On Wiretap Networks II (0807.0821v1)

Abstract: We consider the problem of securing a multicast network against a wiretapper that can intercept the packets on a limited number of arbitrary network links of his choice. We assume that the network implements network coding techniques to simultaneously deliver all the packets available at the source to all the destinations. We show how this problem can be looked at as a network generalization of the Ozarow-Wyner Wiretap Channel of type II. In particular, we show that network security can be achieved by using the Ozarow-Wyner approach of coset coding at the source on top of the implemented network code. This way, we quickly and transparently recover some of the results available in the literature on secure network coding for wiretapped networks. We also derive new bounds on the required secure code alphabet size and an algorithm for code construction.

• The paper generalizes the classical Ozarow-Wyner wiretap channel to multicast networks via network coding techniques.
• The paper applies coset coding to secure transmitted data, ensuring intercepted packets remain uninformative to adversaries.
• The paper derives new bounds on the secure code alphabet size and provides an algorithm for constructing codes that guarantee network security.

"On Wiretap Networks II" presents a detailed examination of securing multicast networks against wiretappers who can intercept packets on a limited number of arbitrary network links. This problem is addressed within the framework of network coding, which is a method that allows for the simultaneous delivery of all packets from the source to multiple destinations.

The paper builds on the foundational concept of the Ozarow-Wyner Wiretap Channel of type II, which is a classical model in information theory analyzing eavesdropping scenarios. By extending this model to network settings, the authors propose using coset coding at the source. This method involves partitioning a vector space into cosets and transmitting coset representatives, thereby securing the information without modifying the underlying network code.

Key contributions of the paper include:

1. Generalization of the Wiretap Channel: The network security problem is framed as a generalization of the Ozarow-Wyner Wiretap Channel of type II. This perspective allows for leveraging insights from well-established information theory principles to address new challenges in network coding.
2. Security through Coset Coding: The authors explain how coset coding can be performed on top of the implemented network code. This method ensures security against wiretappers by making intercepted packets uninformative unless the eavesdropper can access a sufficient number of network links, which is assumed to be restricted.
3. Derivation of Bounds and Algorithm: New theoretical bounds on the required secure code alphabet size are derived. These bounds dictate the minimum number of distinct symbols needed to ensure secure communication. Additionally, an algorithm for constructing such secure codes is provided, which enhances the practical applicability of the theoretical results.
4. Recovery and Extension of Existing Results: By applying coset coding, the paper not only recovers several known results in secure network coding but also extends them, providing a unified framework for understanding and enhancing network security.

The paper thus significantly advances the field of secure network coding by integrating classical wiretap channel concepts with modern network coding techniques, offering both theoretical insights and practical solutions for secure multicast communications.