Broadcast Channels with Confidential Messages by Randomness Constrained Stochastic Encoder

TL;DR

This paper analyzes the trade-offs in stochastic encoding for secure broadcast channels, establishing optimal coding schemes and security proofs to prevent information leakage to eavesdroppers.

Contribution

It introduces a comprehensive analysis of the randomness rate trade-off in stochastic encoding for confidential broadcast channels, with new security proofs and optimal coding strategies.

Findings

Superposition coding achieves strong security

Matching converse theorem confirms optimality

Channel prefixing with simulation is suboptimal

Abstract

In coding schemes for the wire-tap channel or the broadcast channels with confidential messages, it is well known that the sender needs to use a stochastic encoding to avoid the information about the transmitted confidential message to be leaked to an eavesdropper. In this paper, it is investigated that the trade-off between the rate of the random number to realize the stochastic encoding and the rates of the common, private, and confidential messages. For the direct theorem, the superposition coding scheme for the wire-tap channel recently proposed by Chia and El Gamal is employed, and its strong security is proved. The matching converse theorem is also established. Our result clarifies that a combination of the ordinary stochastic encoding and the channel prefixing by the channel simulation is suboptimal.