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.
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.
@cite_21 @cite_0 @cite_23 @cite_16 @cite_10 @cite_12
2964275527 2096296858 2076572416 1970080388 2762198510
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. In this paper, we revisit the problem of characterizing the secrecy capacity of minimum storage regenerating (MSR) codes under the passive @math -eavesdropper model, where the eavesdropper has access to data stored on @math nodes and the repair data for an additional @math nodes. We study it from the information-theoretic perspective. First, some general properties of MSR codes as well as a simple and generally applicable upper bound on secrecy capacity are given. Second, a new concept of stable MSR codes is introduced, where the stable property is shown to be closely linked with secrecy capacity. Finally, a comprehensive and explicit result on secrecy capacity in the linear MSR scenario is present, which generalizes all related works in the literature and also predicts certain results for some unexplored linear MSR codes. 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. 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. With the advent of quantum key distribution (QKD) systems, perfect (i.e., information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model that corresponds to such a setting is the wire tap channel introduced by Wyner in 1975. In this correspondence, we study fundamental limits and coding methods for wire tap channels. We provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity. For the special case of a noiseless main channel and binary erasure channel, we consider encoder and decoder design for codes achieving secrecy on the wiretap channel; we show that it is possible to construct linear-time decodable secrecy codes based on low-density parity-check (LDPC) codes that achieve secrecy. We derive single-letter characterizations of (strong) secrecy capacities for models with an arbitrary number of terminals, each of which observes a distinct component of a discrete memoryless multiple source, with unrestricted and interactive public communication permitted between the terminals. A subset of these terminals can serve as helpers for the remaining terminals in generating secrecy. According to the extent of an eavesdropper's knowledge, three kinds of secrecy capacity are considered: secret key (SK), private key (PK), and wiretap secret key (WSK) capacity. The characterizations of the SK and PK capacities highlight the innate connections between secrecy generation and multiterminal source coding without secrecy requirements. A general upper bound for WSK capacity is derived which is tight in the case when the eavesdropper can wiretap noisy versions of the components of the underlying multiple source, provided randomization is permitted at the terminals. These secrecy capacities are seen to be achievable with noninteractive communication between the terminals. The achievability results are also shown to be universal. This paper studies the secrecy capacity of unicast communication in a wireless erasure network setting in the presence of a wire-tapper. From an information-theoretic setting of perfect secrecy, both upper bounds and achievable secrecy rates are presented. Secrecy capacity is determined in closed form for a class of broadcast constrained erasure networks. This paper investigates the effect of eavesdroppers on network connectivity, using a wiretap model and percolation theory. The wiretap model captures the effect of eavesdroppers on link security. A link exists between two nodes only if the secrecy capacity of that link is positive. Network connectivity is defined in a percolation sense, i.e., connectivity exists if an infinite connected component exists in the corresponding secrecy graph. We consider uncertainty in location of eavesdroppers, which is modeled directly at the network level as correlated failures in the secrecy graph. Our approach attempts to bridge the gap between physical layer security under uncertain channel state information and network level connectivity under secrecy constraints. For square and triangular lattice secrecy graphs, we obtain bounds on the percolation threshold, which is the critical value of the probability of occurrence of an eavesdropper, above which network connectivity does not exist. For Poisson secrecy graphs, degree distribution and mean value of upper and lower bounds on node degree are obtained. Further, inner and outer bounds on the achievable region for network connectivity are obtained. Both analytic and simulation results show that uncertainty in location of eavesdroppers has a dramatic effect on network connectivity in a secrecy graph. We consider a fading wiretap channel model where the transmitter has only statistical channel state information, and the legitimate receiver and eavesdropper have perfect channel state information. We propose a sequence of non-random lattice codes which achieve strong secrecy and semantic security over ergodic fading channels. The construction is almost universal in the sense that it achieves the same constant gap to secrecy capacity over Gaussian and ergodic fading models. Achieving information-theoretic security using explicit coding scheme in which unlimited computational power for eavesdropper is assumed, is one of the main topics is security consideration. It is shown that polar codes are capacity achieving codes and have a low complexity in encoding and decoding. It has been proven that polar codes reach to secrecy capacity in the binary-input wiretap channels in symmetric settings for which the wiretapper's channel is degraded with respect to the main channel. The first task of this paper is to