Multilinear Research Articles

Outsourced attribute‐based signatures with perfect privacy for circuits in cloud computing

SummaryAttribute‐based signature (ABS) is a widely used cryptographic primitive, that provides both data integrity and fine‐grained privacy protection. However, the signing overhead of ABS is usually too large, making it unsuitable for resource‐constrained devices. Using cloud computing technology, the notion of outsourced attribute‐based signatures (OABS) was introduced to overcome this drawback. In OABS, the user can outsource him/her signing tasks to the signing‐cloud service provider (S‐CSP). The previous notion of privacy of OABS does not take the S‐CSP's attack into account, so it is not strong enough. To conform to the reality of cloud computing, we present a more accurate notion of privacy, called perfect privacy, which ensures that any adversary, even the S‐CSP, cannot identify which policy is used to generate the signature. Then, we propose a key‐policy OABS scheme for circuits based on multilinear mapping with perfect privacy. By using the outsourcing technique, in our scheme, the computation cost of the signer is only three or four pairing operations, which is independent of the complexity of the policy and the size of the attribute set. Our scheme achieves three advantages: perfect privacy, expressive policy, and constant signing cost, simultaneously.

АНАЛИЗ ВЛИЯНИЯ КОНСЕРВАТИВНОГО СГЛАЖИВАНИЯ КОНЕЧНО-ЭЛЕМЕНТНОГО РЕШЕНИЯ НА ПОДАВЛЕНИЕ МОД НУЛЕВОЙ ЭНЕРГИИ

The problem of high-speed penetration of a non-deformable cylinder into a steel plate is considered. The defining system of equations is formulated in Lagrange variables in a three-dimensional formulation. The equation of motion is derived from virtual work capacities balance. Kinematic relations are recorded in the metric of the current state. The relations of the flow theory with kinematic and isotropic hardening are used as equations of state. The contact interaction of the cylinder and the plate is modeled by non-penetration conditions. The numerical solution of the problem under given boundary and initial conditions is based on the moment scheme of the finite element method and “cross” type explicit time integration scheme. To discretize the defining system of equations with respect to spatial variables, 8-node isoparametric finite elements with multilinear form functions are used. To suppress the high-frequency oscillations of the numerical solution, the procedure of nodal displacement velocities conservative smoothing is used. The smoothing algorithm is based on the momentum conservation law, focused on finite element grids consisting of blocks that are mutually unambiguously mapped to a unit cube. To analyze the nodal displacement velocities monotonicity, the numerical solution splitting in the directions of the finite element grid lines is used. As the results of computer modeling have shown, the finite elements of the plate are exposed large deformations and rotation angles as a rigid whole during local intense dynamic loading. The conservative smoothing procedure influence on the numerical solution stability is analyzed. It is shown that in the problem under consideration, without applying the conservative smoothing procedure, zero-energy modes develop in the contact zone in the finite-element grid of the plate (an hourglass-type instability) and the collision process cannot be modeled before the cylinder rebounds.

Special Trilinear Functions with Few Applications

Special bilinear functions (SBF) proved to be applicable in many situations and for a good number of problems. Hence it is important to generalize them to a higher degree by expanding previous work. In the beginning, we give a quick review of SBF [or quacroms of second degree and dimension 2 x n]; then we give a few applications based on previously published research concentrating on their use in evaluating some special functions and where we present the evaluation of Chebyshev polynomials as a new work. Following that, we define special trilinear functions (STF) of three n-tuples vectors, which are the generalization of SBF. Finally, a few applications, such as taking the product of three polynomials of degree n, are given stressing the fact that the process of taking the product of three integers using STF techniques, practically, takes place in a very efficient way and with no mentioned effort. A short discussion on the future of the subject constitutes the conclusion of our article.

Simultaneous diagonalization of incomplete matrices and applications

We consider the problem of recovering the entries of diagonal matrices $\{U_a\}_a$ for $a = 1,\ldots,t$ from multiple incomplete samples $\{W_a\}_a$ of the form $W_a=PU_aQ$, where $P$ and $Q$ are unknown matrices of low rank. We devise practical algorithms for this problem depending on the ranks of $P$ and $Q$. This problem finds its motivation in cryptanalysis: we show how to significantly improve previous algorithms for solving the approximate common divisor problem and breaking CLT13 cryptographic multilinear maps.

