In this paper we define the overflow problem of a network coding storage system in which the encoding parameter and the storage parameter are mismatched. Through analyses and experiments, we first show the impacts of the overflow problem in a network coding scheme, which not only waste storage spaces, but also degrade coding efficiency. To avoid the overflow problem, we then develop the network coding based secure storage (NCSS) scheme. Thanks to considering both security and storage requirements in encoding procedures and distributed architectures, the NCSS can improve the performance of a cloud storage system from both the aspects of storage cost and coding processing time. We analyze the maximum allowable stored encoded data under the perfect secrecy criterion, and provide the design guidelines for the secure cloud storage system to enhance coding efficiency and achieve the minimal storage cost.
Another research area of network coding is to prevent data being eavesdropped during transmission. The information-theoretical security problem for an untrusted channel was first discussed in @cite_9 . A network coding system was built to prove that a wiretapper cannot obtain any information from the transmitted message @cite_22 . A weaker type of security issue was investigated in @cite_6 , where a node can decode packets only after receiving sufficient linear independent encoded data. The construction of a secure linear network code for a wiretap network was presented in @cite_3 .
@cite_9 @cite_3 @cite_22 @cite_6
2006947308 2152303628 68293075 2106570206
In the paradigm of network coding, the nodes in a network are allowed to encode the information received from the input links. With network coding, the full capacity of the network can be utilized. In this paper, we propose a model, call the wiretap network, that incorporates information security with network coding. In this model, a collection of subsets of the channels in the network is given, and a wiretapper is allowed to access any one (but not more than one) of these subsets without being able to obtain any information about the message transmitted. Our model includes secret sharing in classical cryptography as a special case. We present a construction of secure linear network codes that can be used provided a certain graph-theoretic condition is satisfied. We also prove the necessity of this condition for the special case that the wiretapper may choose to access any subset of channels of a fixed size. The optimality of our code construction is established for this special case. Finally, we extend our results to the scenario when the wiretapper is allowed to obtain a controlled amount of information about the message. The problem of securing a network coding communication system against an eavesdropper is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the adversary can eavesdrop on μ arbitrarily chosen links. The objective is to provide reliable communication to all receivers, while guaranteeing that the source information remains information-theoretically secure from the adversary. A coding scheme is proposed that can achieve the maximum possible rate of n - μ packets. The scheme, which is based on rank-metric codes, has the distinctive property of being universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying linear network code. The only requirement of the scheme is that the packet length be at least n, which is shown to be strictly necessary for universal communication at the maximum rate. A further scenario is considered where the adversary is allowed not only to eavesdrop but also to inject up to t erroneous packets into the network, and the network may suffer from a rank deficiency of at most ρ. In this case, the proposed scheme can be extended to achieve the rate of n - ρ - 2t - μ packets. This rate is shown to be optimal under the assumption of zero-error communication. In this work we consider the problem of secure data transmission on an acyclic multicast network. A new information theoretic model for security is proposed that defines the system as secure if an eavesdropper is unable to get any “meaningful” information about the source. The “wiretap” network model by Cai and Yeung in which no information of the source is made available to the eavesdropper is a special case in the new model. We consider the case when the number of independent messages available to the eavesdropper is less than the multicast capacity of the network. We show that under the new security requirements communication is possible at the multicast capacity. A linear transformation is provided for networks with a given linear code to make the system secure. The transformation needs to be done only at the source and the operations at the intermediate nodes remain unchanged. We also show that if random coding scheme is used the probability of the system being secure can be made arbitrarily close to one by coding over a large enough field. We consider the problem of securing a multicast network against a wiretapper that can eavesdrop on the packets on a limited number of network edges of its choice. We assume that the network employs network coding to simultaneously deliver the packets available at the source to all the destinations. We show that this problem can be looked at as a network generalization of the wiretap channel of type II introduced in a seminal paper by Ozarow and Wyner. In particular, we show that the transmitted information can be secured by using the Ozarow-Wyner approach of coset coding at the source on top of the existing network code. This way, we quickly and transparently recover some of the results available in the literature on secure network coding for wiretap networks. Moreover, we use this framework to derive new bounds on the code alphabet size that are independent of the network size, and provide algorithms for explicit construction of secure network codes. We also analyze the amount of information that can be leaked to the wiretapper as a function of the number of wiretapped edges.