An online backup system should be quick and reliable in both saving and restoring users' data. To do so in a peer-to-peer implementation, data transfer scheduling and the amount of redundancy must be chosen wisely. We formalize the problem of exchanging multiple pieces of data with intermittently available peers, and we show that random scheduling completes transfers nearly optimally in terms of duration as long as the system is sufficiently large. Moreover, we propose an adaptive redundancy scheme that improves performance and decreases resource usage while keeping the risks of data loss low. Extensive simulations show that our techniques are effective in a realistic trace-driven scenario with heterogeneous bandwidth.
Data maintenance is cheap in our scenario, where it is performed by a data owner with a local copy. When maintenance is delegated to nodes that do not have a local copy of the backup objects, various coding schemes can be used @cite_21 @cite_0 to limit the amount of required data transit. For these settings, cryptographic protocols @cite_15 @cite_18 have been designed to verify the authenticity of stored data.
@cite_0 @cite_15 @cite_21 @cite_18
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Distributed storage systems need to store data redundantly in order to provide some fault-tolerance and guarantee system reliability. Different coding techniques have been proposed to provide the required redundancy more efficiently than traditional replication schemes. However, compared to replication, coding techniques are less efficient for repairing lost redundancy, as they require retrieval of larger amounts of data from larger subsets of storage nodes. To mitigate these problems, several recent works have presented locally repairable codes designed to minimize the repair traffic and the number of nodes involved per repair. Unfortunately, existing methods often lead to codes where there is only one subset of nodes able to repair a piece of lost data, limiting the local repairability to the availability of the nodes in this subset. In this paper, we present a new family of locally repairable codes that allows different trade-offs between the number of contacted nodes per repair, and the number of different subsets of nodes that enable this repair. We show that slightly increasing the number of contacted nodes per repair allows to have repair alternatives, which in turn increases the probability of being able to perform efficient repairs. Finally, we present pg-BLRC, an explicit construction of locally repairable codes with multiple repair alternatives, constructed from partial geometries, in particular from Generalized Quadrangles. We show how these codes can achieve practical lengths and high rates, while requiring a small number of nodes per repair, and providing multiple repair alternatives. One main challenge in the design of distributed storage codes is the Exact Repair Problem: if a node storing encoded information fails, to maintain the same level of reliability, we need to exactly regenerate what was lost in a new node. A major open problem in this area has been the design of codes that i) admit exact and low cost repair of nodes and ii) have arbitrarily high data rates. In this paper, we are interested in the metric of repair locality, which corresponds to the the number of disk accesses required during a node repair. Under this metric we characterize an information theoretic trade-off that binds together locality, code distance, and storage cost per node. We introduce Locally repairable codes (LRCs) which are shown to achieve this tradeoff. The achievability proof uses a “locality aware” flow graph gadget which leads to a randomized code construction. We then present the first explicit construction of LRCs that can achieve arbitrarily high data-rates. 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 single node failure is for a new node to reconstruct the whole encoded data object to generate just one encoded block. We show that this procedure is sub-optimal. We introduce the notion of regenerating codes, which allow a new node to communicate functions 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. 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. Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular. Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular. This paper describes a cryptographic protocol for securing self-organized data storage through periodic verifications. The proposed verification protocol, which goes beyond simple integrity checks and proves data conservation, is deterministic, efficient, and scalable. The security of this scheme relies both on the ECDLP intractability assumption and on the difficulty of finding the order of some specific elliptic curve over Zn. The protocol also makes it possible to personalize replicas and to delegate verification without revealing any secret information. This paper describes a decentralized consistency protocol for survivable storage that exploits local data versioning within each storage-node. Such versioning enables the protocol to efficiently provide linearizability and wait-freedom of read and write operations to erasure-coded data in asynchronous environments with Byzantine failures of clients and servers. By exploiting versioning storage-nodes, the protocol shifts most work to clients and allows highly optimistic operation: reads occur in a single round-trip unless clients observe concurrency or write failures. Measurements of a storage system prototype using this protocol show that it scales well with the number of failures tolerated, and its performance compares favorably with an efficient implementation of Byzantine-tolerant state machine replication. With the increasing adoption of cloud computing for data storage, assuring data service reliability, in terms of data correctness and availability, has been outstanding. While redundancy can be added into the data for reliability, the problem becomes challenging in the “pay-as-you-use” cloud paradigm where we always want to efficiently resolve it for both corruption detection and data repair. Prior distributed storage systems based on erasure codes or network coding techniques have either high decoding computational cost for data users, or too much burden of data repair and being online for data owners. In this paper, we design a secure cloud storage service which addresses the reliability issue with near-optimal overall performance. By allowing a third party to perform the public integrity verification, data owners