Biblio

A new framework is presented in this paper for proving coding theorems for linear codes, where the systematic bits and the corresponding parity-check bits play different roles. Precisely, the noisy systematic bits are used to limit the list size of typical codewords, while the noisy parity-check bits are used to select from the list the maximum likelihood codeword. This new framework for linear codes allows that the systematic bits and the parity-check bits are transmitted in different ways and over different channels. In particular, this new framework unifies the source coding theorems and the channel coding theorems. With this framework, we prove that the Bernoulli generator matrix codes (BGMCs) are capacity-achieving over binary-input output symmetric (BIOS) channels and also entropy-achieving for Bernoulli sources.

This paper studies the secure decentralized Pliable Index CODing (PICOD) problem, where the security constraint forbids users to decode more than one message while the decentralized setting imposes that there is no central transmitter in the system, and thus transmissions occur only among users. A converse bound from the Authors' previous work showed a factor of three difference in optimal code-length between the centralized and the decentralized versions of the problem, under the constraint of linear encoding. This paper first lists all linearly infeasible cases, that is, problems where no linear code can simultaneously achieve both correctness/decodability and security. Then, it proposes linear coding schemes for the remaining cases and shows that their code-length is to within an additive constant gap from the converse bound.

Inter-substation Generic Object Oriented Substation Events (GOOSE) communications that are used for critical protection functions have several cyber-security vulnerabilities. GOOSE messages are directly mapped to the Layer 2 Ethernet without network and transport layer headers that provide data encapsulation. The high-status-number attack is a malicious attack on GOOSE messages that allows hackers to completely take over intelligent electronic devices (IEDs) subscribing to GOOSE communications. The status-number parameter of GOOSE messages, stNum is tampered with in these attacks. Given the strict delivery time requirement of 3 ms for GOOSE messaging, it is infeasible to encrypt the GOOSE payload. This work proposes to secure the sensitive stNum parameter of the GOOSE payload using systematically encoded polynomial codes. Exploiting linear codes allows for the security features to be encoded in linear time, in contrast to complex hashing algorithms. At the subscribing IED, the security feature is used to verify that the stNum parameter has not been tampered with during transmission in the insecure medium. The decoding and verification using syndrome computation at the subscriber IED is also accomplished in linear time.

With the explosive development of big data, it is necessary to sort the data according to their importance or priorities. The sources with different importance levels can be modeled by the multilevel diversity coding systems (MDCS). Another trend in future communication networks, say 5G wireless networks and Internet of Things, is that users may obtain their data from all available sources, even from devices belonging to other users. Then, the privacy of data becomes a crucial issue. In a recent work by Li et al., the secure asymmetric MDCS (S-AMDCS) with wiretap channels was investigated, where the wiretapped messages do not leak any information about the sources (i.e. perfect secrecy). It was shown that superposition (source-separate coding) is not optimal for the general S-AMDCS and the exact full secure rate region was proved for a class of S-AMDCS. In addition, a bound on the key size of the secure rate region was provided as well. As a further step on the SAMDCS problem, this paper mainly focuses on the key size characterization. Specifically, the constraints on the key size of superposition secure rate region are proved and a counterexample is found to show that the bound on the key size of the exact secure rate region provided by Li et al. is not tight. In contrast, tight necessary and sufficient constraints on the secrecy key size of the counterexample, which is the four-encoder S-AMDCS, are proved.

Today's blockchain designs suffer from a trilemma claiming that no blockchain system can simultaneously achieve decentralization, security, and performance scalability. For current blockchain systems, as more nodes join the network, the efficiency of the system (computation, communication, and storage) stays constant at best. A leading idea for enabling blockchains to scale efficiency is the notion of sharding: different subsets of nodes handle different portions of the blockchain, thereby reducing the load for each individual node. However, existing sharding proposals achieve efficiency scaling by compromising on trust - corrupting the nodes in a given shard will lead to the permanent loss of the corresponding portion of data. In this paper, we settle the trilemma by demonstrating a new protocol for coded storage and computation in blockchains. In particular, we propose PolyShard: "polynomially coded sharding" scheme that achieves information-theoretic upper bounds on the efficiency of the storage, system throughput, as well as on trust, thus enabling a truly scalable system.

