Title
Secrecy Capacity-Memory Tradeoff of Erasure Broadcast Channels.
Abstract
This paper derives upper and lower bounds on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">secrecy capacity-memory tradeoff</italic> of a wiretap erasure broadcast channel (BC) with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathsf{K}}_{w} $ </tex-math></inline-formula> weak receivers and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">global secrecy capacity-memory</italic> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">all</italic> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">weak</italic> receivers if the eavesdropper is weaker than the strong receivers.
Year
DOI
Venue
2018
10.1109/tit.2019.2902578
IEEE Transactions on Information Theory
Keywords
Field
DocType
Receivers,Cache memory,Encoding,Libraries,Standards,Zinc,Upper bound
Mathematical optimization,Upper and lower bounds,CPU cache,Cache,Secrecy,Computer network,Coding (social sciences),Broadcast channels,Mathematics,Erasure
Journal
Volume
Issue
ISSN
abs/1801.00606
8
0018-9448
Citations 
PageRank 
References 
0
0.34
13
Authors
4
Name
Order
Citations
PageRank
Sarah Kamel100.34
Mireille Sarkiss2298.79
Michele A. Wigger333738.25
Ghaya Rekaya-Ben Othman416422.84