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.
Another research area of network coding is to prevent data being eavesdropped during transmission. The information-theoretical security problem for an untrusted channel was first discussed in @cite_9 . A network coding system was built to prove that a wiretapper cannot obtain any information from the transmitted message @cite_22 . A weaker type of security issue was investigated in @cite_6 , where a node can decode packets only after receiving sufficient linear independent encoded data. The construction of a secure linear network code for a wiretap network was presented in @cite_3 .
@cite_9 @cite_3 @cite_22 @cite_6
2006947308 2136395129 68293075
In the paradigm of network coding, the nodes in a network are allowed to encode the information received from the input links. With network coding, the full capacity of the network can be utilized. In this paper, we propose a model, call the wiretap network, that incorporates information security with network coding. In this model, a collection of subsets of the channels in the network is given, and a wiretapper is allowed to access any one (but not more than one) of these subsets without being able to obtain any information about the message transmitted. Our model includes secret sharing in classical cryptography as a special case. We present a construction of secure linear network codes that can be used provided a certain graph-theoretic condition is satisfied. We also prove the necessity of this condition for the special case that the wiretapper may choose to access any subset of channels of a fixed size. The optimality of our code construction is established for this special case. Finally, we extend our results to the scenario when the wiretapper is allowed to obtain a controlled amount of information about the message. We consider the problem of securing a multicast network against a wiretapper that can eavesdrop on the packets on a limited number of network edges of its choice. We assume that the network employs network coding to simultaneously deliver the packets available at the source to all the destinations. We show that this problem can be looked at as a network generalization of the wiretap channel of type II introduced in a seminal paper by Ozarow and Wyner. In particular, we show that the transmitted information can be secured by using the Ozarow-Wyner approach of coset coding at the source on top of the existing network code. This way, we quickly and transparently recover some of the results available in the literature on secure network coding for wiretap networks. Moreover, we use this framework to derive new bounds on the code alphabet size that are independent of the network size, and provide algorithms for explicit construction of secure network codes. We also analyze the amount of information that can be leaked to the wiretapper as a function of the number of wiretapped edges. Recent work on network coding renders a new view on multicasting in a network. In the paradigm of network coding, the nodes in a network are allowed to encode the information received from the input links. The usual function of switching at a node is a special case of network coding. The advantage of network coding is that the full capacity of the network can be utilized. In this paper, we propose a new model which incorporates network coding and information security. Specifically, a collection of subsets of links is given, and a wiretapper is allowed to access any one (but not more than one) of these subsets without being able to obtain any information about the message transmitted. Our model includes secret sharing as a special case. We present a construction of secure linear network codes provided a certain graph-theoretic sufficient condition is satisfied. In this work we consider the problem of secure data transmission on an acyclic multicast network. A new information theoretic model for security is proposed that defines the system as secure if an eavesdropper is unable to get any “meaningful” information about the source. The “wiretap” network model by Cai and Yeung in which no information of the source is made available to the eavesdropper is a special case in the new model. We consider the case when the number of independent messages available to the eavesdropper is less than the multicast capacity of the network. We show that under the new security requirements communication is possible at the multicast capacity. A linear transformation is provided for networks with a given linear code to make the system secure. The transformation needs to be done only at the source and the operations at the intermediate nodes remain unchanged. We also show that if random coding scheme is used the probability of the system being secure can be made arbitrarily close to one by coding over a large enough field. In the literature, there exist analytical expressions for the probability of a receiver decoding a transmitted source message that has been encoded using random linear network coding. In this letter, we look into the probability that the receiver will decode at least a fraction of the source message, and present an exact solution to this problem for both non-systematic and systematic network coding. Based on the derived expressions, we investigate the potential of these two implementations of network coding for information-theoretic secure communication and progressive recovery of data. 