are significantly released from the onerous work of periodically checking data integrity. To completely free the data owner from the burden of being online after data outsourcing, this paper proposes an exact repair solution so that no metadata needs to be generated on the fly for repaired data. The performance analysis and experimental results show that our designed service has comparable storage and communication cost, but much less computational cost during data retrieval than erasure codes-based storage solutions. It introduces less storage cost, much faster data retrieval, and comparable communication cost comparing to network coding-based distributed storage systems. Distributed storage systems can store data with erasure coding to maintain data availability with low storage redundancy. One class of erasure coding is based on regenerating codes , which provably minimize the amount of data transferred for failure repair and realize the optimal tradeoff between the storage redundancy and the amount of traffic transferred for repair. Typical regenerating codes often require surviving storage nodes to encode their stored data for repair. In this paper, we study a framework called proxy-assisted regeneration, which offloads the repair process to a centralized proxy. We extend the previous applied work on proxy-assisted regeneration by providing theoretical validation. Specifically, we study a special class of regenerating codes called proxy-assisted minimum storage regenerating (PMSR) codes, which enable uncoded repair without the need of encoding in surviving nodes, while preserving the minimum storage redundancy and minimum amount of traffic transferred for repair. We formally prove the existence of PMSR codes for two configurations: 1) repairing single-node failures under double fault tolerance and 2) repairing double-node failures under triple fault tolerance. We also provide a semi-deterministic PMSR code construction for repairing single-node failures under double fault tolerance. Network codes designed specifically for distributed storage systems have the potential to provide dramatically higher storage efficiency for the same availability. One main challenge in the design of such codes is the exact repair problem: if a node storing encoded information fails, in order to maintain the same level of reliability we need to create encoded information at a new node. One of the main open problems in this emerging area has been the design of simple coding schemes that allow exact and low cost repair of failed nodes and have high data rates. In particular, all prior known explicit constructions have data rates bounded by 1 2. In this paper we introduce the first family of distributed storage codes that have simple look-up repair and can achieve arbitrarily high rates. Our constructions are very simple to implement and perform exact repair by simple XORing of packets. We experimentally evaluate the proposed codes in a realistic cloud storage simulator and show significant benefits in both performance and reliability compared to replication and standard Reed-Solomon codes. Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of off-the-shelf erasure codes is their high-repair cost during single node failure events. A major open problem in this area has been the design of codes that: 1) are repair efficient and 2) achieve arbitrarily high data rates. In this paper, we explore the repair metric of locality, which corresponds to the number of disk accesses required during a single node repair. Under this metric, we characterize an information theoretic tradeoff that binds together the locality, code distance, and storage capacity of each node. We show the existence of optimal locally repairable codes (LRCs) that achieve this tradeoff. The achievability proof uses a locality aware flow-graph gadget, which leads to a randomized code construction. Finally, we present an optimal and explicit LRC that achieves arbitrarily high data rates. Our locality optimal construction is based on simple combinations of Reed-Solomon blocks. In this paper, we consider the security of exact-repair regenerating codes operating at the minimum-storage-regenerating (MSR) point. The security requirement (introduced in Shah et. al.) is that no information about the stored data file must be leaked in the presence of an eavesdropper who has access to the contents of l 1 nodes as well as all the repair traffic entering a second disjoint set of l 2 nodes. We derive an upper bound on the size of a data file that can be securely stored that holds whenever l 2 ≤ d - k + 1. This upper bound proves the optimality of the product-matrix-based construction of secure MSR regenerating codes by Shah et. al. Distributed storage systems are mainly justified due to the limited amount of storage capacity and improving the reliability through distributing data over multiple storage nodes. On the other hand, it may happen the data is stored in unreliable nodes, while it is desirable the end user to have a reliable access to the stored data. So, in an event that a node is damaged, to prevent the system reliability to regress, it is necessary to regenerate a new node with the same amount of stored data as the damaged node to retain the number of storage nodes, thereby having the previous reliability. This requires the new node to connect to some of existing nodes and downloads the required information, thereby occupying some bandwidth, called the repair bandwidth. On the other hand, it is more likely the cost of downloading varies across different nodes. This paper aims at investigating the theoretical cost-bandwidth tradeoff, and more importantly, it is demonstrated that any point on this curve can be achieved through the use of the so called generalized regenerating codes which is an enhancement of the regenerating codes introduced by [1]. Remote backup copies of databases are often maintained to ensure availability of data even in the presence of extensive failures, for which local replication mechanisms may be inadequate. We present two versions of an epoch algorithm for maintaining a consistent remote backup copy of a database. The algorithms ensure scalability, which makes them suitable for very large databases. The correctness and the performance of the algorithms are discussed, and an additional application for distributed group commit is given. Mobile devices with geo-positioning capabilities (e.g., GPS) enable users to access information that is relevant to their present location. Users are interested in querying about