A passive adversary can eavesdrop stored content or downloaded content of some storage nodes, in order to learn illegally about the file stored across a distributed storage system (DSS). Previous work in the literature focuses on code constructions that trade storage capacity for perfect security. In other words, by decreasing the amount of original data that it can store, the system can guarantee that the adversary, which eavesdrops up to a certain number of storage nodes, obtains no information (in Shannon's sense) about the original data. In this work we introduce the concept of block security for DSS and investigate minimum bandwidth regenerating (MBR) codes that are block secure against adversaries of varied eavesdropping strengths. Such MBR codes guarantee that no information about any group of original data units up to a certain size is revealed, without sacrificing the storage capacity of the system. The size of such secure groups varies according to the number of nodes that the adversary can eavesdrop. We show that code constructions based on Cauchy matrices provide block security. The opposite conclusion is drawn for codes based on Vandermonde matrices.
Hereafter we follow the standard notation in the regenerating code literature (see ). In their pioneering work, Dimakis @cite_25 established that the maximum file size to be stored in a DSS @math must satisfy the following inequality A construction of optimal regenerating codes with exact repair at the MBR point for all @math was proposed by Rashmi @cite_22 . When the stored contents of some @math nodes are observed by an adversary Eve, Pawar @cite_9 @cite_27 showed that the maximum file size to be stored satisfies provided that Eve gains (in Shannon's sense) about the file. This type of security is often referred to as or in the literature. The parameter @math is called the . The authors @cite_9 @cite_27 also provided an optimal code construction, based on complete graphs, for the case @math that attains the bound ). We later argue that an extension of their construction based on regular graphs @cite_15 also produces optimal perfectly secure codes for all @math with @math even (see Remark ). Under the same adversary model, Shah @cite_7 constructed optimal codes that attain the bound ) for all @math . The authors used product-matrix codes in their construction.
@cite_22 @cite_7 @cite_9 @cite_27 @cite_15 @cite_25
2063554152 2156663229 2118925326 2949150884 2951800112
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. We address the problem of securing distributed storage systems against adversarial node attacks. An important aspect of these systems is node failures over time, necessitating, thus, a repair mechanism in order to maintain a desired high system reliability. In such dynamic settings, an important security problem is to safeguard the system from a malicious adversary who may come at different time instances during the lifetime of the storage system to corrupt the data stored on some nodes. We provide upper bounds on the maximum amount of information that can be stored safely on the system in the presence of the adversary. For an important operating regime, which we call the bandwidth-limited regime, we show that our upper bounds are tight and provide explicit linear code constructions. Moreover, we provide a way to shortlist the malicious nodes and expurgate the system. We address the problem of securing distributed storage systems against eavesdropping and adversarial attacks. An important aspect of these systems is node failures over time, necessitating, thus, a repair mechanism in order to maintain a desired high system reliability. In such dynamic settings, an important security problem is to safeguard the system from an intruder who may come at different time instances during the lifetime of the storage system to observe and possibly alter the data stored on some nodes. In this scenario, we give upper bounds on the maximum amount of information that can be stored safely on the system. For an important operating regime of the distributed storage system, which we call the bandwidth-limited regime, we show that our upper bounds are tight and provide explicit code constructions. Moreover, we provide a way to short list the malicious nodes and expurgate the system. We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the concatenation of two components: an outer MDS code followed by an inner repetition code. We refer to the inner code as a Fractional Repetition code since it consists of splitting the data of each node into several packets and storing multiple replicas of each on different nodes in the system. Our model for repair is table-based, and thus, differs from the random access model adopted in the literature. We present constructions of Fractional Repetition codes based on regular graphs and Steiner systems for a large set of system parameters. The resulting codes are guaranteed to achieve the storage capacity for random access repair. The considered model motivates a new definition of capacity for distributed storage systems, that we call Fractional Repetition capacity. We provide upper bounds on this capacity while a precise expression remains an open problem. Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing data using an erasure code, in fragments spread across nodes, requires less redundancy than simple replication for the same level of reliability. However, since fragments must be periodically replaced as nodes fail, a key question is how to generate encoded fragments in a distributed way while transferring as little data as possible across the network. For an erasure coded system, a common practice to repair from a node failure is for a new node to download subsets of data stored at a number of surviving nodes, reconstruct a lost coded block using the downloaded data, and store it at the new node. We show that this procedure is sub-optimal. We introduce the notion of regenerating codes, which allow a new node to download of the stored data from the surviving nodes. We show that regenerating codes can significantly reduce the repair bandwidth. Further, we show that there is a fundamental tradeoff between storage and repair bandwidth which we theoretically characterize using flow arguments on an appropriately constructed graph. By invoking constructive results in network coding, we introduce regenerating codes that can achieve any point in this optimal tradeoff.