Secure Communication Of Network Coding

The concept of network coding was proposed by Ahlswede and so on. The keyidea of network coding is that the intermediate nodes in a communication network areallowed to not only forward packets using network scheduling algorithms, but alsoencode/decode them. Network coding changes the existing way of information trans-mission, and renders the network capacity to be used more e?ciently. At the sametime, network coding theory brings new challenges to the areas of coding theory, se-cure communication and so on. At present, the researchers focus mainly on linearnetwork coding. Moreover, a great number of problems can be solved by linear net-work coding.In a communication network, a fundamental problem is how to utilize the net-work capacity e?ciently. Many researchers studied this problem by employing net-work coding as a tool. In this thesis, we consider this issue as well, for this purpose,we point out the shortcomings in the existing conclusions, and give conditions for ef-fective communication via linear network coding method. Furthermore, associatingwith algebraic geometry, we convert the problem of achieving desired communicationon a given network to the problem of seeking a solution of polynomial equations. It isconductive for us to find e?cient algorithms to achieve the desired connections withnetwork coding.The second problem we explore in this thesis is how to securely communicateover a communication network subject to the presence of a wiretapper who can eaves-drop a number of channels. Then three confidential communication schemes are pro-posed. Building on the observation that network coding allows intermediate nodesto mix information from di?erent data ?ows, we present a construction of linear net-work code under certain conditions, which makes the data packets of the network befully mixed with each other, and secure communication be available. This is the firstsecure communication scheme. This scheme doesn't require a key to encrypt the mes-sage packets, and achieves the purpose of confidential communication. It substantiallydi?ers from cryptographic methods. When using network coding cannot secure all source messages, we encrypt a part of source message packets, and blend the unen-crypted message packets with the obtained cryptograms. In this way, we can achievesecure communication on wiretap networks as well. This is secure communicationscheme II. In the last secure communication scheme, we employ the cryptographicmethod and use a key to encrypt all the source message packets. Then the key to betreated as a message packet and transmitted with the ciphertexts together. Under cer-tain conditions, there exist linear network codes such that the wiretapper has no accessto the key. Thus secure communication is feasible. Compared with the existing ap-proaches, the most distinguished advantage of secure communication schemes I and IIis that no network capacity is lost. Scheme III doesn't need a secret channel to transmitthe key, and it enables the utilization of network capacity to reach n?n 1.