Secure Index Coding with Side Information

TL;DR

This paper explores security properties of linear index coding schemes with side information, generalizing weak security to block security, and characterizes their security levels based on code parameters and adversary knowledge.

Contribution

It extends the understanding of security in index coding by relating linear code parameters to block security levels, generalizing previous notions of weak security.

Findings

Linear coding schemes are (d-1-t)-block secure if the adversary knows t  - 2 messages.

Security is compromised if the adversary knows more than n - d^ messages.

The work generalizes weak security to block security in the context of index coding.

Abstract

Security aspects of the Index Coding with Side Information (ICSI) problem are investigated. Building on the results of Bar-Yossef et al. (2006), the properties of linear coding schemes for the ICSI problem are further explored. The notion of weak security, considered by Bhattad and Narayanan (2005) in the context of network coding, is generalized to block security. It is shown that the coding scheme for the ICSI problem based on a linear code C of length n, minimum distance d and dual distance d^\perp, is (d-1-t)-block secure (and hence also weakly secure) if the adversary knows in advance t \le d - 2 messages, and is completely insecure if the adversary knows in advance more than n - d^\perp messages.