Stress-strain state of shell of revolution analysis by using various formulations of three-dimensional finite elements

The aim of the work is to perform a comparative analysis of the results of analyzing arbitrarily loaded shells of revolution using finite element method in various formulations, namely, in the formulation of the displacement method and in the mixed formulation. Methods. To obtain the stiffness matrix of a finite element a functional based on the equality of the actual work of external and internal forces was applied. To obtain the deformation matrix in the mixed formulation the functional obtained from the previous one by replacing the actual work of internal forces in it with the difference of the total and additional work was used. Results. In the formulation of the displacement method for an eight-node hexahedral solid finite element, displacements and their first derivatives are taken as the nodal unknowns. Approximation of the displacements of the inner point of the finite element was carried out through the nodal unknowns on the basis of the Hermite polynomials of the third degree. For a finite element in the mixed formulation, displacements and stresses were taken as nodal unknowns. Approximation of the target finite element values through their nodal values in the mixed formulation was carried out on the basis of trilinear functions. It is shown on a test example that a finite element in the mixed formulation improves the accuracy of the strength parameters of the shell of revolution stress-strain state.

Weighted Entropy Minimization Based Deep Conditional Adversarial Diagnosis Approach Under Variable Working Conditions

Intelligent mechanical fault diagnosis is a crucial measure to ensure the safe operation of equipment. To address the issue of model collapse in domain adversarial training and the problem posed by different training samples having different transferability not considered in transfer tasks, this article proposes a weighted entropy minimization based deep conditional adversarial diagnosis approach of rotating machines under variable working conditions. First, the features of vibration signals in the source domain and target domain are extracted by a weight-sharing one-dimensional deep convolution neural network. The feature vectors and category prediction vectors are then fused by multilinear mapping to carry out adversarial training in domain adaptation. The entropy of the output of the domain discrimination model provides the index by which to measure the transferability of training samples. The transferability weights of samples are applied to the entropy minimization loss to eliminate the influence of these samples that are hard to transfer in adversarial domain adaptation. Experimental datasets under variable working conditions support the value of our approach.

Linear and multilinear functional identities in a prime ring with applications

This paper approaches some universal-algebraic properties of the two kinds of multilinear functions [Formula: see text] and [Formula: see text] in a prime ring [Formula: see text], where [Formula: see text] are variable elements, [Formula: see text]. We shall demonstrate an algebraic procedure of deriving necessary and sufficient conditions for the two multilinear functional identities [Formula: see text] and [Formula: see text] to hold for all [Formula: see text], [Formula: see text]. Subsequently, we use these multilinear functional identities to describe the invariance properties of the products [Formula: see text] [Formula: see text], [Formula: see text], [Formula: see text] with respect to the eight commonly-used types of generalized inverses of two MP-invertible elements [Formula: see text] and [Formula: see text] in a prime ring [Formula: see text] with an identity element 1 and ∗-involution.

Attenuation of ground-motion spectral amplitudes in central and eastern Iran

In this study, more than 2769 seismograms of 633 earthquakes recorded by 18 stations of the Iranian Seismological Center (IRSC) during 2006–2016, were used to estimate the spectral attenuation relation for strong ground motion in central and eastern Iran. First, In frequency domain by using a local regression smoothing method (robust LOWESS), through considering Hinged trilinear function, the distances at which the nature of geometrical spreading attenuation changes significantly was graphically found in 80 km and 124 km distances. Then, using a brute force optimization, it's found that b1 = −1.11 ± 0.27, b2 = 0.09 ± 0.22, and b3 = −0.70 ± 0.23 minimize the average absolute value of the Fourier spectrum amplitude residuals. Finally, the direct quality factor Q in the study region is obtained as Q = 166 ± 1.08f0.62±0.02, using an anelastic attenuation coefficient at different frequencies. The geographical distribution of station corrections at 1 Hz shows a positive station correction for east and the southeastern part of Iran in Kerman province.

Bolted ring flanges in offshore-wind support structures - in-situ validation of load-transfer behaviour