It is notably challenging to design an efficient and secure signature scheme based on error-correcting codes. An approach to build such signature schemes is to derive it from an identification protocol through the Fiat-Shamir transform. All such protocols based on codes must be run several rounds, since each run of the protocol allows a cheating probability of either 2/3 or 1/2. The resulting signature size is proportional to the number of rounds, thus making the 1/2 cheating probability version more attractive. We present a signature scheme based on double circulant codes in the rank metric, derived from an identification protocol with cheating probability of 2/3. We reduced this probability to almost 1/2 to obtain the smallest signature among code-based signature schemes based on the Fiat-Shamir paradigm, around 22 KBytes for 128 bit security level. Furthermore, among all code-based signature schemes, our proposal has the lowest value of signature plus public key size, and the smallest secret and public key sizes. We provide a security proof in the Random Oracle Model, implementation performances, and a comparison with the parameters of similar signature schemes.

{1 We present a construction for exact-repair regenerating codes with an information-theoretic secrecy guarantee against an eavesdropper with access to the content of (up to) ℓ nodes. The proposed construction works for the entire range of per-node storage and repair bandwidth for any distributed storage system with parameters (n

In a linear code, a code symbol with (r, δ)-locality can be repaired by accessing at most r other code symbols in case of at most δ - 1 erasures. A q-ary (n, k, r, δ) locally repairable codes (LRC) in which every code symbol has (r, δ)-locality is said to be optimal if it achieves the Singleton-like bound derived by Prakash et al.. In this paper, we study the classification of optimal ternary (n, k, r, δ)-LRCs (δ \textbackslashtextgreater 2). Firstly, we propose an upper bound on the minimum distance of optimal q-ary LRCs in terms of the field size. Then, we completely determine all the 6 classes of possible parameters with which optimal ternary (n, k, r, δ)-LRCs exist. Moreover, explicit constructions of all these 6 classes of optimal ternary LRCs are proposed in the paper.

In recent years, Edge Computing (EC) has attracted increasing attention for its advantages in handling latencysensitive and compute-intensive applications. It is becoming a widespread solution to solve the last mile problem of cloud computing. However, in actual EC deployments, data confidentiality becomes an unignorable issue because edge devices may be untrusted. In this paper, a secure and efficient edge computing scheme based on linear coding is proposed. Generally, linear coding can be utilized to achieve data confidentiality by encoding random blocks with original data blocks before they are distributed to unreliable edge nodes. However, the addition of a large amount of irrelevant random blocks also brings great communication overhead and high decoding complexities. In this paper, we focus on the design of secure coded edge computing using orthogonal vector to protect the information theoretic security of the data matrix stored on edge nodes and the input matrix uploaded by the user device, while to further reduce the communication overhead and decoding complexities. In recent years, Edge Computing (EC) has attracted increasing attention for its advantages in handling latencysensitive and compute-intensive applications. It is becoming a widespread solution to solve the last mile problem of cloud computing. However, in actual EC deployments, data confidentiality becomes an unignorable issue because edge devices may be untrusted. In this paper, a secure and efficient edge computing scheme based on linear coding is proposed. Generally, linear coding can be utilized to achieve data confidentiality by encoding random blocks with original data blocks before they are distributed to unreliable edge nodes. However, the addition of a large amount of irrelevant random blocks also brings great communication overhead and high decoding complexities. In this paper, we focus on the design of secure coded edge computing using orthogonal vector to protect the information theoretic security of the data matrix stored on edge nodes and the input matrix uploaded by the user device, while to further reduce the communication overhead and decoding complexities.