propose a coding scheme to achieve secrecy capacity in asymmetric nonbinary-input channels while keeping reliability and security conditions satisfied. Our assumption is that the wiretap channel is stochastically degraded with respect to the main channel and message distribution is unspecified. The main idea is to send information set over good channels for Bob and bad channels for Eve and send random symbols for channels that are good for both. In this scheme the frozen vector is defined over all possible choices using polar codes ensemble concept. We proved that there exists a frozen vector for which the coding scheme satisfies reliability and security conditions. It is further shown that uniform distribution of the message is the necessary condition for achieving secrecy capacity. We investigate the secrecy capacity of an ergodic fading wiretap channel when the main and eavesdropper channels are correlated. Assuming that the transmitter knows the full channel state information (CSI) (i.e., the channel gains from the transmitter to the legitimate receiver and eavesdropper), we quantify the loss of the secrecy capacity due to the correlation and investigate the asymptotic behavior of the secrecy capacity in the high signal-to-noise ratio (SNR) regime. While the ergodic capacity of fading channels grows logarithmically with SNR in general, we have found that the secrecy capacity converges to an upper-bound (a closed-form expression is derived) that will be shown to be a function of two channel parameters; the correlation coefficient and the ratio of the main to eavesdropper channel gains. From this, we are able to see how the two channel parameters affect the secrecy capacity and conclude that the excessively large signal power does not help to improve the secrecy capacity and the loss due to the correlation could be significant especially when the ratio of the main to eavesdropper channel gains is low. We consider the communication scenario where a source-destination pair wishes to keep the information secret from a relay node despite wanting to enlist its help. For this scenario, an interesting question is whether the relay node should be deployed at all. That is, whether cooperation with an untrusted relay node can ever be beneficial. We first provide an achievable secrecy rate for the general untrusted relay channel, and proceed to investigate this question for two types of relay networks with orthogonal components. For the first model, there is an orthogonal link from the source to the relay. For the second model, there is an orthogonal link from the relay to the destination. For the first model, we find the equivocation capacity region and show that answer is negative. In contrast, for the second model, we find that the answer is positive. Specifically, we show, by means of the achievable secrecy rate based on compress-and-forward, that by asking the untrusted relay node to relay information, we can achieve a higher secrecy rate than just treating the relay as an eavesdropper. For a special class of the second model, where the relay is not interfering itself, we derive an upper bound for the secrecy rate using an argument whose net effect is to separate the eavesdropper from the relay. The merit of the new upper bound is demonstrated on two channels that belong to this special class. The Gaussian case of the second model mentioned above benefits from this approach in that the new upper bound improves the previously known bounds. For the Cover-Kim deterministic relay channel, the new upper bound finds the secrecy capacity when the source-destination link is not worse than the source-relay link, by matching with achievable rate we present. The secrecy capacity is developed for a class of relay channels with orthogonal components and a passive eavesdropper node. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper can overhear either one or both of the orthogonal channels. Inner and outer bounds on the secrecy capacity are developed for both the discrete memoryless and the Gaussian channel models. For the discrete memoryless case, the secrecy capacity is shown to be achieved by a partial decode-and-forward (PDF) scheme when the eavesdropper can overhear only one of the two orthogonal channels. Two new outer bounds are presented for the Gaussian model using recent capacity results for a Gaussian multi-antenna channel with a multi-antenna eavesdropper. The outer bounds are shown to be tight for two sub-classes of channels. The first sub-class is one in which the source and relay are clustered and the eavesdropper overhears on only one of the two channels for which the PDF strategy is optimal. The second is a sub-class in which the source does not transmit to the relay for which a noise-forwarding strategy is optimal. We investigate the effect of certain active attacks on the secrecy capacity of wiretap channels by considering arbitrarily varying wiretap channels. We establish a lower bound for the secrecy capacity with randomized coding of a class of such channels and an upper bound for that of all such channels. We show that if the arbitrarily varying wiretap channel possesses a bad “averaged” state, namely one in which the legitimate receiver is degraded with respect to the eavesdropper, then secure communication is not possible. We propose a new scheme of wiretap lattice coding that achieves semantic security and strong secrecy over the Gaussian wiretap channel. The key tool in our security proof is the flatness factor, which characterizes the convergence of the conditional output distributions corresponding to different messages and leads to an upper bound on the information leakage. We not only introduce the notion of secrecy-good lattices, but also propose the flatness factor as a