Abstract Can a dealer share a secret without knowing the shareholders? We provide a positive answer to this question by introducing the concept of an attribute-based secret sharing (AB-SS) scheme.With AB-SS, a dealer can distribute a secret based on attributes rather than specific individuals or shareholders. Only authorized users whose attributes satisfy a given access structure can recover the secret. Furthermore, we introduce the concept of attribute-based publicly verifiable secret sharing (AB-PVSS). An AB-PVSS scheme allows external users to verify the correctness of all broadcast messages from the dealer and shareholders, similar to a traditional PVSS scheme. Additionally, AB-SS (or AB-PVSS) distinguishes itself from traditional SS (or PVSS) by enabling a dealer to generate shares according to an arbitrary monotone access structure.To build an AB-PVSS scheme, we first implement a decentralized ciphertext-policy attribute-based encryption (CP-ABE) scheme, though not a fully-fledged one.We then incorporate non-interactive zero-knowledge (NIZK) proofs to enable public verification of the CP-ABE ciphertext. Based on the CP-ABE and NIZK proofs, we construct an AB-PVSS primitive.Finally, we conduct security analysis and comprehensive experiments on the proposed CP-ABE and AB-PVSS schemes. The results demonstrate that both schemes exhibit plausible performance compared to related works.

Traditional email systems rely on centralized servers for message storage and routing, making them vulnerable to single points of failure and privacy breaches. While blockchain technology has emerged as a decentralized alternative for internet infrastructure, its application to email systems remains underexplored. This paper fills the gaps by proposing a blockchain-based mailing system that eliminates trusted intermediaries while enhancing privacy. Our approach integrates four key components: (1) the ECIES scheme to ensure end-to-end confidentiality of email content, (2) BIP-32-derived addresses to achieve sender anonymity, (3) stealth addresses to provide receiver k-anonymity, and (4) a broadcast encryption scheme to enable efficient broadcast messaging. Moreover, our design allows the sender to prove membership in the broadcast mailing while preserving anonymity. Further, the proposed system introduces an incentive mechanism that allows recipients to charge fees for incoming emails, effectively discouraging spam. We present a proof-of-concept implementation on the Ethereum blockchain and evaluate its on-chain performance in terms of gas consumption. Experimental results demonstrate the practicality and efficiency of the proposed system.

As Large Language Model (LLM) agents emerge as intelligent coordinators, they intensify the demand for secure sharing and forwarding of sensitive data in data-driven systems. Existing Attribute-Based Proxy Re-Encryption (ABPRE) offers fine-grained access control and secure data forwarding, but suffers from the key escrow problem and lacks efficient verifiability and fairness guarantees. In this paper, we propose the first Verifiable and Fair Registered ABPRE (VF-RABPRE) scheme to eliminate reliance on trusted authorities and support multi-hop re-encryption for flexible multi-agent data sharing. To ensure efficient verifiability and fairness, we combine a lightweight verifiable tag and a non-interactive zero-knowledge proof to detect misbehavior of the proxy and prevent false accusations. As a trade-off between security and overhead, we design a more secure fairness mechanism that does not reveal plaintext using zero-knowledge Succinct Non-interactive Arguments of Knowledge (zkSNARK). Additionally, we extend VF-RABPRE with dynamic user registration and outsourced decryption, supporting flexible registration and efficient decryption for data users. Finally, we formally prove the security of our scheme and implement a prototype to evaluate its performance. Experimental results demonstrate that VF-RABPRE outperforms state-of-the-art ABPRE schemes and achieves practical efficiency, making it well-suited for secure data sharing in scenarios empowered by LLM agents.

Proximity testing for linear codes is a fundamental problem in coding theory with critical applications in cryptographic protocols, blockchain, and distributed storage systems. This work addresses the proximity gaps for linear codes, a crucial aspect for efficiently verifying whether a batch of words is close to a given code. We present a general framework for deriving proximity gaps from the list-decodability properties of the underlying linear code. Our main result show that for any (p,L)-list-decodable codeC⊆ Fnqwith minimum relative distance ΔC>p, the probability that a random combination of a batch of t words containing a δ-far word (for δ ≤ 1 − √ 1 −p+ ε) remains δ-far fromCis bounded byO(tL2pn/q+t/εq). This result also establishes a form of (mutual) correlated agreement for linear codes, which can be used to strengthen soundness analyses in protocols that rely on proximity testing, thereby reducing query complexity and enabling practical instantiations over smaller finite fields. In particular, we apply our main result to randomly punctured Reed–Solomon codes and folded Reed–Solomon codes—both of which are known to achieve list-decodability up to capacity—and derive linear proximity gaps for these families of codes under the Johnson bound.

Compressed learning (CL), integrating compressed sensing (CS) and machine learning (ML), enables direct inference from few CS measurements. However, existing CL methods either heavily rely on pre-trained models built upon extremely large-scale datasets or perform only relatively simple tasks on small datasets, restricting their scalability in real-world multimedia scenarios. To address these limitations, we propose an efficient CL framework named HTMA-CL for practical multimedia acquisition and edge intelligent processing. HTMA-CL employs CNN-based learnable sampling to realize block-based CS for high-resolution images, significantly decreasing the transmission bandwidth and storage overhead. A hierarchical tokenization module together with a deep-narrow Transformer module progressively models local and global dependencies within the measurements, enabling accurate inference directly in the compressive domain. Various task heads are constructed for performing diverse multimedia analysis tasks such as image classification and semantic segmentation. Extensive experiments demonstrate that our HTMA-CL achieves state-of-the-art performance compared to other CL methods, and nearly comparable performance to the image domain methods at a CS ratio of 10%. Our method further verifies the strong robustness against external interference in the disturbance-prone IoT multimedia environments. The source code is publicly available at https://github.com/acrlife/HTMA-CL.git .

Achieving a fair exchange between two mutually distrusting parties presents significant obstacles. The involvement of trusted third parties is often essential to ensure fairness in such exchanges. In this paper, we propose a blockchain-driven optimistic fair exchange protocol based on publicly verifiable secret sharing (PVSS) and zero-knowledge succinct non-interactive arguments of knowledge (zkSNARKs). In our solution, arbiters, i.e., PVSS shareholders, serve as decentralized trusted third parties, registering on smart contracts with both autonomy and accountability. We assume a majority of arbiters are honest, ensuring that adversaries cannot successfully collude and that the fairness of the exchange protocol is upheld. In cases where both exchange parties are honest, the involvement of arbiters is unnecessary, making the fair exchange protocol optimistic. Additionally, we leverage zkSNARKs to generate non-interactive zero-knowledge (NIZK) proofs that ensure the correctness of the exchanged data. As a result, the exchange protocol is publicly verifiable without revealing any information about the exchanged data. In abnormal cases where arbiters are involved, a threshold number of them can fairly resolve the dispute between the seller and the buyer, and earn digital assets as a reward. In addition to fairness, optimism, and public verifiability, the proposed protocol also ensures completeness, termination, and privacy. Finally, we conduct experiments to illustrate the correctness and feasibility of the optimistic fair exchange protocol.

