Private Index Coding
Varun Narayanan, Jithin Ravi, Vivek K. Mishra, Bikash Kumar Dey,, Nikhil Karamchandani, Vinod M. Prabhakaran

TL;DR
This paper introduces the private index coding problem, analyzing how to achieve private communication with secret keys, characterizing feasible key structures, and exploring optimal coding schemes for different numbers of users.
Contribution
It characterizes key access structures for private index coding, provides conditions for linear schemes, and extends bounds to arbitrary user numbers, highlighting the role of shared randomness.
Findings
Scalar linear codes are optimal for up to three users.
All feasible rates can be achieved with scalar linear coding and time sharing for three users.
Common and private randomness do not affect the rate region.
Abstract
We study the fundamental problem of index coding under an additional privacy constraint that requires each receiver to learn nothing more about the collection of messages beyond its demanded messages from the server and what is available to it as side information. To enable such private communication, we allow the use of a collection of independent secret keys, each of which is shared amongst a subset of users and is known to the server. The goal is to study properties of the key access structures which make the problem feasible and then design encoding and decoding schemes efficient in the size of the server transmission as well as the sizes of the secret keys. We call this the private index coding problem. We begin by characterizing the key access structures that make private index coding feasible. We also give conditions to check if a given linear scheme is a valid private index…
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