The applications in the critical infrastructure systems pose simultaneous resilience and performance requirements to the underlying computer network. To meet such requirements, the networks that use the store-and-forward paradigm poses stringent conditions on the redundancy in the network topology and results in problems that becoming computationally challenging to solve at scale. However, with the advent of programmable data-planes, it is now possible to use linear network coding (NC) at the intermediate network nodes to meet resilience requirements of the applications. To that end, we propose an architecture that realizes linear NC in programmable networks by decomposing the linear NC functions into the atomic coding primitives. We designed and implemented the primitives using the features offered by the P4 ecosystem. Using an empirical evaluation, we show that the theoretical gains promised by linear network coding can be realized with a per-packet processing cost.

Multishot network coding is considered in a worst-case adversarial setting in which an omniscient adversary with unbounded computational resources may inject erroneous packets in up to t links, erase up to ρ packets, and wire-tap up to μ links, all throughout ℓ shots of a (random) linearly-coded network. Assuming no knowledge of the underlying linear network code (in particular, the network topology and underlying linear code may change with time), a coding scheme achieving zero-error communication and perfect secrecy is obtained based on linearized Reed-Solomon codes. The scheme achieves the maximum possible secret message size of ℓn'-2t-ρ-μ packets, where n' is the number of outgoing links at the source, for any packet length m ≥ n' (largest possible range), with only the restriction that ℓ\textbackslashtextless;q (size of the base field). By lifting this construction, coding schemes for non-coherent communication are obtained with information rates close to optimal for practical instances. A Welch-Berlekamp sum-rank decoding algorithm for linearized Reed-Solomon codes is provided, having quadratic complexity in the total length n = ℓn', and which can be adapted to handle not only errors, but also erasures, wire-tap observations and non-coherent communication.

Edge caching has received much attention as a promising technique to overcome the stringent latency and data hungry challenges in the future generation wireless networks. Meanwhile, full-duplex (FD) transmission can potentially double the spectral efficiency by allowing a node to receive and transmit simultaneously. In this paper, we study a cache-aided FD system via delivery time analysis and optimization. In the considered system, an edge node (EN) operates in FD mode and serves users via wireless channels. Two optimization problems are formulated to minimize the largest delivery time based on the two popular linear beamforming zero-forcing and minimum mean square error designs. Since the formulated problems are non-convex due to the self-interference at the EN, we propose two iterative optimization algorithms based on the inner approximation method. The convergence of the proposed iterative algorithms is analytically guaranteed. Finally, the impacts of caching and the advantages of the FD system over the half-duplex (HD) counterpart are demonstrated via numerical results.

In the paradigm of network coding, information-theoretic security is considered in the presence of wiretappers, who can access one arbitrary edge subset up to a certain size, referred to as the security level. Secure network coding is applied to prevent the leakage of the source information to the wiretappers. In this paper, we consider the problem of secure network coding for flexible pairs of information rate and security level with any fixed dimension (equal to the sum of rate and security level). We present a novel approach for designing a secure linear network code (SLNC) such that the same SLNC can be applied for all the rate and security-level pairs with the fixed dimension. We further develop a polynomial-time algorithm for efficient implementation and prove that there is no penalty on the required field size for the existence of SLNCs in terms of the best known lower bound by Guang and Yeung. Finally, by applying our approach as a crucial building block, we can construct a family of SLNCs that not only can be applied to all possible pairs of rate and security level but also share a common local encoding kernel at each intermediate node in the network.

This paper is concerned with three ensembles of systematic low density generator matrix (LDGM) codes, all of which were provably capacity-achieving in terms of bit error rate (BER). This, however, does not necessarily imply that they achieve the capacity in terms of frame error rate (FER), as seen from a counterexample constructed in this paper. We then show that the first and second ensembles are capacity-achieving under list decoding over binary-input output symmetric (BIOS) memoryless channels. We point out that, in principle, the equivocation due to list decoding can be removed with negligible rate loss by the use of the concatenated codes. Simulation results show that the considered convolutional (spatially-coupled) LDGM code is capacity-approaching with an iterative belief propagation decoding algorithm.