Offshore wind turbines are subjected to cyclic loads from wind and waves, ultimately resulting in a fatigue-driven design. These cyclic loads result in cyclic shell forces above the bolted ring flange and ultimately into the cyclic loading of the bolt tension forces. To model the transfer of the shell forces into the bolt, Load Transfer Functions (LTF) are used, of which the tri-linear function according Schmidt/Neuper is the most known approximation but more contemporary approaches exist. As the LTF has a significant impact on the estimated fatigue lifetime of the bolt, it is relevant to investigate the accuracy of the currently used LTF.This paper uses in-situ monitoring data from three offshore wind turbines at the Nobelwind windfarm, each equipped with an instrumented bolt in the monopile to transition piece bolted flange connection and strain-gauges above said flange. Long-term monitoring data is used to derive empirical load transfer coefficients (LTC), i.e. the derivatives of the LTF. In parallel a finite element model (FE model) of the flange connection was developed. The found load transfer coefficients from measurements were compared to the values obtained from the function according to Schmidt/Neuper and the FE model.It is concluded that the observed LTC in the offshore wind farm were favourable compared to the values expected from Schmidt/Neuper. The FE model matched more closely, especially when the MP-flange inclination was included. The inclusion of the MP-flange inclination in the model had a positive effect on the final LTF, which was confirmed by the measurements.

Identification of surface active components in glass forming melts by thermodynamic model

Nine compositional series of 15(Na2O, K2O)•10(CaO, ZnO)•75(ZrO2, SiO2) glass-forming melts were studied, all with the ZrO2 content of 0, 1, 3, 5 and 7 mol.%. The investigated glass compositions were obtained by equimolar substitutions ZrO2 / SiO2, ZnO / CaO and K2O / Na2O. Surface tension of studied glassforming melts was determined by the sessile and pendant drop profile numerical analysis in the temperature range (1250 - 1500) °C. The experimental values of melt density were used. The linear temperature dependence of surface tension was observed for all samples with only small differences between values obtained from sessile and pendant drop profiles. The Shakhmatkin and Vedishcheva thermodynamic model (TDM) was evaluated for each glass melt at temperature of 1400 °C. The total number of 36 components was considered in TDM. Only 26 components were present with non-negligible equilibrium amount. The surface tension was described by the multilinear function of equilibrium amounts of statistically independent non-negligible components of the TDM. The surface active components were identified by negative values of their coefficients. Such way the N3S8 and C2ZrS4 were identified as “strongly” surface active and NCS5 and KS4 as probably surface active. Regarding the oxide compositional point of view, the surface tension was mostly influenced by ZnO (increase with the addition of the oxide) and by K2O (decrease with the addition of the oxide).

On Ulam Stability of a Functional Equation

In this note, we study the Ulam stability of a functional equation both in Banach and m-Banach spaces. Particular cases of this equation are, among others, equations which characterize multi-additive and multi-Jensen functions. Moreover, it is satisfied by the so-called multi-linear mappings.

Congruence of matrix spaces, matrix tuples, and multilinear maps

Two matrix vector spaces V,W⊂Cn×n are said to be equivalent if SVR=W for some nonsingular S and R. These spaces are congruent if R=ST. We prove that if all matrices in V and W are symmetric, or all matrices in V and W are skew-symmetric, then V and W are congruent if and only if they are equivalent.Let F:U×…×U→V and G:U′×…×U′→V′ be symmetric or skew-symmetric k-linear maps over C. If there exists a set of linear bijections φ1,…,φk:U→U′ and ψ:V→V′ that transforms F to G, then there exists such a set with φ1=…=φk.

Practical CCA-Secure Functional Encryptions for Deterministic Functions

Functional encryption (FE) can implement fine-grained control to encrypted plaintext via permitting users to compute only some specified functions on the encrypted plaintext using private keys with respect to those functions. Recently, many FEs were put forward; nonetheless, most of them cannot resist chosen-ciphertext attacks (CCAs), especially for those in the secret-key settings. This changed with the work, i.e., a generic transformation of public-key functional encryption (PK-FE) from chosen-plaintext (CPA) to chosen-ciphertext (CCA), where the underlying schemes are required to have some special properties such as restricted delegation or verifiability features. However, examples for such underlying schemes with these features have not been found so far. Later, a CCA-secure functional encryption from projective hash functions was proposed, but their scheme only applies to inner product functions. To construct such a scheme, some nontrivial techniques will be needed. Our key contribution in this work is to propose CCA-secure functional encryptions in the PKE and SK environment, respectively. In the existing generic transformation from (adaptively) simulation-based CPA- (SIM-CPA-) secure ones for deterministic functions to (adaptively) simulation-based CCA- (SIM-CCA-) secure ones for randomized functions, whether the schemes were directly applied to CCA settings for deterministic functions is not implied. We give an affirmative answer and derive a SIM-CCA-secure scheme for deterministic functions by making some modifications on it. Again, based on this derived scheme, we also propose an (adaptively) indistinguishable CCA- (IND-CCA-) secure SK-FE for deterministic functions. The final results show that our scheme can be instantiated under both nonstandard assumptions (e.g., hard problems on multilinear maps and indistinguishability obfuscation (IO)) and under standard assumptions (e.g., DDH, RSA, LWE, and LPN).

