Previous Constructions Research Articles

A Survey of Key Technologies for Constructing Network Covert Channel

In order to protect user privacy or guarantee free access to the Internet, the network covert channel has become a hot research topic. It refers to an information channel in which the messages are covertly transmitted under the network environment. In recent years, many new construction schemes of network covert channels are proposed. But at the same time, network covert channel has also received the attention of censors, leading to many attacks. The network covert channel refers to an information channel in which the messages are covertly transmitted under the network environment. Many users exploit the network covert channel to protect privacy or guarantee free access to the Internet. Previous construction schemes of the network covert channel are based on information steganography, which can be divided into CTCs and CSCs. In recent years, there are some covert channels constructed by changing the transmission network architecture. On the other side, some research work promises that the characteristics of emerging network may better fit the construction of the network covert channel. In addition, the covert channel can also be constructed by changing the transmission network architecture. The proxy and anonymity communication technology implement this construction scheme. In this paper, we divide the key technologies for constructing network covert channels into two aspects: communication content level (based on information steganography) and transmission network level (based on proxy and anonymity communication technology). We give an comprehensively summary about covert channels at each level. We also introduce work for the three new types of network covert channels (covert channels based on streaming media, covert channels based on blockchain, and covert channels based on IPv6). In addition, we present the attacks against the network covert channel, including elimination, limitation, and detection. Finally, the challenge and future research trend in this field are discussed.

New Sets of Binary Cross Z-Complementary Sequence Pairs

Spatial modulation (SM) is a special kind of multiple-input multiple-output (MIMO) technique, in which one transmit antenna is activated during each symbol duration. Recently, cross Z-complementary sequence pairs (CZCPs) have been evolved as a new sequence pair to be used for pilot design in SM over frequency-selective channels. CZCPs are sequence pairs having zero autocorrelation sums and zero cross-correlation sums within specific time-shifts. In this letter, we propose systematic constructions of binary CZCPs with new lengths of the form $2^\alpha 10^\beta 26^\gamma ~(\alpha \geq 1)$ , $10^\beta $ , $26^\gamma $ and $10^\beta 26^\gamma $ . We have also proved that for a specific kind of binary CZCP, the magnitude of non-zero aperiodic cross-correlation sums at each time shift outside the zero cross-correlation zone is lower bounded by 4. Finally, we have compared our proposed constructions with the previous constructions.

Geometric invariants of representations of finite groups

For a finite group τ and a field k of characteristic p dividing the order of τ, we construct a map pτ:Uτ→PYτ of varieties over k with unions of affine spaces as fibers and with (PYτ)/τp-isogenous to ProjH•(τ,k). On Uτ, we construct a “universal p-nilpotent operator” PΘτ which leads to the construction of τ-equivariant coherent sheaves associated to finite dimensional kτ-modules M. These coherent sheaves are algebraic vector bundles on Uτ if M has constant Jordan type. For any finite dimensional kτ-module M, these coherent sheaves are vector bundles when restricted to the complements of the generalized support varieties of M.For a linear algebraic group G, we compare these constructions for the finite group G(Fp) to previous constructions for the infinitesimal group scheme G(r). Our comparison of bundle invariants for a rational G-module M of exponential type <pr upon restriction to G(Fp) and to G(r) is a strengthened form of earlier comparisons of support varieties for M. Our constructions extend to semi-direct products G⋊τ of an infinitesimal group scheme G and a finite group τ, thus to all finite group schemes if k is algebraically closed.

Category of C-motives over finite fields

In this article we introduce and study a motivic category in the arithmetic of function fields, namely the category of motives over an algebraic closure L of a finite field with coefficients in a global function field over this finite field. It is semi-simple, non-neutral Tannakian and possesses all the expected fiber functors. This category generalizes the previous construction due to Anderson and is more relevant for applications to the theory of G-Shtukas, such as formulating the analog of the Langlands-Rapoport conjecture over function fields. We further develop the analogy with the category of motives over L with coefficients in Q for which the existence of the expected fiber functors depends on famous unproven conjectures.