Nowadays public-key cryptography is based on number theory problems, such as computing the discrete logarithm on an elliptic curve or factoring big integers. Even though these problems are considered difficult to solve with the help of a classical computer, they can be solved in polynomial time on a quantum computer. Which is why the research community proposed alternative solutions that are quantum-resistant. The process of finding adequate post-quantum cryptographic schemes has moved to the next level, right after NIST's announcement for post-quantum standardization. One of the oldest quantum-resistant proposition goes back to McEliece in 1978, who proposed a public-key cryptosystem based on coding theory. It benefits of really efficient algorithms as well as a strong mathematical background. Nonetheless, its security has been challenged many times and several variants were cryptanalyzed. However, some versions remain unbroken. In this paper, we propose to give some background on coding theory in order to present some of the main flawless in the protocols. We analyze the existing side-channel attacks and give some recommendations on how to securely implement the most suitable variants. We also detail some structural attacks and potential drawbacks for new variants.

How to construct good linear codes is an important problem in coding theory. This paper considers the construction of linear codes from functions with two variables, presents a class of two-weight and three-weight ternary linear codes and employs the Gauss sums and exponential sums to determine the parameters and weight distribution of these codes. Linear codes with few weights have applications in consumer electronics, communication and date storage systems. Linear codes with two weights have applications in strongly regular graphs and linear codes with three weights can be applied in association schemes.

Today's major concern is not only maximizing the information rate through linear network coding scheme which is intelligent combination of information symbols at sending nodes but also secured transmission of information. Though cryptographic measure of security (computational security) gives secure transmission of information, it results system complexity and consequent reduction in efficiency of the communication system. This problem leads to alternative way of optimally secure and maximized information transmission. The alternative solution is secure network coding which is information theoretic approach. Depending up on applications, different security measures are needed during the transmission of information over wiretapped network with potential attack by the adversaries. In this research work, mathematical model for different security constraints with upper and lower boundaries were studied depending up on the randomness added to the source message and hence the security constraints on linear network code for randomized source messages depends both on randomness added and number of random source symbols. If the source generates large number random symbols, lesser number of random keys can give higher security to the information but information theoretic security bounds remain same. Hence maximizing randomness to the source is equivalent to adding security level.

We consider the problem of communicating information over a network secretly and reliably in the presence of a hidden adversary who can eavesdrop and inject malicious errors. We provide polynomial-time distributed network codes that are information-theoretically rate-optimal for this scenario, improving on the rates achievable in prior work by Ngai Our main contribution shows that as long as the sum of the number of links the adversary can jam (denoted by ZO) and the number of links he can eavesdrop on (denoted by ZI) is less than the network capacity (denoted by C) (i.e., ), our codes can communicate (with vanishingly small error probability) a single bit correctly and without leaking any information to the adversary. We then use this scheme as a module to design codes that allow communication at the source rate of C- ZO when there are no security requirements, and codes that allow communication at the source rate of C- ZO- ZI while keeping the communicated message provably secret from the adversary. Interior nodes are oblivious to the presence of adversaries and perform random linear network coding; only the source and destination need to be tweaked. We also prove that the rate-region obtained is information-theoretically optimal. In proving our results, we correct an error in prior work by a subset of the authors in this paper.

We consider the problem of communicating information over a network secretly and reliably in the presence of a hidden adversary who can eavesdrop and inject malicious errors. We provide polynomial-time distributed network codes that are information-theoretically rate-optimal for this scenario, improving on the rates achievable in prior work by Ngai Our main contribution shows that as long as the sum of the number of links the adversary can jam (denoted by ZO) and the number of links he can eavesdrop on (denoted by ZI) is less than the network capacity (denoted by C) (i.e., ), our codes can communicate (with vanishingly small error probability) a single bit correctly and without leaking any information to the adversary. We then use this scheme as a module to design codes that allow communication at the source rate of C- ZO when there are no security requirements, and codes that allow communication at the source rate of C- ZO- ZI while keeping the communicated message provably secret from the adversary. Interior nodes are oblivious to the presence of adversaries and perform random linear network coding; only the source and destination need to be tweaked. We also prove that the rate-region obtained is information-theoretically optimal. In proving our results, we correct an error in prior work by a subset of the authors in this paper.