A Path-Based Partial Information Decomposition.

Based on the conceptual basis of information theory, we propose a novel mutual information measure—‘path-based mutual information’. This information measure results from the representation of a set of random variables as a probabilistic graphical model. The edges in this graph are modeled as discrete memoryless communication channels, that is, the underlying data is ergodic, stationary, and the Markov condition is assumed to be applicable. The associated multilinear stochastic maps, tensors, transform source probability mass functions into destination probability mass functions. This allows for an exact expression of the resulting tensor of a cascade of discrete memoryless communication channels in terms of the tensors of the constituting communication channels in the paths. The resulting path-based information measure gives rise to intuitive, non-negative, and additive path-based information components—redundant, unique, and synergistic information—as proposed by Williams and Beer. The path-based redundancy satisfies the axioms postulated by Williams and Beer, the identity axiom postulated by Harder, and the left monotonicity axiom postulated Bertschinger. The ordering relations between redundancies of different joint collections of sources, as captured in the redundancy lattices of Williams and Beer, follow from the data processing inequality. Although negative information components can arise, we speculate that these either result from unobserved variables, or from adding additional sources that are statistically independent from all other sources to a system containing only non-negative information components. This path-based approach illustrates that information theory provides the concepts and measures for a partial information decomposition.

Is mainstream LCA linear?

PurposeIt is frequently mentioned in literature that LCA is linear, without a proof, or even without a clear definition of the criterion for linearity. Here we study the meaning of the term linear, and in relation to that, the question if LCA is indeed linear.MethodsWe explore the different meanings of the term linearity in the context of mathematical models. This leads to a distinction between linear functions, homogeneous functions, homogenous linear functions, bilinear functions, and multilinear functions. Each of them is defined in accessible terms and illustrated with examples.ResultsWe analyze traditional, matrix-based, LCA, and conclude that LCA is not linear in any of the senses defined.Discussion and conclusionsDespite the negative answer to the research question, there are many respects in which LCA can be regarded to be, at least to some extent, linear. We discuss a few of such cases. We also discuss a few practical implications for practitioners of LCA and for developers of new methods for LCI and LCIA.

SUPERVISED MANIFOLD-LEARNING ALGORITHM FOR POLSAR FEATURE EXTRACTION AND LULC CLASSIFICATION

Abstract. In this paper, a supervised manifold-learning method is proposed for PolSAR feature extraction and classification. Based on the tensor algebra, the proposed method characterizes each pixel with a local neighbourhood centered at it, thereby combining the spatial and polarimetric information within the image. The inherent spatial information is beneficial to alleviate the influence of speckle noise and improve the stability of the extracted features. In addition, the label information of training samples is utilized in feature extraction, therefore the discriminability of different classes can be well preserved. The tensor discriminative locality alignment (TDLA) method is applied to find the multilinear transformation from the original feature space to the low-dimensional feature space. Based on the extracted features in the low-dimensional space, the SVM classifier is applied to achieve the final classification result. A real PolSAR data set acquired over San Francisco is adopted for performance evaluation. The experimental results show that the proposed method can not only improve the classification accuracy, but also alleviate the influence of speckle noise. In addition, the spatial details can be well preserved, demonstrating the superior performance of the proposed method.

Determination of Local Magnitude for Earthquakes Recorded from the Texas Seismological Network (TexNet)

AbstractIn this study, we present a local magnitude (ML) relation for the earthquakes recorded from the Texas Seismological Network (TexNet) between the dates of 1 January 2017 and 31 July 2019. Using a comprehensive seismic dataset from earthquakes in Texas, we propose a distance correction term −logA0, which is consistent with the original definition of the Richter magnitude. The proposed distance correction calculation for the TexNet events accounts for the attenuation characteristics of the direct and refracted waves over different distance ranges. Regression analysis of Wood–Anderson amplitudes results in the following trilinear function, which represents the attenuation attributes of the events under investigation: −logA0={2.07×log(Rhyp)+0.0002×(Rhyp−100)−0.72Rhyp≤16 km1.54×log(Rhyp)+0.0002×(Rhyp−100)−0.0816 km<Rhyp≤105 km,0.29×log(Rhyp)+0.0002×(Rhyp−100)+2.45Rhyp>105 km in which Rhyp is the hypocentral distance (km). The derived distance correction relationship results in an accurate ML relationship for Texas that is unbiased over a 200 km distance range. Compared with other ML relations, the proposed relation in this study gives lower ML values over all distances than those calculated by Richter (1958), Hutton and Boore (1987), Babaie Mahani and Kao (2019), and Quinones et al. (2019) by an average of 0.01, 0.12, 0.16, and 0.15 units, respectively; this study’s proposed relation gives higher ML values over all distances than those calculated by Scales et al. (2017), Yenier (2017), and Greig et al. (2018) by an average of 0.28, 0.01, and 0.08 units, respectively.