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. The problem of securing a network coding communication system against an eavesdropper is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the adversary can eavesdrop on μ arbitrarily chosen links. The objective is to provide reliable communication to all receivers, while guaranteeing that the source information remains information-theoretically secure from the adversary. A coding scheme is proposed that can achieve the maximum possible rate of n - μ packets. The scheme, which is based on rank-metric codes, has the distinctive property of being universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying linear network code. The only requirement of the scheme is that the packet length be at least n, which is shown to be strictly necessary for universal communication at the maximum rate. A further scenario is considered where the adversary is allowed not only to eavesdrop but also to inject up to t erroneous packets into the network, and the network may suffer from a rank deficiency of at most ρ. In this case, the proposed scheme can be extended to achieve the rate of n - ρ - 2t - μ packets. This rate is shown to be optimal under the assumption of zero-error communication. The classical wiretap channel models secure communication in the presence of a nonlegitimate wiretapper who has to be kept ignorant. Traditionally, the wiretapper is passive in the sense that he only tries to eavesdrop the communication using his received channel output. In this paper, more powerful active wiretappers are studied. In addition to eavesdropping, these wiretappers are able to influence the communication conditions of all users by controlling the corresponding channel states. Since legitimate transmitters and receivers do not know the actual channel realization or the wiretapper's strategy of influencing the channel states, they are confronted with arbitrarily varying channel (AVC) conditions. The corresponding secure communication scenario is, therefore, given by the arbitrarily varying wiretap channel (AVWC). In the context of AVCs, common randomness (CR) has been shown to be an important resource for establishing reliable communication, in particular, if the AVC is symmetrizable. But availability of CR also affects the strategy space of an active wiretapper as he may or may not exploit the common randomness for selecting the channel states. Several secrecy capacity results are derived for the AVWC. In particular, the CR-assisted secrecy capacity of the AVWC with an active wiretapper exploiting CR is established and analyzed in detail. Finally, it is demonstrated for active wiretappers how two orthogonal AVWCs, each useless for transmission of secure messages, can be super-activated to a useful channel allowing for secure communication at nonzero secrecy rates. To the best of our knowledge, this is not possible for passive wiretappers and, further, provides the first example of such super-activation, which has been expected to appear only in the area of quantum communication. Such knowledge is particularly important as it provides valuable insights for the design and the medium access control of future wireless communication systems. Secrecy issues of free-space optical links realizing information theoretically secure communications and high transmission rates are discussed. We numerically study secrecy communication rates of optical wiretap channel based on on–off keying (OOK) modulation under typical conditions met in satellite-ground links. It is shown that, under reasonable degraded conditions on a wiretapper, information theoretically secure communications should be possible in a much wider distance range than a range limit of quantum key distribution, enabling secure optical links between geostationary Earth orbit satellites and ground stations with currently available technologies. We also provide the upper bounds on the decoding error probability and the leaked information to estimate a necessary code length for given required levels of performances. This result ensures that a reasonable length of wiretap channel code for our proposed scheme must exist. We focus on secure data exchange among a group of wireless clients. The clients exchange data by broadcasting linear combinations of packets over a lossless channel. The data exchange is performed in the presence of an eavesdropper who has access to the channel and can obtain all transmitted data. Our goal is to develop a weakly secure coding scheme that prevents the eavesdropper from being able to decode any of the original packets held by the clients. We present a randomized algorithm based on Generalized Reed-Solomon (GRS) codes. The algorithm has two key advantages over the previous solutions: it operates over a small (polynomial-size) finite field and provides a way to verify that constructed code is feasible. In contrast, the previous approaches require exponential field size and do not provide an efficient (polynomial-time) algorithm to verify the secrecy properties of the constructed code. We formulate an algebraic-geometric conjecture that implies the correctness of our algorithm and prove its validity for special cases. Our simulation results indicate that the algorithm is efficient in practical settings. In this tutorial paper, we focus on the basic theory of linear secure network coding. Our goal is to present fundamental results and provide preliminary knowledge for anyone interested in the area. We first present a model for secure network coding and then a necessary and sufficient condition for a linear network code to be secure. Optimal methods to construct linear secure network codes are also provided. For further investigation of the secure properties of linear network codes, we illuminate different secure criteria and requirements, with a few alternative models. Opportunistic relaying has the potential to achieve full diversity gain, while random linear network coding (RLNC) can reduce latency and energy consumption. In recent years, there has been a growing interest in the integration of both schemes into wireless networks in order to reap their benefits, while considering security concerns. This paper considers a multi-relay network, where relay nodes employ RLNC to encode confidential data and transmit coded packets to a destination in the presence of an eavesdropper. Four relay selection protocols are studied covering a range of network capabilities, such as the availability of the eavesdropper’s channel state information or the possibility to pair the selected relay with a node that intentionally generates interference. For each case, expressions for the probability that a coded packet will not be recovered by a receiver, which can be either the destination or the eavesdropper, are derived. Based on those expressions, a framework is developed that characterizes the probability of the eavesdropper intercepting a sufficient number of coded packets and partially or fully recovering the confidential data. Simulation results confirm the validity and accuracy of the theoretical framework and unveil the security-reliability trade-offs attained by each RLNC-enabled relay selection protocol. A coding scheme for the Gaussian wiretap channel based on low-density parity-check (LDPC) codes is presented. The messages are transmitted over punctured bits to hide data from eavesdroppers. It is shown by means of density evolution that the BER of an eavesdropper, who operates below the code's SNR threshold and has the ability to use a bitwise MAP decoder, increases to 0.5 within a few dB. It is shown how asymptotically optimized LDPC codes can be designed with differential evolution where the goal is to achieve high reliability between friendly parties and security against a passive eavesdropper while keeping the security gap as small as possible. The proposed coding scheme is also efficiently encodable in almost linear time. 