Full Family of Flattening Solitary Waves for the Critical Generalized KdV Equation

For the critical generalized KdV equation partial _t u + partial _x (partial _x^2 u + u^5)=0 on {mathbb {R}}, we construct a full family of flattening solitary wave solutions. Let Q be the unique even positive solution of Q''+Q^5=Q. For any nu in (0,frac{1}{3}), there exist global (for tge 0) solutions of the equation with the asymptotic behavior u(t,x)=t-ν2Qt-ν(x-x(t))+w(t,x)\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} u(t,x)= t^{-\\frac{\\nu }{2}} Q\\left( t^{-\\nu } (x-x(t))\\right) +w(t,x) \\end{aligned}$$\\end{document}where, for some c>0, x(t)∼ct1-2νand‖w(t)‖H1(x>12x(t))→0ast→+∞.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} x(t)\\sim c t^{1-2\\nu } \\quad \\text{ and }\\quad \\Vert w(t)\\Vert _{H^1(x>\\frac{1}{2} x(t))} \\rightarrow 0\\quad \\text{ as } t\\rightarrow +\\infty . \\end{aligned}$$\\end{document}Moreover, the initial data for such solutions can be taken arbitrarily close to a solitary wave in the energy space. The long-time flattening of the solitary wave is forced by a slowly decaying tail in the initial data. This result and its proof are inspired and complement recent blow-up results for the critical generalized KdV equation. This article is also motivated by previous constructions of exotic behaviors close to solitons for other nonlinear dispersive equations such as the energy-critical wave equation.

CW-complex Nagata idealizations

We introduce a construction which allows us to identify the elements of the skeletons of a CW-complex P(m) and the monomials in m variables. From this, we infer that there is a bijection between finite CW-subcomplexes of P(m), which are quotients of finite simplicial complexes, and certain bigraded standard Artinian Gorenstein algebras, generalizing previous constructions of Faridi and ourselves.We apply this to a generalization of Nagata idealization for level algebras. These algebras are standard graded Artinian algebras whose Macaulay dual generator is given explicitly as a bigraded polynomial of bidegree (1,d). We consider the algebra associated to polynomials of the same bidegree (d1,d2).

6D dual superconformal algebra

We construct and study the 6D dual superconformal algebra. Our construction is inspired by the dual superconformal symmetry of massless 4D SYM and extends the previous construction of the enhanced dual conformal algebra for 6D SYM to the full 6D dual superconformal algebra for chiral theories. We formulate constraints in 6D spinor helicity formalism and find all generators of the 6D dual superconformal algebra. Next, we check that they agree with the dual superconformal generators of known 3D and 4D theories. We show that it is possible to significantly simplify the form of generators and compactly write the dual superconformal algebra using superindices. Finally, we work out some examples of algebra invariants.

Variational order for forced Lagrangian systems II. Euler–Poincaré equations with forcing

In this paper we provide a variational derivation of the Euler–Poincaré equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others Martín de Diego and Martín de Almagro (2018 Nonlinearity 31 3814–3846), Galley (2013 Phys. Rev. Lett. 110 174301), Galley et al (2014 (arXiv:[math-Ph] 1412.3082)). Moreover, we study in detail the underlying geometry which is related to the notion of Poisson groupoid. Finally, we apply the previous construction to the formal derivation of the variational error for numerical integrators of forced Euler–Poincaré equations and the application of this theory to the derivation of geometric integrators for forced systems.