Structure-based design and activity modeling of novel epidermal growth factor receptor kinase inhibitors; an in silico approach

The development of EGFR kinase inhibitors to treat non-small cell lung cancers is an important medical necessity due to persistent development of resistance by the mutations. In-view of this, a model with a very high predictive ability on thirty (30) EGFR kinase inhibitors was built using QSAR molecular modeling technique. Density Functional Theory method at B3LYP/6-311G* level of theory was used to identify the optimum conformation of the EGFR kinase inhibitors. A Multi-linear regression Genetic Function Algorithm method (MLR-GFA) was used to build five models. The described model among others was selected and reported since it has passed the requirements for good model validation with resulting parameters: R2 of 0.927451, R2adj of 0.901845, Q2CV of 0.869431R2test of 0.767984 and cRp2 of 0.625651. Molecular docking, drug-likeness and ADME studies were carried out to virtually screen these EGFR kinase inhibitors in order to identify a compound with the highest affinity toward the target protein (EGFR kinase enzyme with pdb entry 3IKA) with good pharmacokinetic profile. Compound 11 was identified as the lead compound with the highest binding affinity of −9.8 kcal/mol (and also with good ADME and drug-likeness properties) and was retained as template for designing new EGFR kinase inhibitors. Six new EGFR kinase inhibitors were designed using compound 11 as template. The newly designed compounds were found to have better affinity toward their target protein than the template and Gefitinib (positive control). The reported model predictive performance was further confirmed by predicting the pIC50 of these newly designed compounds.

Location Privacy-Preserving Distance Computation for Spatial Crowdsourcing

Data privacy, especially location privacy, is paramountly important for protecting individual's information in smart cities in the big data era. One of the examples is in spatial crowdsourcing (SC). It enables people not only to issue spatiotemporal tasks to ask for help as requesters but also to solve others' tasks as workers on the SC platform. While SC brings convenience to people, it also produces severe location privacy problems, which have been recently paid more attention from both academia and industries. In this article, we address the location privacy problem in SC in a practical and secure way. We propose a location privacy-preserving framework for almost all existed mainstream distance computations in the SC system, namely, Euclidean-L3P, Minkowski-L3P, Manhattan-L3P, and Chebyshev-L3P, among which the first two are constructed based on homomorphic encryption and composite-order multilinear mapping while the latter two on the homomorphic encryption and prefix membership verification approach. Location privacy is resolved because of the above techniques having enabled that all distance computations are evaluated through ciphertexts without disclosing any location information. Security analysis shows that our framework can prevent a strong adversary from obtaining participants' location privacy. Performance analysis evaluates computation and communication overheads between protocols. The results show that Euclidean-L3P is more efficient than Manhattan-L3P and Chebyshev-L3P in terms of computation overheads when the SC applications require a small number of participants, a large plaintext space, and a small number of base stations. Moreover, compared with Manhattan-L3P and Chebyshev-L3P, Euclidean-L3P is a better choice in terms of communication overhead.

Security analysis of indistinguishable obfuscation for internet of medical things applications

As a powerful cryptographic primitive, indistinguishable obfuscation has been widely used to protect data privacy on the Internet of Medical Things (IoMT) systems. Basically, the cryptographic technique protects data privacy using a function to obfuscate medical applications to perform outputs computationally indistinguishable. The state-of-the-art obfuscation technique (GGH13) utilizes a variant of the multilinear map to enhance security. However, in such schemes, it can be observed that noise lies in each element of the matrix, which means the matrix is a full rank matrix with a probability of almost 1 and results that it is unable to establish the relationship between the matrix determinant and rank. In this paper, we propose an attack to break such obfuscator. Specifically, we use approximate eigenvalues to remove the influence of noise on the matrix eigenvalues and build a specific relationship between the determinant and matrix rank. Our analysis shows the structural weakness of the state-of-the-art indistinguishable obfuscation mechanism, and we further discuss the future direction to resolve such privacy issues for IoMT applications.