Watermarking photographs is a crucial tool for safeguarding copyrights and can serve as a more aesthetically pleasing alternative to QR codes. In recent years, watermarking methods based on deep learning have proved superior robustness against complex physical distortions than traditional watermarking methods. However, they have some limitations that render them less effective in practice. For instance, current solutions necessitate physical photographs to be rectangular for accurate localization, can’t handle physical bending or folding, and require the hidden area to be completely captured at a close distance and small angle. To overcome these challenges, we propose a novel deep watermarking framework dubbed Aparecium. Specifically, we preprocess secrets (i.e., watermarks) into a visible pattern and then embed it into the cover image invisibly, which is symmetrical to the final decoding-then-extracting process. To capture the watermarked region from complex physical scenarios, edge distortion is also introduced. Finally, we adopt a three-stage training strategy for training convergence. Extensive experiments demonstrate that Aparecium is not only robust against different digital distortions, but also can resist different physical distortions, such as screen-shooting and printing-shooting, even in severe cases including different shapes, curvature, folding, incompleteness, long distances, and big angles while maintaining high visual quality. Furthermore, some ablation studies are also conducted to verify our design.

With the widespread application of federated learning in sensitive domains such as healthcare and finance, preserving the privacy of participants’ local data while maintaining model performance has become a critical challenge. Existing secure aggregation schemes based on homomorphic encryption or pairwise masking still suffer from substantial computational and communication overhead. To address this problem, this paper presents RESA, an efficient secure aggregation protocol based on Ring Learning with Errors (RLWE) encryption. By replacing pairwise masking with the RLWE-based encryption scheme, gradients can be efficiently encrypted and decrypted. Furthermore, by combining Paillier homomorphic encryption with the homomorphic pseudorandom generator (HPRG) to aggregate all clients’ RLWE keys, our scheme effectively protects the privacy of honest clients. Also, the proposed protocol is resilient to client dropouts due to the application of secret sharing. The experimental results show that the proposed protocol achieves 5-10× speedup in the server-side computation, compared to Bell et al. (USENIX Security’23).

As a global virtual environment, the metaverse poses various challenges regarding data storage, sharing, interoperability, and privacy preservation. Typically, a trusted third party (TTP) is considered necessary in these scenarios. However, relying on a single TTP may introduce biases, compromise privacy, or lead to single-point-of-failure problem. To address these challenges and enable secure data exchange in the metaverse, we propose a system based on decentralized TTPs and the Ethereum blockchain. First, we use the threshold ElGamal cryptosystem to create the decentralized TTPs, employing verifiable secret sharing (VSS) to force owners to share data honestly. Second, we leverage the Ethereum blockchain to serve as the public communication channel, automatic verification machine, and smart contract engine. Third, we apply discrete logarithm equality (DLEQ) algorithms to generate non-interactive zero knowledge (NIZK) proofs when encrypted data is uploaded to the blockchain. Fourth, we present an incentive mechanism to benefit data owners and TTPs from data-sharing activities, as well as a penalty policy if malicious behavior is detected. Consequently, we construct a data exchange framework for the metaverse, in which all involved entities are accountable. Finally, we perform comprehensive experiments to demonstrate the feasibility and analyze the properties of the proposed system.

Data sharing is ubiquitous in the metaverse, which adopts blockchain as its foundation. Blockchain is employed because it enables data transparency, achieves tamper resistance, and supports smart contracts. However, securely sharing data based on blockchain necessitates further consideration. Ciphertext-policy attribute-based encryption (CP-ABE) is a promising primitive to provide confidentiality and fine-grained access control. Nonetheless, authority accountability and key abuse are critical issues that practical applications must address. Few studies have considered CP-ABE key confidentiality and authority accountability simultaneously. To our knowledge, we are the first to fill this gap by integrating non-interactive zero-knowledge (NIZK) proofs into CP-ABE keys and outsourcing the verification process to a smart contract. To meet the decentralization requirement, we incorporate a decentralized CP-ABE scheme into the proposed data sharing system. Additionally, we provide an implementation based on smart contract to determine whether an access control policy is satisfied by a set of CP-ABE keys. We also introduce an open incentive mechanism to encourage honest participation in data sharing. Hence, the key abuse issue is resolved through the NIZK proof and the incentive mechanism. We provide a theoretical analysis and conduct comprehensive experiments to demonstrate the feasibility and efficiency of the data sharing system. Based on the proposed accountable approach, we further illustrate an application in GameFi, where players can play to earn or contribute to an accountable DAO, fostering a thriving metaverse ecosystem.

The problem of designing explicit bent and plateaued functions has been researched for several decades. However, finding new bent functions outside the well-known completed Maiorana-McFarland class$\mathcal {M}^{\#}$is still a challenge. Plateaued functions have been characterized in many different ways, but there is no general and rigorous mathematical method to generate them directly, except for the ones in the spirit of the well-known Maiorana-McFarland constructions or those obtained through adaptations of the secondary constructions of bent functions. Jeong and Lee recently made significant advances regarding algorithms for constructing balanced plateaued functions with maximal algebraic degrees in [IEEE Trans. Inf. Theory, 70(2), 1408-1421, 2024]. Due to the gap between our significant interest in the notion of plateaued functions and the knowledge we have on it, our motivation is to bring further results on the constructions of plateaued functions that allow us to understand their structure better. This article creates a framework of new generic constructions of bent and plateaued functions by studying Boolean functions of the form$h(x)=f(x)+F(f_{1}(x),\ldots, f_{r}(x))$, where$f_{i}(x)=f(x)+f(x+\mu _{i})$for each$1\leq i\leq r$. We firstly prove that h and f have the same extended Walsh-Hadamard spectrum if$D_{\mu _{i}}D_{\mu _{j}}f=0$for any$1\leq i\lt j\leq r$. This result extends a previous construction of bent functions to any Boolean functions. The strength of such a result is that it allows us to obtain several plateaued functions of high algebraic degrees from known ones with low algebraic degrees, which was a significant and challenging problem raised in the literature. Such a result is a real challenge and breaks a deadlock since no mathematical method allows the general constructions of plateaued functions. We next give an extended affine equivalent form of the function h, which provides us with another compelling perspective to design new bent functions (including those which are outside$\mathcal {M}^{\#}$from certain known ones inside$\mathcal {M}^{\#}$) and plateaued functions. Finally, we present four generic constructions of bent functions outside$\mathcal {M}^{\#}$from generalized Maiorana-McFarland functions.

In this paper, we propose and studyr-minimal codes, a natural extension of minimal codes which have been extensively studied with respect to Hamming metric, rank metric and sum-rank metric. We first proposer-minimal codes in a general setting where the ambient space is a finite dimensional left module over a division ring and is supported on a lattice. We characterize minimal subcodes andr-minimal codes, derive a general singleton bound, and give existence results forr-minimal codes by using combinatorial arguments. We then considerr-minimal rank metric codes over a field extension E/F of degreem, where E can be infinite unless otherwise specified. We characterize these codes in terms of cuttingr-blocking sets, generalized rank weights of the codes and those of the dual codes, and classify codes whoser-dimensional subcodes have constant rank support weight. Next, with the help of the evasiveness property of cuttingr-blocking sets and some upper bounds for the dimensions of evasive subspaces, we derive several lower and upper bounds for the minimal length ofr-minimal codes. Furthermore, when E is finite, we establish a general upper bound which generalizes and improves the counterpart for minimal codes in the literature. As a corollary, we show that ifm= 3, then for anyk⩾ 2, the minimal length ofk-dimensional minimal codes is equal to 2k. To the best of our knowledge, whenm⩾ 3, there is no known explicit formula for the minimal length ofk-dimensional minimal codes for arbitrarykin the literature.