Process-independent construction stage analysis of self-anchored suspension bridges

The construction process of self-anchored suspension (SAS) bridges undergoes frequent system transformations and loadings, accompanied by complex strong geometric and contact nonlinear behaviours. The accurate state assessment of such a process generally requires the nonlinear finite element analysis (FEA) to perform a stage-by-stage forward, cumulative calculation based on the principle of incremental superposition. This sort of calculation means that the structural equilibrium of any intermediate state of the process, referred to as a construction stage, must be accumulated from its previous construction loading history, which is susceptible to computational effort and divergence limitations. This paper overcomes these limitations by proposing a direct and fast method that is independent of the cumulative calculation in the analysis of any specified construction stage, in favour of the construction optimization design and uncertainty analysis. The unstrained assembly formats for the typical construction process of SAS bridges are established, and the elements with constant physical quantities as the characteristic parameters are used to describe the various structures, boundaries, loads and their changes during the construction. On this basis, an interactive analysis framework integrating the numerical iteration with the FEA is established to achieve an accurate equilibrium for the construction stages. An enhanced interval-genetic algorithm (IGA) is employed as the optimization engine to smoothly accelerate global convergence. The proposed framework is applied to an SAS bridge under construction, and the validity and performance of this approach are demonstrated by considering the in-field test data.

Gluing affine Yangians with bi-fundamentals

The affine Yangian of {mathfrak{gl}}_1 is isomorphic to the universal enveloping algebra of {mathcal{W}}_{1+infty } and can serve as a building block in the construction of new vertex operator algebras. In [1], a two-parameter family generalization of mathcal{N} = 2 supersymmetric {mathcal{W}}_{infty } algebra was constructed by “gluing” two affine Yangians of {mathfrak{gl}}_1 using operators that transform as (□, overline{square} ) and ( overline{square} , □) w.r.t. the two affine Yangians. In this paper we realize a similar (but non-isomorphic) two-parameter gluing construction where the gluing operators transform as (□, □) and ( overline{square} , overline{square} ) w.r.t. the two affine Yangians. The corresponding representation space consists of pairs of plane partitions connected by a common leg whose cross-section takes the shape of Young diagrams, offering a more transparent geometric picture than the previous construction.

Simplified Bounds on FHSs Set and Its Strictly Optimal Construction

Frequency-hopping sequences (FHSs) with favorite partial Hamming correlation properties are intensively needed in many synchronization and multiple-access systems. Strictly optimal FHS sets are a kind of FHS sets which has optimal Hamming correlation for any correlation window. In this paper, firstly we present simplified representations of the generalized Lempel–Greenberger bound on the partial Hamming autocorrelation of an FHS and the generalized Peng-Fan bound on the partial Hamming correlation of an FHS set, respectively. Secondly, we propose a direct construction of strictly optimal FHS sets, which interprets the previous construction proposed by Cai, Zhou, Yang and Tang. By choosing appropriate parameters and bijections, we present more flexible constructions of strictly optimal FHS sets.

New Constructions of Identity-Based Dual Receiver Encryption from Lattices.

Dual receiver encryption (DRE), being originally conceived at CCS 2004 as a proof technique, enables a ciphertext to be decrypted to the same plaintext by two different but dual receivers and becomes popular recently due to itself useful application potentials such secure outsourcing, trusted third party supervising, client puzzling, etc. Identity-based DRE (IB-DRE) further combines the bilateral advantages/facilities of DRE and identity-based encryption (IBE). Most previous constructions of IB-DRE are based on bilinear pairings, and thus suffers from known quantum algorithmic attacks. It is interesting to build IB-DRE schemes based on the well-known post quantum platforms, such as lattices. At ACISP 2018, Zhang et al. gave the first lattice-based construction of IB-DRE, and the main part of the public parameter in this scheme consists of matrices where n is the bit-length of arbitrary identity. In this paper, by introducing an injective map and a homomorphic computation technique due to Yamada at EUROCRYPT 2016, we propose another lattice-based construction of IB-DRE in an even efficient manner: The main part of the public parameters consists only of matrices of the same dimensions, where is a flexible constant. The larger the p and n, the more observable of our proposal. Typically, when and according to the suggestion given by Peikert et al., the size of public parameters in our proposal is reduced to merely 12% of Zhang et al.’s method. In addition, to lighten the pressure of key generation center, we extend our lattice-based IB-DRE scheme to hierarchical scenario. Finally, both the IB-DRE scheme and the HIB-DRE scheme are proved to be indistinguishable against adaptively chosen identity and plaintext attacks (IND-ID-CPA).

