Secrecy Capacity-Memory Tradeoff of Erasure Broadcast Channels

TL;DR

This paper analyzes the secrecy capacity-memory tradeoff in erasure broadcast channels with eavesdroppers, deriving bounds and optimal cache strategies to maximize secure communication under various conditions.

Contribution

It provides new bounds and exact capacity results for cache-aided secure broadcast channels, including optimal cache allocation strategies under different eavesdropper strengths.

Findings

Bounds on secrecy capacity-memory tradeoff derived.

Exact capacity identified when only weak receivers cache.

Optimal cache distribution depends on eavesdropper strength.

Abstract

This paper derives upper and lower bounds on the secrecy capacity-memory tradeoff of a wiretap erasure broadcast channel (BC) with Kw weak receivers and Ks strong receivers, where weak receivers, respectively strong receivers, have same erasure probabilities and cache sizes. The lower bounds are achieved by schemes that meticulously combine joint cache-channel coding with wiretap coding and key-aided one-time pads. The presented upper bound holds more generally for arbitrary degraded BCs and arbitrary cache sizes. When only weak receivers have cache memories, upper and lower bounds coincide for small and large cache memories, thus providing the exact secrecy capacity-memory tradeoff for this setup. The derived bounds allow to further conclude that the secrecy capacity is positive even when the eavesdropper is stronger than all the legitimate receivers with cache memories. Moreover, they show that the secrecy capacity-memory tradeoff can be significantly smaller than its non-secure counterpart, but it grows much faster when cache memories are small. The paper also presents a lower bound on the global secrecy capacity-memory tradeoff where one is allowed to optimize the cache assignment subject to a total cache budget. It is close to the best known lower bound without secrecy constraint. For small total cache budget, the global secrecy capacity-memory tradeoff is achieved by assigning all the available cache memory uniformly over all receivers if the eavesdropper is stronger than all legitimate receivers, and it is achieved by assigning the cache memory uniformly only over the weak receivers if the eavesdropper is weaker than the strong receivers.