Abstract Fair exchange is a challenging problem for two mutually distrusting players. It is widely known that fair exchange is impossible without a trusted third party (TTP). However, relying on a single TTP can cause a single-point failure. An intuitive idea is to adopt multiple TTPs to distribute trust. This paper constructs a two-party optimistic fair exchange (OFE) protocol using decentralized ciphertext-policy attribute-based encryption (CP-ABE), achieving decentralized TTPs. This is achievable because decentralized CP-ABE ciphertext supports a nested access control policy. A nested access control policy fits perfectly in a fair exchange protocol which contains multiple roles (i.e. players and TTPs). Further, we apply non-interactive zero knowledge proofs to prove the well-formedness of ciphertexts, so as to enforce players to follow the protocol specification honestly. Consequently, we construct an OFE protocol in which each player’s operations are publicly verifiable without revealing secret information. Also, we obtain decentralized TTPs with optimism (i.e. the TTPs are involved only when arbitration is required), autonomy (i.e. the TTPs do not need to interact with each other), statelessness (i.e. the TTPs do not need to store data for the exchange protocol) and verifiability (i.e. the TTPs are publicly verifiable). Compared with previous work, our protocol assumes only a public communication channel and each party’s operations are publicly verifiable. Besides, it achieves a favorable $O(n)$ verification complexity in the normal case, where $n$ is the number of TTPs. Finally, we present a proof-of-concept implementation to demonstrate the feasibility.

Abstract Graph products have been extensively applied to model complex networks with striking properties observed in real-world complex systems. In this paper, we study the hitting times for random walks on a class of graphs generated iteratively by edge corona product. We first derive recursive solutions to the eigenvalues and eigenvectors of the normalized adjacency matrix associated with the graphs. Based on these results, we further obtain interesting quantities about hitting times of random walks, providing iterative formulas for two-node hitting time, as well as closed-form expressions for the Kemeny’s constant defined as a weighted average of hitting times over all node pairs, as well as the arithmetic mean of hitting times of all pairs of nodes.

Let$\mathbf {H}$be the Cartesian product of a family of left modules over a ring$S$, indexed by a finite set$\Omega $. We study the MacWilliams extension property (MEP) with respect to$(\mathbf {P},\omega)$-weight on$\mathbf {H}$, where$\mathbf {P}=(\Omega,\preccurlyeq _{\mathbf {P}})$is a poset and$\omega:\Omega \longrightarrow \mathbb {R}^{+}$is a weight function. We first give a characterization of the group of$(\mathbf {P},\omega)$-weight isometries of$\mathbf {H}$, which is then used to show that MEP implies the unique decomposition property (UDP) of$(\mathbf {P},\omega)$, which, for the case that$\omega $is identically 1, further implies that$\mathbf {P}$is hierarchical. When$\mathbf {P}$is hierarchical or$\omega $is identically 1, with some weak additional assumptions, we give necessary and sufficient conditions for$\mathbf {H}$to satisfy MEP with respect to$(\mathbf {P},\omega)$-weight in terms of MEP with respect to Hamming weight. With the help of these results, when$S$is a finite field, we compare MEP with various well studied coding-theoretic properties including the property of admitting MacWilliams identity (PAMI), reflexivity of partitions, UDP, transitivity of the group of isometries and whether$(\mathbf {P},\omega)$induces an association scheme; in particular, we show that MEP is always stronger than all the other properties.

Abstract It is well known that in many real networks, such as brain networks and scientific collaboration networks, there exist higher order nonpairwise relations among nodes, i.e. interactions between more than two nodes at a time. This simplicial structure can be described by simplicial complexes and has an important effect on topological and dynamical properties of networks involving such group interactions. In this paper, we study analytically resistance distances in iteratively growing networks with higher order interactions characterized by the simplicial structure that is controlled by a parameter $q$. We derive exact formulas for interesting quantities about resistance distances, including Kirchhoff index, additive degree-Kirchhoff index, multiplicative degree-Kirchhoff index, as well as average resistance distance, which have found applications in various areas elsewhere. We show that the average resistance distance tends to a $q$-dependent constant, indicating the impact of simplicial organization on the structural robustness measured by average resistance distance.

We prove the covering radius of the third-order Reed-Muller code$\mathrm {RM}(3,7)$is 20, which was previously known to be between 20 and 23 (inclusive). The covering radius of$\mathrm {RM}(3,7)$is the maximum third-order nonlinearity among all 7-variable Boolean functions. It was known that there exist 7-variable Boolean functions with third-order nonlinearity 20. We prove the third-order nonlinearity cannot achieve 21. According to the classification of the quotient space of$\mathrm {RM}(6,6)/\mathrm {RM}(3,6)$, we classify all 7-variable Boolean functions into 66 types. Firstly, we prove 62 types (among 66) cannot have third-order nonlinearity 21; Secondly, we prove that any function in the remaining 4 types can be transformed into a type (6, 10) function, if its third-order nonlinearity is 21; Finally, we transform type (6, 10) functions into a specific form, and prove the functions in that form cannot achieve the third-order nonlinearity 21 (with the assistance of computers). By the way, we prove that the affine transformation group over any finite field can be generated by two elements.

Recently, much progress has been made to construct minimal linear codes due to their preference in secret sharing schemes and secure two-party computation. In this paper, we put forward a new method to construct minimal linear codes by using vectorial Boolean functions. Firstly, we give a necessary and sufficient condition for a generic class of linear codes from vectorial Boolean functions to be minimal. Based on that, we derive some new three-weight minimal linear codes and determine their weight distributions. Secondly, by studying deeply the construction of linear codes in this paper, we find a necessary and sufficient condition of the linear codes to be minimal and to be violated the AB condition. As a result, we get three infinite families of minimal linear codes violating the AB condition. To the best of our knowledge, this is the first time that minimal liner codes are constructed from vectorial Boolean functions. Compared the parameters with other known ones, in general the minimal liner codes obtained in this paper have higher dimensions.

Let$\mathbf {H}$be the Cartesian product of a family of finite abelian groups. Via a polynomial approach, we give sufficient conditions for a partition of$\mathbf {H}$induced by weighted poset metric to be reflexive, which also become necessary for some special scenarios. Moreover, by examining the roots of the Krawtchouk polynomials, we give sufficient conditions for a partition of$\mathbf {H}$induced by combinatorial metric to be non-reflexive, and then give several examples of non-reflexive partitions. When$\mathbf {H}$is a vector space over a finite field$\mathbb {F}$, we consider the property of admitting MacWilliams identity (PAMI) and the MacWilliams extension property (MEP) for partitions of$\mathbf {H}$. More specifically, under some invariance assumptions, we show that two partitions of$\mathbf {H}$admit MacWilliams identity if and only if they are mutually dual and reflexive, and any partition of$\mathbf {H}$satisfying MEP is in fact an orbit partition induced by some subgroup of$\mathrm {Aut}\,_{\mathbb {F}}(\mathbf {H})$, which is necessarily reflexive. Furthermore, we show that the aforementioned non-reflexive partitions induced by combinatorial metric do not satisfy MEP, which further enables us to disprove a conjecture proposed by Pinheiro et al., (2019).

