Abstract
This paper investigates the problem of secure communication in a wireline noiseless scenario where a source wishes to communicate to a number of destinations in the presence of a passive external adversary. Different from the multicast scenario, where all destinations are interested in receiving the same message, in this setting different destinations are interested in different messages. The main focus of this paper is on characterizing the secure capacity region, when the adversary has unbounded computational capabilities, but limited network presence. Towards this end, an outer bound on the secure capacity region is derived, and secure transmission schemes are designed and analyzed in terms of achieved rate performance. It is first shown that, for the case of two destinations, the designed scheme matches the outer bound, hence characterizing the secure capacity region. Then, a particular class of networks referred to as two-layer networks is considered, where the source communicates with the destinations by hopping information through one layer of relays. It is shown that the designed scheme is indeed capacity achieving for any two-layer network for which one of the following three conditions is satisfied: (i) the number of destinations is three, (ii) the number of edges eavesdropped by the adversary is one, (iii) the min-cut capacities assume specific values. It is also shown that two-layer networks can be used to model and study a more general class of networks, referred to as separable. The key feature of separable networks is that they can be partitioned into edge disjoint networks that satisfy specific min-cut properties. In particular, it is proved that the secure capacity region of any separable network can be characterized from the secure capacity region of the corresponding two-layer network. Finally, for an arbitrary network topology, a two-phase scheme is designed and its rate performance is compared with the capacity-achieving scheme for networks with two destinations.
| Original language | English (US) |
|---|---|
| Article number | 9039716 |
| Pages (from-to) | 5204-5227 |
| Number of pages | 24 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 66 |
| Issue number | 8 |
| DOIs | |
| State | Published - Aug 2020 |
Bibliographical note
Funding Information:Manuscript received July 26, 2018; revised December 28, 2019; accepted March 6, 2020. Date of publication March 17, 2020; date of current version July 14, 2020. This work was supported in part by NSF Award under Grant 1740047 and Grant 1954800, and in part by UC-NL under Grant LFR-18-548554. This article was presented in part at the 10th International Conference on Information Theoretic Security. (Corresponding author: Gaurav Kumar Agarwal.) Gaurav Kumar Agarwal was with the Electrical and Computer Engineering Department, University of California, Los Angeles (UCLA), Los Angeles, CA 90095 USA. He is now with Google, Mountain View, CA 94043 USA (e-mail: gauravagarwal@ucla.edu).
Publisher Copyright:
© 1963-2012 IEEE.
Keywords
- Network coding
- information security
- physical layer