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Private Function Retrieval
The widespread use of cloud computing services raises the question of how one
can delegate the processing tasks to the untrusted distributed parties without
breeching the privacy of its data and algorithms. Motivated by the algorithm
privacy concerns in a distributed computing system, in this paper, we introduce
the private function retrieval (PFR) problem, where a user wishes to
efficiently retrieve a linear function of messages from
non-communicating replicated servers while keeping the function hidden from
each individual server. The goal is to find a scheme with minimum communication
cost. To characterize the fundamental limits of the communication cost, we
define the capacity of PFR problem as the size of the message that can be
privately retrieved (which is the size of one file) normalized to the required
downloaded information bits. We first show that for the PFR problem with
messages, servers and a linear function with binary coefficients the
capacity is . Interestingly, this
is the capacity of retrieving one of messages from servers while
keeping the index of the requested message hidden from each individual server,
the problem known as private information retrieval (PIR). Then, we extend the
proposed achievable scheme to the case of arbitrary number of servers and
coefficients in the field with arbitrary and obtain
On Cache-Aided Multi-User Private Information Retrieval with Small Caches
In this paper, we propose a scheme for the problem of cache-aided multi-user
private information retrieval with small caches, in which users are
connected to non-colluding databases via shared links. Each database
contains a set of files, and each user has a dedicated cache of size
equivalent to the size of files. All the users want to retrieve a file
without revealing their demands to the databases. During off-peak hours, all
the users will fill their caches, and when required, users will demand their
desired files by cooperatively generating query sets for each database. After
receiving the transmissions from databases, all the users should get their
desired files using transmitted data and their cache contents. This problem has
been studied in [X. Zhang, K. Wan, H. Sun, M. Ji and G. Caire, \tqt{Fundamental
limits of cache-aided multiuser private information retrieval}, IEEE Trans.
Commun., 2021], in which authors proposed a product design scheme. In this
paper, we propose a scheme that gives a better rate for a particular value of
than the product design scheme. We consider a slightly different approach
for the placement phase. Instead of a database filling the caches of all users
directly, a database will broadcast cache content for all users on a shared
link, and then the users will decide unitedly which part of the broadcasted
content will be stored in the cache of each user. This variation facilitates
maintaining the privacy constraint at a reduced rate.Comment: 32 pages, 7 tables and 1 figur
Single-Server Single-Message Online Private Information Retrieval with Side Information
In many practical settings, the user needs to retrieve information from a
server in a periodic manner, over multiple rounds of communication. In this
paper, we discuss the setting in which this information needs to be retrieved
privately, such that the identity of all the information retrieved until the
current round is protected. This setting can occur in practical situations in
which the user needs to retrieve items from the server or a periodic basis,
such that the privacy needs to be guaranteed for all the items been retrieved
until the current round. We refer to this setting as an \emph{online private
information retrieval} as the user does not know the identities of the future
items that need to be retrieved from the server.
Following the previous line of work by Kadhe \emph{et al.}~we assume that the
user knows a random subset of messages in the database as a side
information which are unknown to the server. Focusing on scalar-linear
settings, we characterize the \emph{per-round capacity}, i.e., the maximum
achievable download rate at each round, and present a coding scheme that
achieves this capacity. The key idea of our scheme is to utilize the data
downloaded during the current round as a side information for the subsequent
rounds. We show for the setting with messages stored at the server, the
per-round capacity of the scalar-linear setting is for round
and for round , provided that
is a power of .Comment: 7 pages; This work is a long version of an article submitted to IEEE
for possible publicatio
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