DOI: 10.25549/usctheses-c3-204887
title: Efficient methods for enhancing secure network codes

description: Network coding has been studied extensively in the last decade, during which it has been linked to applications in throughput gain, error correction, robustness to non-ergodic link failures, confidentiality, and security. It can be efficiently implemented through low com- plexity linear operations, over both wired and wireless networks. Network coding may also be utilized in both centralized and decentralized designs, where it has been shown to outperform traditional routing techniques. Despite its potential, network coding must still abide by the same fundamental tradeoffs. These tradeoffs are rarely treated in the literature that studies each of its merits in isolation. We feature a holistic approach to network coding in the areas of security, efficiency, and robustness against erasures. Joint examination yields design considerations that require flexible parameters to analyze tradeoffs between desired algorithmic features. ❧ For the first topic, we present a novel algorithm that achieves robust and secure shar- ing based on network coding among multiple trusted peers in wireless erasure networks. In the considered communication model, an eavesdropper can take advantage of the broadcast medium to tap messages along a min-cut. The fundamental tradeoff between secrecy, robustness and efficiency enforced by the wireless environment is examined. In situations where there is no secure capacity, we give a convolutional NC scheme that achieves weak secrecy to decrease the number of symmetric keys required. We further propose methods to increase communication efficiency using the algorithm at the cost of robustness or privacy. Finally, we show that network erasures can actually increase the amount of secrecy in the proposed scheme but at the cost of decreased efficiency. ❧ For the second topic, an algorithm is presented that efficiently hides the global coding kernels as an alternative method to providing privacy in a single source multicast network that employs network coding. Unlike the majority of secure network coding algorithms, the proposed algorithm continues a very recent trend that instead focuses on preventing the adversary from ascertaining any global or local mappings. Without the global coding matrix, the adversary is unable to recover the secret source messages. We address a more powerful adversary that not only removes all wiretap restrictions featured in previous works, but we also assume that the adversary has the ability to manipulate source messages. The adversarial goal is therefore to obtain information about the global coding matrix by chosen plaintext attacks. Our algorithm is novel in the sense that the source node codes messages based on the secretly indexed set of coding vectors, rather than independently selecting each coefficient. By reducing the size of this finite pool, we may achieve enormous gains in overhead savings, which increase utilizable network capacity. The impact of the field size and the size of the vector pool on both security and efficiency is discussed. The cost metric used is the number of bits that need to be encrypted each generation.