In this paper, we study sensing data collection of IoT devices in a sparse IoT-sensor network, using an energy-constrained Unmanned Aerial Vehicle (UAV), where the sensory data is stored in IoT devices while the IoT devices may or may not be within the transmission range of each other. We formulate two novel data collection problems to fully or partially collect data stored from IoT devices using the UAV, by finding a closed tour for the UAV that consists of hovering locations and the sojourn duration at each of the hovering locations such that the accumulative volume of data collected within the tour is maximized, subject to the energy capacity on the UAV, where the UAV consumes energy on both hovering for data collection and flying from one hovering location to another hovering location. To this end, we first propose a novel data collection framework that enables the UAV to collect sensory data from multiple IoT devices simultaneously if these IoT devices are within the coverage range of the UAV, through adopting the orthogonal frequency division multiple access (OFDMA) technique. We then formulate two data collection maximization problems to deal with full or partial data collection from IoT devices at each hovering location, and show that both defined problems are NP-hard. We instead devise approximation and heuristic algorithms for the problems. We finally evaluate the performance of the proposed algorithms through experimental simulations. Simulation results demonstrated that the proposed algorithms are promising.

Edge computing fundamentally changes the architecture in which applications are deployed and how resources are managed, especially in the 5G/6G era. Automated guided vehicles (AGV) are critical means of transportation in future society. We aim at investigating a privacy-preserving AGV collision-resistance paradigm leveraging edge computing. We define a model containing all potential collision occasions and propose a method to handle collisions using “virtual” traffic lights generated by edge servers. The proposed paradigm is AGV-centered, for AGVs ought not to care about where the nearby edge servers are in a broadcasting environment. In case of privacy leakage, we incorporate ciphertext-policy attribute-based encryption (CP-ABE) to protect AGV information. Besides, the use of CP-ABE leads to a location-based encryption (LBE) scheme, where AGV encrypts its running state information leveraging its current position rather than an edge server's public key. That is achievable due to the support of integer comparison in the CP-ABE access policy. To our knowledge, we are the first to implement an LBE scheme based on CP-ABE. Part of the paradigm has been deployed in a wharf yard in Shanghai. Throughout the article, we take a yard as an example and conduct concrete experiments to highlight the feasibility and efficiency.

Patient-centered healthcare data sharing and data usage consent are gaining popularity. Cross-enterprise document sharing (XDS) is the crucial system of sharing personalized healthcare data. Furthermore, dynamic consent is vital to the XDS system, because it respects people's autonomy and achieves recognition of data sovereignty. Because of its transparency, blockchain is a powerful system for managing storage and computing without a trusted third party. Besides, ciphertext-policy attribute-based encryption (CP-ABE) extends public-key encryption by implying access control policies in ciphertexts, making it suitable for protecting the privacy of individual healthcare data in versatile cases. Particularly, we use hospital name, "date" and "department" as attribute strings in the access control policies. Consequently, based on consortium blockchain and CP-ABE, we propose a patient-centered XDS and a dynamic consent framework. Compared with previous related literature, we make the proposed framework consistent with current practices and achieve favorable criteria, such as data confidentiality, data recoverability and time-aware ciphertext. Further, we conduct comprehensive experiments to show the feasibility and practicality.

For $R \triangleq Ma{t_m}({\mathbb{F}})$, the ring of all m × m matrices over the finite field ${\mathbb{F}}$ with $|{\mathbb{F}}| = q$, and the left R-module $A \triangleq Ma{t_{m,k}}({\mathbb{F}})$ with m + 1 ⩽ k, by deriving the minimal length of solutions of the related isometry equation, Dyshko has proved in [3], [4] that the minimal code length n for Annot satisfying the MacWilliams extension property (MEP) with respect to Hamming weight is equal to $\prod\nolimits_{i = 1}^m {\left( {{q^i} + 1} \right)}$. In this paper, using the Möbius functions, we derive the minimal length of nontrivial solutions of the isometry equation for a finite lattice. For the finite vector space ${\mathbf{H}} \triangleq \prod\nolimits_{i \in \Omega } {{{\mathbb{F}}^{{k_i}}}}$, a poset P = (Ω, ≼P) and a map ω: Ω → ℝ+give rise to the (P, ω)-weight on H, which has been proposed by Hyun, Kim and Park in [18]. For such a weight, we study the relations between the MEP and other properties including admitting MacWilliams identity, Fourier-reflexivity of involved partitions and the Unique Decomposition Property (UDP) defined for (P, ω). We give necessary and sufficient conditions for H to satisfy the MEP with the additional assumption that either P is hierarchical or ω is identically 1, i.e., (P, ω)-weight coincides with P-weight, which further allow us to partly answer a conjecture proposed by Machado and Firer in [22].

Let H be the cartesian product of a family of abelian groups indexed by a nonempty finite set Ω. A given poset P = (Ω, ≼P) and a map ω : Ω → ℝ+give rise to the (P, ω)-weight on H, which further leads to a partition $\mathcal{Q}\left( {{\text{H}},{\text{P}},\omega } \right)$ of H. For the case that H is finite, we give sufficient conditions for two codewords to belong to the same block of Λ, the dual partition of $\mathcal{Q}\left( {{\text{H}},{\text{P}},\omega } \right)$, and sufficient conditions for $\mathcal{Q}\left( {{\text{H}},{\text{P}},\omega } \right)$ to be Fourier-reflexive. By relating the involved partitions with certain polynomials, we show that such sufficient conditions are also necessary if P is hierarchical and ω is integer valued. With H further set to be a finite vector space over a finite field $\mathbb{F}$, from a partition perspective, we extend the property of "admitting MacWilliams identity" to arbitrary pairs of partitions of H, and prove that a pair of $\mathbb{F}$-invariant partitions (Λ, Γ) with |Λ| = |Γ| admits MacWilliams identity if and only if (Λ, Γ) is a pair of mutually dual Fourier-reflexive partitions. Such a result is applied to the partition $\mathcal{Q}\left( {{\text{H}},{\text{P}},\omega } \right)$. Finally, with H set to be a (possibly infinite) left module over a ring S, we show that each (P, ω)- weight isometry of H uniquely induces an order automorphism of P, which further leads to a group homomorphism from the group of (P, ω)-weight isometries to Aut (P), whose kernel consists of isometries preserving the P-support.

We aim at building a generic future-generation, secure communication framework on top of blockchain using signcryption. A publicly verifiable signcryption scheme not only ensures data confidentiality and authentication, but also enables messages to be verified or audited non-interactively. With blockchain as trustworthy computation and storage services, the proposed secure communication framework achieves tamper-resistance, non-repudiation, availability and public verification. Moreover, we consider both large-size data (e.g., file) and small-size data (e.g., cryptographic hash or key) transfer paradigms, where blockchain and signcryption schemes are seamlessly combined. In particular, IPFS is used as a hash oracle and decentralized storage platform in big data transfer.

Abstract The power-law behavior is ubiquitous in a majority of real-world networks, and it was shown to have a strong effect on various combinatorial, structural and dynamical properties of graphs. For example, it has been shown that in real-life power-law networks, both the matching number and the domination number are relatively smaller, compared with homogeneous graphs. In this paper, we study analytically several combinatorial problems for two power-law graphs with the same number of vertices, edges and the same power exponent. For both graphs, we determine exactly or recursively their matching number, independence number, domination number, the number of maximum matchings, the number of maximum independent sets and the number of minimum dominating sets. We show that power-law behavior itself cannot characterize the combinatorial properties of a heterogenous graph. Since the combinatorial properties studied here have found wide applications in different fields, such as structural controllability of complex networks, our work offers insight in the applications of these combinatorial problems in power-law graphs.