points of interest (POI) in their physical proximity, such as restaurants, cafes, ongoing events, etc. Entities specialized in various areas of interest (e.g., certain niche directions in arts, entertainment, travel) gather large amounts of geo-tagged data that appeal to subscribed users. Such data may be sensitive due to their contents. Furthermore, keeping such information up-to-date and relevant to the users is not an easy task, so the owners of such data sets will make the data accessible only to paying customers. Users send their current location as the query parameter, and wish to receive as result the nearest POIs, i.e., nearest-neighbors (NNs). But typical data owners do not have the technical means to support processing queries on a large scale, so they outsource data storage and querying to a cloud service provider. Many such cloud providers exist who offer powerful storage and computational infrastructures at low cost. However, cloud providers are not fully trusted, and typically behave in an honest-but-curious fashion. Specifically, they follow the protocol to answer queries correctly, but they also collect the locations of the POIs and the subscribers for other purposes. Leakage of POI locations can lead to privacy breaches as well as financial losses to the data owners, for whom the POI data set is an important source of revenue. Disclosure of user locations leads to privacy violations and may deter subscribers from using the service altogether. In this paper, we propose a family of techniques that allow processing of NN queries in an untrusted outsourced environment, while at the same time protecting both the POI and querying users’ positions. Our techniques rely on mutable order preserving encoding (mOPE), the only secure order-preserving encryption method known to-date. We also provide performance optimizations to decrease the computational cost inherent to processing on encrypted data, and we consider the case of incrementally updating data sets. We present an extensive performance evaluation of our techniques to illustrate their viability in practice. Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously. We consider the setting of data storage across n nodes in a distributed manner. A data collector (DC) should be able to reconstruct the entire data by connecting to any k out of the n nodes and downloading all the data stored in them. When a node fails, it has to be regenerated back using the existing nodes. In a recent paper, have obtained an information theoretic lower bound for the repair bandwidth. Also, there has been additional interest in storing data in systematic form as no post processing is required when DC connects to k systematic nodes. Because of their preferred status there is a need to regenerate back any systematic node quickly and exactly. Replacement of a failed node by an exact replica is termed Exact Regeneration.In this paper, we consider the problem of minimizing the repair bandwidth for exact regeneration of the systematic nodes. The file to be stored is of size B and each node can store alpha = B k units of data. A failed systematic node is regenerated by downloading beta units of data each from d existing nodes. We give a lower bound for the repair bandwidth for exact regeneration of the systematic nodes which matches with the bound given by For d >= 2k-1 we give an explicit code construction which minimizes the repair bandwidth when the existing k-1 systematic nodes participate in the regeneration. We show the existence and construction of codes that achieve the bound for d >= 2k-3. Here we also establish the necessity of interference alignment. We prove that the bound is not achievable for d = 2k-1. Geo-replicated storage systems are at the core of current Internet services. The designers of the replication protocols used by these systems must choose between either supporting low-latency, eventually-consistent operations, or ensuring strong consistency to ease application correctness. We propose an alternative consistency model, Explicit Consistency, that strengthens eventual consistency with a guarantee to preserve specific invariants defined by the applications. Given these application-specific invariants, a system that supports Explicit Consistency identifies which operations would be unsafe under concurrent execution, and allows programmers to select either violation-avoidance or invariant-repair techniques. We show how to achieve the former, while allowing operations to complete locally in the common case, by relying on a reservation system that moves coordination off the critical path of operation execution. The latter, in turn, allows operations to execute without restriction, and restore invariants by applying a repair operation to the database state. We present the design and evaluation of Indigo, a middleware that provides Explicit Consistency on top of a causally-consistent data store. Indigo guarantees strong application invariants while providing similar latency to an eventually-consistent system in the common case. In distributed storage systems, storage nodes intermittently go offline for numerous reasons. On coming back online, nodes need to update their contents to reflect any modifications to the data in the interim. In this paper, we consider a setting where no information regarding modified data needs to be logged in the system. In such a setting, a ‘stale’ node needs to update its contents by downloading data from already updated nodes, while neither the stale node nor the updated nodes have any knowledge as to which data symbols are modified and what their value is. We investigate the fundamental limits on the amount of communication necessary for such an oblivious update process. We first present a generic lower bound on the amount of communication that is necessary under any storage code with a linear encoding (while allowing non-linear update protocols). This lower bound is derived under a set of extremely weak conditions, giving all updated nodes access to the entire modified data and the stale node access to the entire stale data as side information. We then present codes and update algorithms that are optimal in that they meet this lower bound. Next, we present a lower bound for an important subclass of codes, that of linear Maximum-Distance-Separable (MDS) codes. We then present an MDS code construction and an associated update algorithm that meets this lower bound. These results thus establish the capacity of oblivious updates in terms of the communication requirements under these settings.