Dyon in the SU(2) Yang\u2013Mills theory with a gauge-invariant gluon mass toward quark confinement

In the previous paper, we have shown the existence of magnetic monopoles in the pure SU(2) Yang–Mills theory with a gauge-invariant mass term for the gluon field being introduced. In this paper, we extend our previous construction of magnetic monopoles to obtain dyons with both magnetic and electric charges. In fact, we solve under the static and spherically symmetric ansatz the field equations of the SU(2) “complementary” gauge-scalar model, which is the SU(2) Yang–Mills theory coupled to a single adjoint scalar field whose radial degree of freedom is eliminated. We show that the novel dyon solution can be identified with the gauge field configuration of a dyon with a minimum magnetic charge in the massive Yang–Mills theory. Moreover, we compare the dyon of the massive Yang–Mills theory obtained in this way with the Julia–Zee dyon in the Georgi–Glashow gauge-Higgs scalar model and the dyonic extension of the Wu–Yang magnetic monopole in the pure Yang–Mills theory. Finally, we identify the novel dyon solution found in this paper with a dyon configuration on S^1 times {mathbb {R}}^3 space with nontrivial holonomy and propose to use it to understand the confinement/deconfinement phase transition in the Yang–Mills theory at finite temperature, instead of using the dyons constituting the Kraan–van Baal–Lee–Lu caloron.

Hierarchical Identity-Based Signature in Polynomial Rings

Abstract Hierarchical identity-based signature (HIBS) plays a core role in a large community as it significantly reduces the workload of the root private key generator. To make HIBS still available and secure in post-quantum era, constructing lattice-based schemes is a promising option. In this paper, we present an efficient HIBS scheme in polynomial rings. Although there are many lattice-based signatures proposed in recent years, to the best of our knowledge, our HIBS scheme is the first ring-based construction. In the center of our construction are two new algorithms to extend lattice trapdoors to higher dimensions, which are non-trivial and of independent interest. With these techniques, the security of the new scheme can be proved, assuming the hardness of the Ring-SIS problem. Since operations in the ring setting are much faster than those over integers and the new construction is the first ring-base HIBS scheme, our scheme is more efficient and practical in terms of computation and storage cost when comparing to the previous constructions.

Extending the weak order on Coxeter groups

We introduce a new family of complete lattices, arising from a digraph together with a valuation on its vertices and generalizing a previous construction of the author. We then apply this to the study of two long-standing conjectures of Dyer, and we provide a description of the Tamari lattice with this theory.

Post quantum proxy signature scheme based on the multivariate public key cryptographic signature

Proxy signature is a very useful technique which allows the original signer to delegate the signing capability to a proxy signer to perform the signing operation. It finds wide applications especially in the distributed environment where the entities such as the wireless sensors are short of computational power and needed to be convinced to the authenticity of the server. Due to less proxy signature schemes in the post-quantum cryptography aspect, in this article, we investigate the proxy signature in the post-quantum setting so that it can resist against the potential attacks from the quantum adversaries. A general multivariate public key cryptographic proxy scheme based on a multivariate public key cryptographic signature scheme is proposed, and a heuristic security proof is given for our general construction. We show that the construction can reach Existential Unforgeability under an Adaptive Chosen Message Attack with Proxy Key Exposure assuming that the underlying signature is Existential Unforgeability under an Adaptive Chosen Message Attack. We then use our general scheme to construct practical proxy signature schemes for three well-known and promising multivariate public key cryptographic signature schemes. We implement our schemes and compare with several previous constructions to show our efficiency advantage, which further indicates the potential application prospect in the distributed network environment.