A striking discovery in the field of network science is that the majority of real networked systems have some universal structural properties. In general, they are simultaneously sparse, scale-free, small-world, and loopy. In this article, we investigate the second-order consensus of dynamic networks with such universal structures subject to white noise at vertices. We focus on the network coherenceHSOcharacterized in terms of the$\mathcal {H}_{2}$-norm of the vertex systems, which measures the mean deviation of vertex states from their average value. We first study numerically the coherence of some representative real-world networks. We find that their coherenceHSOscales sublinearly with the vertex number$N$. We then study analyticallyHSOfor a class of iteratively growing networks—pseudofractal scale-free webs (PSFWs), and obtain an exact solution toHSO, which also increases sublinearly in$N$, with an exponent much smaller than 1. To explain the reasons for this sublinear behavior, we finally studyHSOfor Sierpinśki gaskets, for whichHSOgrows superlinearly in$N$, with a power exponent much larger than 1. Sierpinśki gaskets have the same number of vertices and edges as the PSFWs but do not display the scale-free and small-world properties. We thus conclude that the scale-free, small-world, and loopy topologies are jointly responsible for the observed sublinear scaling ofHSO.

Distributed key generation (DKG) is widely used in multi-party computation and decentralized applications. DKG has two phases, namely sharing and reconstruction. Most of the prior DKG protocols need at least 2 rounds for the sharing phase, in case some party raises a dispute. The existing 1-round DKG protocol [Fouqueet al., PKC’01], built based on a publicly verifiable secret sharing (PVSS) scheme, assumes a static adversary model and its reconstruction phase requires$O(n^{2})$communication complexity. Motivated by the observation that a ciphertext-policy attribute-based encryption (CP-ABE) scheme hides secret sharing (SS) in ciphertext, we utilize decentralized CP-ABE to achieve the first adaptively secure 1-round DKG protocol. Firstly, a CP-ABE scheme enables the ciphertexts in DKG to be externally decrypted, making our protocol superior to the PVSS-based DKG protocol in reconstruction. The communication and computation complexities are both lowered to$O(n)$thanks to the constant-sized decryption key and the proposed batch decryption. The use of CP-ABE also makes our DKG protocol storage-friendly, i.e., the parties store no ciphertext after the sharing phase. Secondly, we add non-interactive zero-knowledge (NIZK) proofs to make the CP-ABE ciphertext publicly verifiable by leveraging the sigma protocol and the Fiat-Shamir heuristic. Thirdly, we demonstrate our protocol’s feasibility by presenting a proof-of-concept implementation over Ethereum, which is used as a public channel and a trustworthy computation platform. The implementation is a non-trivial task due to Ethereum’s incompatibility with the bilinear mapping group.

In 1991, Wei proved a duality theorem that established an interesting connection between the generalized Hamming weights of a linear code and those of its dual code. Wei’s duality theorem has since been extensively studied from different perspectives and extended to other settings. In this paper, we re-examine Wei’s duality theorem and its various extensions, henceforth referred to as Wei-type duality theorems, from a new Galois connection perspective. Our approach is based on the observation that the generalized Hamming weights and the dimension/length profiles of a linear code form a Galois connection. The central result of this paper is a general Wei-type duality theorem for two Galois connections between finite subsets of$\mathbb {Z}$, from which all the known Wei-type duality theorems can be recovered. As corollaries of our central result, we prove new Wei-type duality theorems for$w$-demi-matroids defined over finite sets and$w$-demi-polymatroids defined over modules with a composition series, which further allows us to unify and generalize all the known Wei-type duality theorems established for codes endowed with various metrics.

Locally Repairable codes (LRCs) have gained significant interest due to applications in distributed storage systems since they enable systems to recover a failed node by accessing few other active nodes. In particular, LRCs with large availability are highly desirable for parallel reading of hot data. In addition to the above applications in distributed storage systems, it was shown by Fazeli et al. that an LRC with large availability can produce a good private information retrieval (PIR) code which allows to reduce the storage overhead of a PIR protocol. Roughly speaking, one can obtain a good PIR code as long as there exists an LRC with large availability. One of the main tasks in studying PIR codes is to design a$t$-server PIR code with small length for the given dimension. In particular, the construction of binary PIR codes is of great interest. In this paper, we consider a construction of binary LRCs from polynomial evaluations. As a result, a new class of binary LRCs with large availability are obtained. Applying such LRCs to PIR codes, we obtain a new class of binary PIR codes. On one hand, the binary LRCs constructed are new in the sense that the parameter regime is not covered by the known LRCs. On the other hand, the parameters of PIR codes derived from our LRCs outperform the known results in certain parameter regimes and achieve the lower bound given by Fazeli et al. up to an absolute constant.

This article is devoted to Boolean and vectorial bent functions and their duals. Our ultimate objective is to increase such functions’ corpus by designing new ones covering many previous bent functions’ constructions. To this end, we provide several new infinite families of bent functions, including idempotent bent functions of any algebraic degree, bent functions in univariate trace form, and self-dual bent functions. Those bent functions are of great theoretical and practical interest because of their special structures and relationship with self-dual codes. In particular, many well-known bent functions are special cases of our bent functions. Moreover, we extend our results to vectorial bent functions and obtain three new infinite classes of vectorial bent functions of any possible degree by determining the explicit duals of three classes of well-known bent functions.

Let$\mathbf {H}$be the cartesian product of a family of finite abelian groups indexed by a finite set$\Omega $. A given poset (i.e., partially ordered set)$\mathbf {P}=(\Omega,\preccurlyeq _{\mathbf {P}})$gives rise to a poset metric on$\mathbf {H}$, which further leads to a partition$\mathcal {Q}(\mathbf {H},\mathbf {P})$of$\mathbf {H}$. We prove that if$\mathcal {Q}(\mathbf {H},\mathbf {P})$is Fourier-reflexive, then its dual partition$\Lambda $coincides with the partition of$\hat {\mathbf {H}}$induced by$\mathbf {\overline {P}}$, the dual poset of$\mathbf {P}$, and moreover,$\mathbf {P}$is necessarily hierarchical. This result establishes a conjecture proposed by Gluesing-Luerssen in Gluesing-Luerssen, 2015. We also show that with some other assumptions,$\Lambda $is finer than the partition of$\hat {\mathbf {H}}$induced by$\mathbf {\overline {P}}$. In addition, we give some necessary and sufficient conditions for$\mathbf {P}$to be hierarchical, and for the case that$\mathbf {P}$is hierarchical, we give an explicit criterion for determining whether two codewords in$\hat {\mathbf {H}}$belong to the same block of$\Lambda $. We prove these results by relating the involved partitions with certain family of polynomials, a generalized version of which is also proposed and studied to generalize the aforementioned results.

