We study security in partial repair in wireless caching networks where parts of the stored packets in the caching nodes are susceptible to be erased. Let us denote a caching node that has lost parts of its stored packets as a sick caching node and a caching node that has not lost any packet as a healthy caching node. In partial repair, a set of caching nodes (among sick and healthy caching nodes) broadcast information to other sick caching nodes to recover the erased packets. The broadcast information from a caching node is assumed to be received without any error by all other caching nodes. All the sick caching nodes then are able to recover their erased packets, while using the broadcast information and the nonerased packets in their storage as side information. In this setting, if an eavesdropper overhears the broadcast channels, it might obtain some information about the stored file. We thus study secure partial repair in the senses of information-theoretically strong and weak security. In both senses, we investigate the secrecy caching capacity, namely, the maximum amount of information which can be stored in the caching network such that there is no leakage of information during a partial repair process. We then deduce the strong and weak secrecy caching capacities, and also derive the sufficient finite field sizes for achieving the capacities. Finally, we propose optimal secure codes for exact partial repair, in which the recovered packets are exactly the same as erased packets.
We focus on the problem of secure distributed storage over multiple untrusted clouds or networks. Our main contribution is a low complexity scheme that relies on erasure coding techniques for achieving prescribed levels of confidentiality and reliability. Using matrices that have no singular square submatrices, we subject the original data to a linear transformation. The resulting coded symbols are then stored in different networks. This scheme allows users with access to a threshold number of networks to reconstruct perfectly the original data, while ensuring that eavesdroppers with access to any number of networks smaller than this threshold are unable to decode any of the original symbols. This holds even if the attackers are able to guess some of the missing symbols. We further quantify the achievable level of security, and analyze the complexity of the proposed scheme. We investigate the repair problem for wireless caching networks when parts of stored packets in cashing nodes are lost. We first develop theoretical lower bounds on the number of necessary transmission packets over error-free broadcast channels for repair. Then we discuss the impact of the distribution of the lost packets among caching nodes. Finally, we study the construction of repair codes and propose the optimal exact repair for some special scenarios. 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. When there are multiple storage node failures in distributed storage system, regenerating them individually is suboptimal as far as repair bandwidth minimization is concerned. The tradeoff between storage and repair bandwidth is derived in the case where data exchange among the newcomers is enabled. The tradeoff curve with cooperation is strictly better than the one without cooperation. An explicit construction of cooperative regenerating code is given. 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. 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. Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures at the nodes or links, during the data-reconstruction and node-repair operations. We provide explicit regenerating codes that are resilient to errors and erasures, and show that these codes are optimal with respect to storage and bandwidth requirements. As a special case, we also establish the capacity of a class of distributed storage systems in the presence of malicious adversaries. While our code constructions are based on previously constructed Product-Matrix codes, we also provide necessary and sufficient conditions for introducing resilience in any regenerating code. This paper studies the recovery from multiple node failures in distributed storage systems. We design a mutually cooperative recovery (MCR) mechanism for multiple node failures. Via a cut-based analysis of the information flow graph, we obtain a lower bound of maintenance bandwidth based on MCR. For MCR, we also propose a transmission scheme and design a linear network coding scheme based on (?, ?) strong-MDS code, which is a generalization of (?, ?) MDS code. We prove that the maintenance bandwidth based on our transmission and coding schemes matches the lower bound, so the lower bound is tight and the transmission scheme and coding scheme for MCR are optimal. We also give numerical comparisons of MCR with other redundancy recovery mechanisms in storage cost and maintenance bandwidth to show the advantage of MCR. 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. 