text: 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.
  @cite_21: Regenerating codes are a class of codes for distributed storage networks that provide reliability and availability of data, and also perform efficient node repair. Another important aspect of a distributed storage network is its security. In this paper, we consider a threat model where an eavesdropper may gain access to the data stored in a subset of the storage nodes, and possibly also, to the data downloaded during repair of some nodes. We provide explicit constructions of regenerating codes that achieve information-theoretic secrecy capacity in this setting.
  @cite_0: The problem of securing data against eavesdropping in distributed storage systems is studied. The focus is on systems that use linear codes and implement exact repair to recover from node failures. The maximum file size that can be stored securely is determined for systems in which all the available nodes help in repair (i.e., repair degree d = n -1, where n is the total number of nodes) and for any number of compromised nodes. Similar results in the literature are restricted to the case of at most two compromised nodes. Moreover, new explicit upper bounds are given on the maximum secure file size for systems with d <; n - 1. The key ingredients for the contribution of this paper are new results on subspace intersection for the data downloaded during repair. The new bounds imply the interesting fact that the maximum amount of data that can be stored securely decreases exponentially with the number of compromised nodes. Whether this exponential decrease is fundamental or is a consequence of the exactness and linearity constraints remains an open question.
  @cite_23: This paper addresses the issue of securing information stored on a distributed storage system from a passive eavesdropping attack. The security notion is perfect secrecy, i.e., the system is said to be secure only if the mutual information between the stored information and the observations at the adversary is zero. The paper summarizes state of the art on securing repair-efficient distributed storage systems. Then, storage systems that employ locally repairable codes with minimum bandwidth regenerating codes as local codes (MBR-LRCs) are investigated. A secure file size upper bound and a construction of secure MBR-LRCs are provided. These two are shown to match under special cases, establishing the secrecy capacity of these systems.
  @cite_16: 
  @cite_10: We address the problem of securing distributed storage systems against passive eavesdroppers that can observe a limited number of storage nodes. An important aspect of these systems is node failures over time, which demand a repair mechanism aimed at maintaining a targeted high level of system reliability. If an eavesdropper observes a node that is added to the system to replace a failed node, it will have access to all the data downloaded during repair, which can potentially compromise the entire information in the system.We are interested in determining the secrecy capacity of distributed storage systems under repair dynamics, i.e., the maximum amount of data that can be securely stored and made available to a legitimate user without revealing any information to any eavesdropper. We derive a general upper bound on the secrecy capacity and show that this bound is tight for the bandwidth-limited regime which is of importance in scenarios such as peer-to-peer distributed storage systems. We also provide a simple explicit code construction that achieves the capacity for this regime.
  @cite_12: The capacity of heterogeneous distributed storage systems under repair dynamics is studied. Examples of these systems include peer-to-peer storage clouds, wireless, and Internet caching systems. Nodes in a heterogeneous system can have different storage capacities and different repair bandwidths. Lower and upper bounds on the system capacity are given. These bounds depend on either the average resources per node, or on a detailed knowledge of the node characteristics. Moreover, the case in which nodes may be compromised by an adversary (passive or active) is addressed and bounds on the secure capacity of the system are derived. One implication of these new results is that symmetric repair maximizes the capacity of a homogeneous system, which justifies the model widely used in the literature.
summary: The secrecy capacity for a network-coded cloud storage system was investigated in @cite_10 @cite_16 , where the secrecy capacity is defined as the maximum amount of data that can be securely stored under the perfect secrecy condition. The perfect secrecy condition ensure the eavesdropper cannot obtain any information of source data. The secrecy capacity for nodes with different storage capacities was derived in @cite_12 . The coding scheme that can achieve the storage upper bound of secrecy capacity was proposed in @cite_23 . The maximum data size being stored under the perfect secrecy condition for any number of eavesdropped nodes was determined in @cite_0 . The authors of @cite_21 considered how to achieve the information-theoretical secrecy when an eavesdropper can access some data in the storage nodes.