16 research outputs found
Efficient Recovery of a Shared Secret via Cooperation: Applications to SDMM and PIR
This work considers the problem of privately outsourcing the computation of a
matrix product over a finite field to helper servers. These
servers are considered to be honest but curious, i.e., they behave according to
the protocol but will try to deduce information about the user's data.
Furthermore, any set of up to servers is allowed to share their data.
Previous works considered this collusion a hindrance and the download cost of
the schemes increases with growing . We propose to utilize such linkage
between servers to the user's advantage by allowing servers to cooperate in the
computational task. This leads to a significant gain in the download cost for
the proposed schemes. The gain naturally comes at the cost of increased
communication load between the servers. Hence, the proposed cooperative scheme
can be understood as outsourcing both computational cost and communication
cost.
While the present work exemplifies the proposed server cooperation in the
case of a specific secure distributed matrix multiplication (SDMM) scheme, the
same idea applies to many other use cases as well. For instance, other SDMM
schemes as well as linear private information retrieval (PIR) as a special case
of SDMM are instantly covered.Comment: 10 pages, 2 figure
Double Blind -Private Information Retrieval
Double blind -private information retrieval (DB-TPIR) enables two users,
each of whom specifies an index (, resp.), to efficiently
retrieve a message labeled by the two indices, from a
set of servers that store all messages , such that the two users'
indices are kept private from any set of up to colluding servers,
respectively, as well as from each other. A DB-TPIR scheme based on
cross-subspace alignment is proposed in this paper, and shown to be
capacity-achieving in the asymptotic setting of large number of messages and
bounded latency. The scheme is then extended to -way blind -secure
-private information retrieval (MB-XS-TPIR) with multiple () indices,
each belonging to a different user, arbitrary privacy levels for each index
(), and arbitrary level of security () of data
storage, so that the message can be
efficiently retrieved while the stored data is held secure against collusion
among up to colluding servers, the user's index is private against
collusion among up to servers, and each user's index is
private from all other users. The general scheme relies on a tensor-product
based extension of cross-subspace alignment and retrieves
bits of desired message per bit of download.Comment: Accepted for publication in IEEE Journal on Selected Areas in
Information Theory (JSAIT
Weakly Private Information Retrieval from Heterogeneously Trusted Servers
We study the problem of weakly private information retrieval (PIR) when there
is heterogeneity in servers' trustfulness under the maximal leakage (Max-L)
metric and mutual information (MI) metric. A user wishes to retrieve a desired
message from N non-colluding servers efficiently, such that the identity of the
desired message is not leaked in a significant manner; however, some servers
can be more trustworthy than others. We propose a code construction for this
setting and optimize the probability distribution for this construction. For
the Max-L metric, it is shown that the optimal probability allocation for the
proposed scheme essentially separates the delivery patterns into two parts: a
completely private part that has the same download overhead as the
capacity-achieving PIR code, and a non-private part that allows complete
privacy leakage but has no download overhead by downloading only from the most
trustful server. The optimal solution is established through a sophisticated
analysis of the underlying convex optimization problem, and a reduction between
the homogeneous setting and the heterogeneous setting. For the MI metric, the
homogeneous case is studied first for which the code can be optimized with an
explicit probability assignment, while a closed-form solution becomes
intractable for the heterogeneous case. Numerical results are provided for both
cases to corroborate the theoretical analysis.Comment: 23 pages 3 figures. arXiv admin note: text overlap with
arXiv:2205.0161