Let$n=2m$. In 2020, Budaghyan, Helleseth and Kaleyski [IEEE TIT 66(11): 7081-7087, 2020] considered a family of quadrinomials over$\mathbb {F}_{2^{n}}$of the form$x^{3}+a(x^{2^{s}+1})^{2^{k}}+bx^{3\cdot 2^{m}}+c(x^{2^{s+m}+2^{m}})^{2^{k}}$. They showed that two infinite classes of almost perfect nonlinear (APN) functions belong to this family when$\gcd (6,m)=1$. We observe that these two infinite classes of APN quadrinomials and the infinite class of APN polynomials from the Budaghyan-Carlet family belong to a more general family of polynomials over$\mathbb {F}_{2^{n}} $with the form$f(x)=a{\mathrm{ Tr}}^{n}_{m}(F(x))+a^{2^{m}}{\mathrm{ Tr}}^{n}_{m}(G(x))$, where$a \in \mathbb {F}_{2^{n}}\backslash \mathbb {F}_{2^{m}} $, and both$F$and$G$are quadratic functions over$\mathbb {F}_{2^{n}}$. We characterize when$f(x) $is APN. With the help of our characterization, letting$F(x)=bx^{2^{i}+1} $and$G(x)=cx^{2^{s}+1}$with$b, c\in \mathbb {F}_{2^{n}} $, we obtain an infinite family of APN functions of the form$f(x) $when${\mathrm{ gcd}}(2,m)=1 $and verify that for$n=10 $two APN instances from this infinite family are CCZ-inequivalent to each other, and to any APN function over$\mathbb {F}_{2^{10}} $from the previously known infinite families.

Let$\mathrm{H}=\prod\nolimits_{i\in\Omega}H_{i}$be the cartesian product of finite abelian groups$H_{i}$indexed by a finite set$\Omega$. Any partition of H gives rise to a dual partition of its character group$\hat{\mathrm{H}}$. A given poset (i.e., partially ordered set) P on$\Omega$gives rise to the corresponding poset metric on H, which further leads to a partition$\Gamma$of H. We prove that if$\Gamma$is Fourier-reflexive, then its dual partition$\hat{\Gamma}$coincides with the partition of$\hat{\mathrm{H}}$induced by$\overline{\mathrm{P}}$, the dual poset of P, and moreover, P is necessarily hierarchical. This result establishes a conjecture proposed by Heide Gluesing-Luerssen in [4]. We also show that with some other assumptions,$\hat{\Gamma}$is finer than the partition of$\hat{\mathrm{H}}$induced by$\overline{\mathrm{P}}$. We prove these results by relating the partitions with certain family of polynomials, whose basic properties are studied in a slightly more general setting.

Abstract In 2012, Carlet et al. developed two secondary constructions of bent functions (Advances in Mathematics of Communications, 6: 305‐314) and proposed some applications for their constructions. However, the duals of bent functions in their constructions were not presented. In order to find more general applications to these constructions and obtain new classes of bent functions, an open problem was proposed by Carlet in 2014. Hence, in this study, a class of vectorial bent functions for answering that open problem, which also addresses another open problem on vectorial bent functions proposed by Mesnager in 2014, is constructed. In addition, a new secondary construction of bent functions that generalises one of Carlet et al.'s constructions in 2012 is presented. Based on that, two new classes of bent functions were obtained and their duals were presented explicitly. In particular, some self‐dual bent functions are constructed. Moreover, it can be proved that our bent functions can be EA‐inequivalent to those constructed by Carlet et al. in 2012.

Wireless energy charging has emerged as a very promising technology for prolonging sensor lifetime in wireless rechargeable sensor networks (WRSNs). Existing studies focused mainly on the one-to-one charging scheme that a single sensor can be charged by a mobile charger at each time, this charging scheme however suffers from poor charging scalability and inefficiency. Recently, another charging scheme, the multi-node charging scheme that allows multiple sensors to be charged simultaneously by a mobile charger, becomes dominant, which can mitigate charging scalability and improve charging efficiency. However, most previous studies on this multi-node energy charging scheme focused on the use of a single mobile charger to charge multiple sensors simultaneously. For large scale WRSNs, it is insufficient to deploy only a single mobile charger to charge many lifetime-critical sensors, and consequently sensor expiration durations will increase dramatically. To charge many lifetime-critical sensors in large scale WRSNs as early as possible, it is inevitable to adopt multiple mobile chargers for sensor charging that can not only speed up sensor charging but also reduce expiration times of sensors. This however poses great challenges to fairly schedule the multiple mobile chargers such that the longest charging delay among sensors is minimized. One important constraint is that no sensor can be charged by more than one mobile charger at any time due to the fact that the sensor cannot receive any energy from either of the chargers or the overcharging will damage the recharging battery of the sensor. Thus, finding a closed charge tour for each of the multiple chargers such that the longest charging delay is minimized is crucial. In this paper we address the challenge by formulating a novel longest charging delay minimization problem. We first show that the problem is NP-hard. We then devise the very first approximation algorithm with a provable approximation ratio for the problem. We finally evaluate the performance of the proposed algorithms through experimental simulations. Experimental results demonstrate that the proposed algorithm is promising, and outperforms existing algorithms in various settings.

The mean hitting time from a node i to a node j selected randomly according to the stationary distribution of random walks is called the Kemeny constant, which has found various applications. It was proved that over all graphs with N vertices, complete graphs have the exact minimum Kemeny constant, growing linearly with N. Here we study numerically or analytically the Kemeny constant on many sparse real-world and model networks with scale-free small-world topology, and show that their Kemeny constant also behaves linearly with N. Thus, sparse networks with scale-free and small-world topology are favorable architectures with optimal scaling of Kemeny constant. We then present a theoretically guaranteed estimation algorithm, which approximates the Kemeny constant for a graph in nearly linear time with respect to the number of edges. Extensive numerical experiments on model and real networks show that our approximation algorithm is both efficient and accurate.

Locally repairable codes with more than one recovering set are demanded in the application to distributed storage. For each failure node (or disk), it is desired to have as many recovering sets as possible. In this paper, we make use of automorphisms of rational function fields to construct locally repairable codes with multiple recovering sets. Although we focus on two recovering sets, our construction can be easily generalized to the case of multiple recovering sets. In particular, we obtain a class of locally repairable codes with minimum distance only 1 less than the upper bound.

Along with Network Function Virtualization (NFV), Mobile Edge Computing (MEC) is becoming a new computing paradigm that enables accommodating innovative applications and services with stringent response delay and resource requirements, including autonomous vehicles and augmented reality. Provisioning reliable network services for users is the top priority of most network service providers, as unreliable services or severe service failures can result in tremendous losses of users, particularly for their mission-critical applications. In this paper, we study reliability-aware VNF instances provisioning in an MEC, where different users request different network services with different reliability requirements through paying their requested services with the aim to maximize the network throughput. To this end, we first formulate a novel reliability-aware VNF instance placement problem by provisioning primary and secondary VNF instances at different cloudlets in MEC for each user while meeting the specified reliability requirement of the user request. We then show that the problem is NP-hard and formulate an Integer Linear Programming (ILP) solution. Due to the NP-hardness of the problem, we instead devise an approximation algorithm with a logarithmic approximation ratio for the problem. Moreover, we also consider two special cases of the problem. For one special case where each request only requests one primary and one secondary VNF instances, the problem is still NP-hard, and we devise a constant approximation algorithm for it. For another special case where different VNFs have the same amounts of computing resource demands, we show that it is polynomial-time solvable by developing a dynamic programming solution for it. We finally evaluate the performance of the proposed algorithms through experimental simulations. Experimental results demonstrate that the proposed algorithms are promising, and the empirical results of the algorithms outperform their analytical counterparts as theoretical estimations usually are very conservative.

