evaluation using substantially less effort than doing the
evaluation on its own. We consider how to privately outsource computations
using {\em privacy preserving} VC schemes whose executions reveal no
information on the client's input or function to the server. We construct VC
schemes with {\em input privacy} for univariate polynomial evaluation and
matrix multiplication and then extend them such that the {\em function privacy}
is also achieved. Our tool is the recently developed {mutilinear maps}. The
proposed VC schemes can be used in outsourcing {private information retrieval
(PIR)}.Comment: 23 pages, A preliminary version appears in the 12th International
Conference on Cryptology and Network Security (CANS 2013
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