# An Equivalence Between Secure Network and Index Coding

## TL;DR

This paper establishes a theoretical equivalence between secure network coding and secure index coding, including randomized encoding, extending previous non-secure equivalences to the secure communication context.

## Contribution

It demonstrates that the most general secure network coding and secure index coding setups, with randomized encoding, are fundamentally equivalent.

## Key findings

- Secure network coding and index coding are equivalent in the secure setting.
- Includes randomized encoding in the equivalence.
- Extends previous non-secure equivalence results to secure scenarios.

## Abstract

We extend the equivalence between network coding and index coding by Effros, El Rouayheb, and Langberg to the secure communication setting in the presence of an eavesdropper. Specifically, we show that the most general versions of secure network-coding setup by Chan and Grant and the secure index-coding setup by Dau, Skachek, and Chee, which also include the randomised encoding setting, are equivalent.