Secrecy Capacity-Memory Tradeoff of Erasure Broadcast Channels

• Published in: IEEE transactions on information theory Vol. 65; no. 8; pp. 5094 - 5124
• Main Authors: Kamel, Sarah, Sarkiss, Mireille, Wigger, Michele, Rekaya-Ben Othman, Ghaya
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Broadcast channel; Cache memory; caching; Coding; Computer memory; Computer Science; Electronic surveillance; Encoding; Information Theory; Libraries; Lower bounds; Receivers; secrecy; secure capacity-memory tradeoff; Tradeoffs; Upper bound; Upper bounds; wiretap channel; Wiretapping; Zinc; wiretap channel; secure capacity-memory tradeoff; Index Terms-Broadcast channel; secrecy; caching
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2019.2902578

This paper derives upper and lower bounds on the secrecy capacity-memory tradeoff of a wiretap erasure broadcast channel (BC) with <inline-formula> <tex-math notation="LaTeX">{\mathsf{K}}_{w} </tex-math></inline-formula> weak receivers and <inline-formula> <tex-math notation="LaTeX">{\mathsf {K}}_{s} </tex-math></inline-formula> strong receivers, where weak receivers and strong receivers have the same erasure probabilities and cache sizes, respectively. The lower bounds are achieved by the 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 further allow us to 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. This 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 the receivers if the eavesdropper is stronger than all the 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.