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. A (layered) broadcast approach is studied for fading wiretap channels. The basic idea is to employ superposition coding to encode information into a number of layers and use stochastic encoding for each layer to keep the corresponding information secret from an eavesdropper. The legitimate receiver successively decodes information one layer after another by canceling the interference caused by the layers that the receiver has already decoded. The advantage of this approach is that the transmitter does not need to know the channel states to the legitimate receiver and the eavesdropper, but can still securely transmit certain layers of information to the legitimate receiver. The layers that can be securely transmitted are determined by the channel states to the legitimate receiver and the eavesdropper. The Gaussian wiretap channel with fixed channel gains is first studied to illustrate the idea of the broadcast approach. Three cases of block fading wiretap channels with a stringent delay constraint are then studied, in which either the legitimate receiver's channel, the eavesdropper's channel, or both channels are fading. For each case, the secrecy rate that can be achieved by using the broadcast approach is obtained, and the optimal power allocation over the layers (or the conditions on the optimal power allocation) is also derived. 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. Recent research has shown that network coding can be used in content distribution systems to improve the speed of downloads and the robustness of the systems. However, such systems are very vulnerable to attacks by malicious nodes, and we need to have a signature scheme that allows nodes to check the validity of a packet without decoding. In this paper, we propose such a signature scheme for network coding. Our scheme makes use of the linearity property of the packets in a coded system, and allows nodes to check the integrity of the packets received easily. We show that the proposed scheme is secure, and its overhead is negligible for large files. Recently, physical layer security in the optical layer has gained significant traction. Security treats in optical networks generally impact the reliability of optical transmission. Linear Network Coding (LNC) can protect from both the security treats in form of eavesdropping and faulty transmission due to jamming. LNC can mix original data to become incomprehensible for an attacker and also extend original data by coding redundancy, thus protecting a data from errors injected via jamming attacks. In this paper, we study the effectiveness of LNC to balance reliable transmission and security in optical networks. To this end, we combine the coding process with data flow parallelization of the source and propose and compare optimal and randomized path selection methods for parallel transmission. The study shows that a combination of data parallelization, LNC and randomization of path selection increases security and reliability of the transmission. We analyze the so-called catastrophic security treat of the network and show that in case of conventional transmission scheme and in absence of LNC, an attacker could eavesdrop or disrupt a whole secret data by accessing only one edge in a network. Network coding substantially increases network throughput. But since it involves mixing of information inside the network, a single corrupted packet generated by a malicious node can end up contaminating all the information reaching a destination, preventing decoding. This paper introduces distributed polynomial-time rate-optimal network codes that work in the presence of Byzantine nodes. We present algorithms that target adversaries with different attacking capabilities. When the adversary can eavesdrop on all links and jam links, our first algorithm achieves a rate of , where is the network capacity. In contrast, when the adversary has limited eavesdropping capabilities, we provide algorithms that achieve the higher rate of . Our algorithms attain the optimal rate given the strength of the adversary. They are information-theoretically secure. They operate in a distributed manner, assume no knowledge of the topology, and can be designed and implemented in polynomial time. Furthermore, only the source and destination need to be modified; nonmalicious nodes inside the network are oblivious to the presence of adversaries and implement a classical distributed network code. Finally, our algorithms work over wired and wireless networks. We consider the problem of using a multicast network code to transmit information securely in the presence of a “wire-tap” adversary who can eavesdrop on a bounded number of network edges. Cai & Yeung (ISIT, 2002) gave a method to alter any given linear network code into a new code that is secure. However, their construction is in general inefficient, and requires a very large field size; in many cases this is much greater than the field size required by standard network code construction algorithms to achieve the min-cut capacity (without a security guarantee). In this paper we generalize and simplify the method of Cai & Yeung, and show that the problem of making a linear network code secure is equivalent to the problem of finding a linear code with certain generalized distance properties. We show that if we give up a small amount of overall capacity, then a random code achieves these properties using a much smaller field size — in some cases a field of constant size suffices — than the construction of Cai & Yeung. We add further support to this approach by showing that if we are not willing to give up any capacity, then a large field size may sometimes be required to achieve security.