On the General Construction of Tightly Secure Identity-Based Signature Schemes

AbstractA tightly secure scheme has a reduction, where the reduction loss is a small constant. Identity-based signature (IBS) is an important cryptographic primitive, and tightly secure IBS schemes enjoy the advantage that the security parameter can be optimal to achieve a certain security level. General constructions of IBS schemes (Bellare, M., Namprempre, C., and Neven, G. (2004) Security Proofs for Identity-Based Identification and Signature Schemes. In Proc. EUROCRYPT 2004, May 2–6, pp. 268–286. Springer, Berlin, Interlaken, Switzerland; Galindo, D., Herranz, J., and Kiltz, E. (2006) On the Generic Construction of Identity-Based Signatures With Additional Properties. In Proceedings of ASIACRYPT 2006, December 3–7, pp. 178–193. Springer, Berlin, Shanghai, China) and their security have been extensively studied. However, the security is not tight and how to generally construct a tightly secure IBS scheme remains unknown. In this paper, we concentrate on the general constructions of IBS schemes. We first take an insight into previous constructions and analyze the reason why it cannot achieve tight security. To further study possible tightly secure constructions, we propose another general construction, which could be seen as a different framework of IBS schemes. Our construction requires two traditional signature schemes, whereas the construction by Bellare et al. uses one scheme in a two-round iteration. There are no additional operations in our general construction. Its main advantage is providing the possibility of achieving tight security for IBS schemes in the random oracle model. Combining two known signature schemes, we present an efficient IBS scheme with tight security as an example.

Nonsingular bilinear maps revisited

AbstractA bilinear map $\varPhi :\mathbb {R}^r\times \mathbb {R}^s\to \mathbb {R}^n$ is nonsingular if $\varPhi (\overrightarrow {a},\overrightarrow {b})=\overrightarrow {0}$ implies $\overrightarrow {a}=\overrightarrow {0}$ or $\overrightarrow {b}=\overrightarrow {0}$. These maps are of interest to topologists, and are instrumental for the study of vector bundles over real projective spaces. The main purpose of this paper is to produce examples of such maps in the range $24\leqslant r\leqslant 32,\ 24\leqslant s\leqslant 32,$ using the arithmetic of octonions (otherwise known as Cayley numbers) as an effective tool. While previous constructions in lower dimensional cases use ad hoc techniques, our construction follows a systematic procedure and subsumes those techniques into a uniform perspective.

Extended complex Yang–Mills instanton sheaves

In the search of Yang–Mills (YM) instanton sheaves with topological charge two, the rank of [Formula: see text] matrix in the monad construction can be dropped from the bundle case with rank [Formula: see text] to either rank [Formula: see text] [S. H. Lai, J. C. Lee and I. H. Tsai, Yang–Mills instanton sheaves, Ann. Phys. 377 (2017) 446] or 0 on some points of [Formula: see text] of the sheaf cases. In this paper, we first show that the sheaf case with rank [Formula: see text] does not exist for the previous construction of [Formula: see text] complex YM instantons [S. H. Lai, J. C. Lee and I. H. Tsai, Biquaternions and ADHM construction of concompact [Formula: see text] Yang–Mills instantons, Ann. Phys. 361 (2015) 14]. We then show that in the new “extended complex YM instantons” discovered in this paper, rank [Formula: see text] can be either 2 on the whole [Formula: see text] (bundle) with some given ADHM data or 1, 0 on some points of [Formula: see text] with other ADHM data (sheaves). These extended [Formula: see text] complex YM instantons have no real instanton counterparts. Finally, the potential applications to real physics systems are noted in the end of the paper.

The RedBlue family of universal constructions

A universal construction is a general mechanism for obtaining a concurrent implementation of any shared object from its sequential implementation. We present the family of RedBlue universal constructions which produce adaptive, linearizable, wait-free, concurrent implementations of shared objects. The proposed universal constructions improve upon previous universal constructions in terms of their step and/or space complexity. The first of these universal constructions, which serves as the keystone for the design of the other RedBlue algorithms, produces concurrent implementations with better step complexity than those produced by all previously presented universal constructions but it uses large LL/SC registers. The second universal construction significantly reduces the size of the required registers, whereas the last two are appropriate for the purpose of simulating large objects.