Wireless energy charging has emerged as a very promising technology for prolonging sensor lifetime in Wireless Rechargeable Sensor Networks (WRSNs). Existing studies focused mainly on the 'one-to-one' charging scheme that a sensor can be charged by a single mobile charger at each time, this charging scheme however suffers from poor charging scalability and inefficiency. Recently, another charging scheme - the 'multiple-to-one' charging scheme that allows multiple sensors to be charged simultaneously by a single charger, becomes dominant and can mitigate charging scalability and improve the charging efficiency. Most research studies on this latter scheme focused on the use of a mobile charger to charge multiple sensors simultaneously. However, for large scale WRSNs, it is insufficient to deploy just a single mobile charger to charge many lifetime-critical sensors, and consequently sensor expiration durations will increase dramatically. Instead, in order to charge as many as lifetime-critical sensors, the use of multiple mobile chargers for charging sensors can speed up sensor charging significantly, thereby reducing their expiration durations and improving the monitoring quality of WRSNs. However, this poses great challenges to schedule multiple mobile chargers for sensor charging at the same time such that the longest delay among the chargers is minimized due to multiple critical constraints. One such an important constraint in multiple mobile chargers is that each sensor cannot be charged by more than one mobile charger at each time; otherwise, the sensor cannot receive any energy from either of the chargers. In this paper we address this challenge by first formulating a novel longest delay minimization problem that is NP-hard. We then devise the very first approximation algorithm with a provable approximation ratio for the problem. We finally evaluate the performance of the proposed algorithm through experimental simulations. Simulation results demonstrate that the proposed algorithm is very promising, which outperforms the other heuristics in various settings.

In recent years, self-dual MDS codes have attracted a lot of attention due to theoretical interest and practical importance. Similar to self-dual MDS codes, self-dual near MDS (NMDS for short) codes have nice structures as well. From both theoretical and practical points of view, it is natural to study self-dual NMDS codes. Although there has been lots of work on NMDS codes in literature, little is known for self-dual NMDS codes. It seems more challenging to construct self-dual NMDS codes than self-dual MDS codes. The only work on construction of self-dual NMDS codes shows existence of q-ary self-dual NMDS codes of length q - 1 for odd prime power q or length up to 16 for some small primes q with q ≤ 197. In this paper, we make use of properties of elliptic curves to construct selfdual NMDS codes. It turns out that, as long as 2|q and n is even with 4 ≤ n ≤ q + 12√qJ - 2, one can construct a self-dual NMDS code of length n over Fq. Furthermore, for odd prime power q, there exists a self-dual NMDS code of length n over Fq if q ≥ 4n+3x (n + 3)2.

Maximum distance separable (MDS) erasure codes are widely used in distributed storage systems (DSS) for better storage efficiency and protection against Byzantine attacks. In this paper, we aim at enhancing the error-correction capacity of DSS in a hostile network. Firstly, we apply Hermitian code in DSS and presented a special placing mode for the encoded symbols. A reconstruction algorithm in error-free network is given. Next we show that the burst-error-correcting algorithm by Ren can correct more errors than Reed-Solomon code. We proposed an erasure rollback strategy in decoding. The new reconstructing algorithm improves both the lower and upper bound of error-correcting capacity. It has better computing complexity than Reed-Solomon code with the same storage efficiency.

State-of-the-art cache-oblivious parallel algorithms for dynamic programming (DP) problems usually guarantee asymptotically optimal cache performance without any tuning of cache parameters, but they often fail to exploit the theoretically best parallelism at the same time. While these algorithms achieve cache-optimality through the use of a recursive divide-and-conquer (DAC) strategy, scheduling tasks at the granularity of task dependency introduces artificial dependencies in addition to those arising from the defining recurrence equations. We removed the artificial dependency by scheduling tasks ready for execution as soon as all its real dependency constraints are satisfied, while preserving the cache-optimality by inheriting the DAC strategy. We applied our approach to a set of widely known dynamic programming problems, such as Floyd-Warshall's All-Pairs Shortest Paths, Stencil, and LCS. Theoretical analyses show that our techniques improve the span of 2-way DAC-based Floyd Warshall's algorithm on an $n$ node graph from $Thn^2n$ to $Thn$, stencil computations on a $d$-dimensional hypercubic grid of width $w$ for $h$ time steps from $Th(d^2 h) w^ (d+2) - 1$ to $Thh$, and LCS on two sequences of length $n$ each from $Thn^_2 3$ to $Thn$. In each case, the total work and cache complexity remain asymptotically optimal. Experimental measurements exhibit a $3$ - $5$ times improvement in absolute running time, $10$ - $20$ times improvement in burdened span by Cilkview, and approximately the same L1/L2 cache misses by PAPI.

In this paper, we study the decoding of dual-containing codes from Hermitian tower and applications to quantum codes. The contribution of this paper is threefold. First, we construct the quantum stabilizer codes from the Hermitian tower. Second, we provide a deterministic decoding algorithm with decoding radius that almost achieves the optimal decoding radius, i.e., (1-R)/4 , where R is the rate. Last and most importantly, we present a Monte Carlo algorithm with decoding radius roughly equal to (1-R)/3 , which is beyond the optimal decoding radius (1-R)/4 . There are several features in this paper. First of all, we employ a differential for the Hermitian tower. This differential plays a crucial role for decoding. We also extend our decoding by passing to the constant field extension. This constant field extension makes the decoding work perfectly.

A complex orthogonal design (COD) with parameter [p, n, k] is a combinatorial design used in space-time block codes (STBCs). For STBCs, n is the number of antennas, k/p is the rate, and p is the decoding delay. A class of rate 1/2 CODs called balanced complex orthogonal designs (BCODs) has been proposed by Adams et al., who constructed BCODs with rate k/p = 1/2 and decoding delay p = 2mfor n = 2m. Furthermore, they proved that the constructions have optimal decoding delay when m is congruent to 1, 2, or 3 modulo 4. They conjectured that for the case m ≡ 0 (mod 4), 2mis also a lower bound on p. In this paper, we prove this conjecture.

In this paper, we propose an efficient interpolation-based systematic encoder for low-rate Blaum-Roth codes. Our algorithm is based upon an equivalent definition of [p, k] Blaum-Roth codes from the perspective of generator matrices. Moreover, applying the interpolation method first proposed by D.J.J. Versfeld et al. to the generator matrix, we then derive a formula to resolve the erasure-only decoding problem. Finally, we present a straightforward systematic encoder based on this formula. Compared to the encoders in [5] and [14], it is more efficient for low-rate codes.

