A Numerical Study on the Capacity Region of a Three-Layer Wiretap Network.

Area of Science:

• Information Theory
• Network Security
• Coding Theory

Background:

• Investigates secure communication in a three-layer wiretap network with source, middle, and sink nodes.
• Focuses on ensuring message recovery by sink nodes while preventing eavesdropper information leakage.

Purpose of the Study:

• To characterize the capacity region for secure message transmission in a multi-layer wiretap network.
• To generalize secret sharing problems within this network architecture.

Main Methods:

• Characterization of the Shannon region as an outer bound for the capacity region.
• Characterization of the common information region as an outer bound for the linear capacity region.
• Development of linear schemes to achieve these bounds.

Main Results:

• Fully characterizes the capacity region as a polyhedral cone for networks with N ≤ 4 middle nodes.
• Determines capacity regions for specific decoding/eavesdropping patterns when N = 5.
• Identifies linear capacity regions for remaining N=5 cases.

Conclusions:

• Provides a complete understanding of secure communication capacity for smaller networks (N ≤ 4).
• Offers partial characterization and linear solutions for larger networks (N = 5).
• Establishes a framework for analyzing secure multi-layer network performance.