Research On Secure Network Coding

The advent of network coding broke the traditional basic operating regulation that was the pattern of storage and forwarding followed by communication network. Network coding not only reserved original function at network nodes, but also allowed coding at network nodes, which increased the transmitting capacity of the network greatly, and achieved the upper bound prescribed by the Shannon Max-Flow Min-Cut Theorem, while just used the traditional pattern of storage and forwarding at network codes reached this max-flow bound impossibly at all. Moreover, the theory innovation of network coding had pervasive significance, and its application foreground was extensive thoroughly, therefore, in recent years, network coding was a very attractive interdisciplinary study area that poses interesting questions across diverse areas such as information theory, coding theory, network switching, wireless communications, computer sciences, information security, operational research, matrix theory and so on.The original intention of network coding was improving the throughput of the network; however, it was found that network coding was a better method for constructing secure network transmission in the further study. Thus, with the advent of network coding, network coding was applied network security increasingly in the academic study. Concretely, network coding can hide and bear the weight of data in the executed process, so it enhanced the information's security, which was safer than traditional encryption techniques used to encrypt the data in the network. For instance, there were two bit groups A and B, and the "exclusive or" operation was executed for A and B. From the results, those data of two bit groups can't be seen. Some bits of the data may be acquired, but the whole data of the bit group A can't be reverted, unless the data of the bit group B was completely captured.The basic theory of network coding was introduced detailedly at beginning, and then after mastering various basic academic knowledge of network coding, the author made a deep research on secure network coding.Firstly, based on the free delay linear communications network, the CSWN was introduced. Secondly, the security theorem of the single source and single sink network coding was displayed, which was mentioned by Kamal Jain. Based on this theorem, a kind of arithmetic that searching a security path was designed and an example was given, while a new concept that wiretap matrix was proposed by author. Thirdly, the author analyzed the situation of the secure coding of the single source and multi-sink network detailedly. After a counterexample was analyzed, the author found that the security condition of the single source and single sink network coding can't be directly "copy" to the single source and multi-sink network. However, if the number of edge disjoint paths in the collection of network path corresponding to all the edges in the wiretap set was less than the max-flow value, the network was safe. And a wider secure theorem of the single source and multi-sink network was proposed and proved. In the proof process, the wiretap matrix was quoted. And in the end, a tighter secure theorem of the single source and multi-sink network was elicited that if the rank of wiretap matrix was less than the max-flow value, the wire taper does not get any useful information about the message bit. Finally, the author compared the situation of using the pure random number on coding nodes with using the pseudo random function, and educed that it's better to use the pseudo random function to make the network safer and stronger.