Complex orthogonal designs (CODs) are used to construct space-time block codes in wireless transmission. COD Ozwith parameter [p, n, k] is a p × n matrix, where nonzero entries are filled by ±zior ±zi* , i = 1, 2, ..., k, such that equation. In practice, n is the number of antennas, k=p the code rate, and p the decoding delay. One fundamental problem is to construct COD to maximize k/p and minimize p when n is given. Recently, this problem is completely solved by Liang and Adams et al. It's proved that when n = 2m or 2m - 1, the maximal possible rate is (m + 1)/(2m) and the minimum delay (m-12m)(with the only exception n ≡2 (mod 4) where it is 2(m-12m)). However, when the number of antennas increase, the minimum delay grows fast and eats the otherwise fast decoding. For example, when n = 14 the minimal delay for a code with maximal rate is 6006! Therefore, it is very important to study whether it is possible, by lowering the rate slightly, to shorten the decoding delay considerably. In this paper, we demonstrate this possibility by constructing a series of CODs with parameter [p, n, k] = [(w - 1n)+(w + 1n), n, (wn)], where 0 ≤ w ≤ n. Besides that, all optimal CODs, which achieve the maximal rate and minimal delay, are contained in our explicit-form constructions. And this is the first explicit-form construction, while the previous are recursive or algorithmic.

In this study, the authors investigate the resistance of Boolean functions against fast algebraic attacks and deduce a bound between fast algebraic immunity and higher-order non-linearity (it is the first time that a bound between these two cryptographic criteria is given). The authors then show that the fast algebraic immunity of the following two classes of Boolean functions is not good: (a) The repaired functions of the Tu–Deng function proposed by Carlet. The Tu–Deng function has optimum algebraic degree, optimum algebraic immunity and a very good non-linearity. However, it is weak against fast algebraic attacks. Carlet found this weakness and also tried to repair it. (b) An infinite class of balanced functions proposed by Tang et al., having optimum algebraic degree, optimum algebraic immunity and a very high non-linearity.

Complex orthogonal designs (CODs) are used to construct space-time block codes. COD Ozwith parameter [p, n, k] is a p × n matrix, where nonzero entries are filled ±ziby ±zi*, i = 1,2...,k, or , such that OzHOz= (|z1|2+ |z2|2+ ...+ |zk|2)In×n. Define Oza first type COD if and only if Ozdoes not contain submatrix (±zj,0:0,±zj*) or (±zj*,0:0,±zj). It is already known that all CODs with maximal rate, i.e., maximal k/p, are of the first type. In this paper, we will determine all achievable parameters [p, n, k] of first type COD, as well as all their possible structures. The existence of parameters is proved by explicit-form constructions. New CODs with parameters [p, n, k] = [(n:w-1) + (n:w+1),n, (n:w)], for 0 ≤ w ≤ n, are constructed, which demonstrate the possibility of sacrificing code rate to reduce decoding delay. It is worth mentioning that all maximal rate, minimal delay CODs are contained in our constructions, and their uniqueness under equivalence operation is proved.

Given a positive even integer n, it is found that the weight distribution of any n-variable symmetric Boolean function with maximum algebraic immunity (AI) n/2 is determined by the binary expansion of n . Based on the foregoing, all n-variable symmetric Boolean functions with maximum AI are constructed. The amount is (2 wt(n)+1)2[log2n].

We propose a new systematic encoding procedure for Blaum-Roth codes, i.e., Reed-Solomon(RS) codes over the polynomial rings modulo Σi=op-1xiover GF(q), where p is a prime. Our method generalizes the interpolation-based erasure-only decoder for RS codes proposed by D.J.J. Versfeld et al., which is efficient for low-rate RS codes. Later, we derive a systematic encoder from this decoder, since encoding can be implemented as a special case of decoding. Compared to the systematic encoding procedure introduced by M. Blaum an R. Roth, our encoding procedure is very efficient for low-rate Blaum-Roth codes.

In this paper, we put forward an efficient method to study the symmetric Boolean functions with high algebraic immunity on even number of variables. We obtain some powerful necessary conditions for symmetric Boolean functions to achieve high algebraic immunity by studying the weight support of some specific types of Boolean functions of low degrees. With these results, we prove that the algebraic immunity of a large class of symmetric correlation immune Boolean functions, namely the symmetric palindromic functions, is not high. Besides, we construct all symmetric Boolean functions with maximum algebraic immunity and give a description for those with submaximum algebraic immunity. We also determine the Hamming weight, degrees and nonlinearity of the symmetric Boolean functions with maximum algebraic immunity.

It is known that Boolean functions used in stream and block ciphers should have good cryptographic properties to resist algebraic attacks. Up until now, there have been several constructions of Boolean functions achieving optimum algebraic immunity. However, most of their nonlinearities are very low. Carlet and Feng studied a class of Boolean functions with optimum algebraic immunity and deduced the lower bound of its nonlinearity, which is good, but not very high. Moreover, the main practical problem with this construction is that it cannot be implemented efficiently. In this paper, we put forward a new method to construct cryptographically significant Boolean functions by using primitive polynomials, and construct three infinite classes of Boolean functions with good cryptographic properties: balancedness, optimum algebraic degree, optimum algebraic immunity, and a high nonlinearity.

This paper investigates the feasibility to use chaotic communications in MIMO channel. Differential chaos shift keying modulation is chosen as a benchmark and Alamouti space-time code scheme is used for the 2 transmit and 2 receiver antennas wireless system. Based on the evaluation of system performance, improvements are also discussed.

In this paper we investigate the problems of searching for the capacity factors and determining the capacity ranks of edges in a network coding-based network, which were first proposed in (K. Cai and P.Y. Fan, 2007). For the former problem, we prove that it is computationally hard by reducing the well known NP-complete SUB-SUM problem to the current problem. For the latter problem, we devise efficient algorithms in a special case of networks and conjecture that in general case the problem is also hard.

In this paper, several investigations have been performed for solving the open problem that if small quaternion orthogonal design can be used to build larger one. The so called coordinate interleaved orthogonal designs (CIODs) are generalized into quaternion in the paper, and consequently it introduces a new construction technique for 4 n times 4 m rectangular matrices whose elements are quaternion variables based on any existing n times m quaternion orthogonal design for space-time block codes (STBCs). Analysis shows that maximum likelihood (ML) decoding can be applied for this design with reduced complexity , and the design reaches full diversity. As examples, 8 times 8 quaternion designs are constructed.

The maximal rates and the minimal delays are basic problems of space-time block codes from complex orthogonal designs. Liang systematically solved the problem on the maximal rates of complex orthogonal designs, and posed an open problem on the minimal delays. Recently, the authors gave the negative answer for the open problem. In this letter, we give lower bounds on the minimal delays.

The maximal rates and the minimal delays are basic problems of space-time block codes from complex orthogonal designs. Liang [5] systematically solved the problem on the maximal rates for a special kind of complex othogonal designs, and posed an open problem on the minimal delays. Recently, Kan & Shen [3] gave a negative answer for the open problem. In the paper, we prove that the maximal code rates that Liang gave in [5] also hold for more general complex orthogonal designs.

X. Liang systematically investigated orthogonal designs with maximal rates, gave the maximal rates of complex orthogonal designs and a concrete construction procedure for complex orthogonal designs with the maximal rates. He also posed an open problem on the minimal decoding delays of complex orthogonal designs with maximal rates, and proved that the problem is correct for less than or equal to six transmit antennas. In this correspondence, we give a counterexample for the open problem for n=8 and prove that the minimal delay for complex orthogonal designs with eight columns is 56. Hence, we give a negative answer for the open problem.

It was conjectured by Koetter and Vardy that if the k characteristic generators of a linear code C are linearly independent, then the corresponding n-k characteristic generators of the dual code C/sup /spl perp// are also linearly independent. In this correspondence, we prove that the conjecture is true for self-dual codes and cyclic codes.