design criterion of such lattices. Both the modulo-lattice Gaussian channel and genuine Gaussian channel are considered. In the latter case, we propose a novel secrecy coding scheme based on the discrete Gaussian distribution over a lattice, which achieves the secrecy capacity to within a half nat under mild conditions. No a priori distribution of the message is assumed, and no dither is used in our proposed schemes. This paper aims to go beyond resilience into the study of security and local-repairability for distributed storage systems (DSSs). Security and local-repairability are both important as features of an efficient storage system, and this paper aims to understand the trade-offs between resilience, security, and local-repairability in these systems. In particular, this paper first investigates security in the presence of colluding eavesdroppers, where eavesdroppers are assumed to work together in decoding the stored information. Second, this paper focuses on coding schemes that enable optimal local repairs. It further brings these two concepts together to develop locally repairable coding schemes for DSS that are secure against eavesdroppers. The main results of this paper include: 1) an improved bound on the secrecy capacity for minimum storage regenerating codes; 2) secure coding schemes that achieve the bound for some special cases; 3) a new bound on minimum distance for locally repairable codes; 4) code construction for locally repairable codes that attain the minimum distance bound; and 5) repair-bandwidth-efficient locally repairable codes with and without security constraints. Suppose that Alice wishes to send messages to Bob through a communication channel C1, but her transmissions also reach an eavesdropper Eve through another channel C2. This is the wiretap channel model introduced by Wyner in 1975. The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and securely. Reliability is measured in terms of Bob's probability of error in recovering the message, while security is measured in terms of the mutual information between the message and Eve's observations. Wyner showed that the situation is characterized by a single constant Cs, called the secrecy capacity, which has the following meaning: for all e >; 0, there exist coding schemes of rate R ≥ Cs-e that asymptotically achieve the reliability and security objectives. However, his proof of this result is based upon a random-coding argument. To date, despite consider able research effort, the only case where we know how to construct coding schemes that achieve secrecy capacity is when Eve's channel C2 is an erasure channel, or a combinatorial variation thereof. Polar codes were recently invented by Arikan; they approach the capacity of symmetric binary-input discrete memoryless channels with low encoding and decoding complexity. In this paper, we use polar codes to construct a coding scheme that achieves the secrecy capacity for a wide range of wiretap channels. Our construction works for any instantiation of the wiretap channel model, as long as both C1 and C2 are symmetric and binary-input, and C2 is degraded with respect to C1. Moreover, we show how to modify our construction in order to provide strong security, in the sense defined by Maurer, while still operating at a rate that approaches the secrecy capacity. In this case, we cannot guarantee that the reliability condition will also be satisfied unless the main channel C1 is noiseless, although we believe it can be always satisfied in practice. Due to the broadcast nature of the wireless medium, wireless communication is susceptible to adversarial eavesdropping. This paper describes how eavesdropping can potentially be defeated by exploiting the superposition nature of the wireless medium. A Gaussian wire-tap channel with a helping interferer (WTC-HI) is considered in which a transmitter sends confidential messages to its intended receiver in the presence of a passive eavesdropper and with the help of an interferer. The interferer, which does not know the confidential message assists the confidential message transmission by sending a signal that is independent of the transmitted message. An achievable secrecy rate and a Sato-type upper bound on the secrecy capacity are given for the Gaussian WTC-HI. Through numerical analysis, it is found that the upper bound is close to the achievable secrecy rate when the interference is weak for symmetric interference channels, and under more general conditions for asymmetric Gaussian interference channels. In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feed-forward and feedback signals share the same noisy channel in the present model. Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting. More specifically, the discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that the judicious use of feedback increases the secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. In the half-duplex scheme, a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source. Finally, this scheme is extended to the continuous real valued modulo-Lambda channel where it is shown that the secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper. The problem of when all terminals must talk to achieve the secrecy capacity in the multiterminal source model is investigated. Two conditions under which respectively a given terminal does not need to and must talk to achieve the secrecy capacity are characterized. The cases when all terminals must talk to achieve secrecy capacity are shown to be many more than those conjectured in [1] for systems with four or more terminals. There is a gap between the above two conditions, in which whether a given terminal need to talk is not clear. A conjecture is further made in order to narrow down the gap.