Novel Scheme for Robust Confusion Component Selection Based on Pythagorean Fuzzy Set

The substitution box,often known as an S-box,is a nonlinear component that is a part of several block ciphers.Its purpose is to protect cryptographic algorithms from a variety of cryptanalytic assaults.A Multi-Criteria Decision Making(MCDM)problem has a complex selection procedure because of having many options and criteria to choose from.Because of this,statistical methods are necessary to assess the performance score of each S-box and decide which option is the best one available based on this score.Using the Pythagorean Fuzzy-based Technique for Order of Preference by Similarity to Ideal Solution(TOPSIS)method,the major objective of this investigation is to select the optimal S-box to be implemented from a pool of twelve key choices.With the help of the Pythagorean fuzzy set(PFS),the purpose of this article is to evaluate whether this nonlinear component is suitable for use in a variety of encryption applications.In this article,we have considered various characteristics of S-boxes,including nonlinearity,algebraic degree,strict avalanche criterion(SAC),absolute indicator,bit independent criterion(BIC),sum of square indicator,algebraic immunity,transparency order,robustness to differential cryptanalysis,composite algebraic immunity,signal to noise ratio-differential power attack(SNR-DPA),and confusion coefficient variance on some standard S-boxes that are Advanced Encryption Following this,the findings of the investigation are changed into Pythagorean fuzzy numbers in the shape of a matrix.This matrix is then subjected to an analysis using the TOPSIS method,which is dependent on the Pythagorean fuzzy set,to rank the most suitable S-box for use in encryption applications.

Classification of Nonlinear Confusion Component Using Hybrid Multi-Criteria Decision Making

In today’s digital world,the most inevitable challenge is the protection of digital information.Due to the weak confidentiality preserving techniques,the existing world is facing several digital information breaches.To make our digital data indecipherable to the unauthorized person,a technique forfinding a crypto-graphically strong Substitution box(S-box)have presented.An S-box with sound cryptographic assets such as nonlinearity(NL),strict avalanche criterion(SAC),bit independence criteria(BIC),bit independence criteria of nonlinearity(BIC-NL),Bit independence criteria of Strict avalanche criteria(BIC-SAC),and Input/output XOR is considered as the robust S-box.The Decision-Making Trial and Evaluation Laboratory(DEMATEL)approach of multi-criteria decision making(MCDM)is proposed forfinding the interrelation among cryptographic properties.A combination of two MCDM methods namely Entropy and multi-objective optimization based on ratio analysis(MOORA)is applied for the best S-box selection.A robust substitution box is selected for secure communications in cryptography by using the combination of DEMETAL selection criteria,entro-py weight assigning,and MOORA ranking scheme.The combination of these three methods provides a fast selection procedure for the secure confusion com-ponent.The offered selection method can also be utilized for the choice of the best cryptosystem with highly secure properties and resistive against all possible linear and differential attacks in the cryptanalysis.

Hydrocephalic cerebrospinal fluid flowing rotationally with pulsatile boundaries:A mathematical simulation of the thermodynamical approach

To study the kinematics of flow rate and ventricular dilatation,an analytical perturbation approach of hydrocephalus has been devised.This research provides a comprehensive investigation of the characteristics of cerebrospinal fluid(CSF)flow and pressure in a hydrocephalic patient.The influence of hydrocephalic CSF,flowing rotationally with realistic dynamical characteristics on pulsatile boundaries of subarachnoid space,was demonstrated using a nonlinear controlling system of CSF.An analytical perturbation method of hydrocephalus has been developed to investigate the biomechanics of fluid flow rate and the ventricular enlargement.In this paper presents a detailed analysis of CSF flow and pressure dynamics in a hydrocephalic patient.It was elaborated with a nonlinear governing model of CSF to show the influence of hydrocephalic CSF,flowing rotationally with realistic dynamical behaviors on pulsatile boundaries of subarachnoid space.In accordance with the suggested model,the elasticity factor changes depending on how much a porous layer,in this case the brain parenchyma,is stretched.It was improved to include the relaxation of internal mechanical stresses for various perturbation orders,modelling the potential plasticity of brain tissue.The initial geometry that was utilised to create the framework of CSF with pathological disease hydrocephalus and indeed the output of simulations using this model were compared to the actual progression of ventricular dimensions and shapes in patients.According to this observation,the non-linear and elastic mechanical phenomena incorporated into the current model are probably true.Further modelling of ventricular dilation at a normal pressure may benefit from the existence of a valid model whose parameters approximate genuine mechanical characteristics of the cerebral cortex.

Generalization of Advanced Encryption Standard Based on Field of Any Characteristic

Nowadays most communications are done by utilizing digital transmission mechanisms.The security of this digital information transmitted through different communication systems is quite important.The secrecy of digital data is one of the burning topics of the digitally developed world.There exist many traditional algorithms in the literature to provide methods for robust communication.The most important and recent modern block cipher named the advanced encryption standard(AES)is one of the extensively utilized encryption schemes with binary based.AES is a succession of four fundamental steps:round key,sub-byte,shift row,and mix column.In this work,we will provide an innovative methodology for extending the AES in a Galois fieldwith any characteristic p.All four steps in the fundamental process with binary characteristics will be adjusted because of the new enhancement.By applying double affine transformations,we have enhanced the number of options in our suggested substitution boxes.The reconstruction of the nonlinear confusion component and encryption structure provides robustness in the generalized AES.The increase in the keyspace due to the Galois field generalization implies that we have improved additional confusion abilities and broadened the current notions.The implementation of the proposed structure of AES for image,audio,and video encryption will provide high security for secure communication.

An Efficient Three-Factor Authenticated Key Agreement Technique Using FCM Under HC-IoT Architectures

The Human-Centered Internet of Things(HC-IoT)is fast becoming a hotbed of security and privacy concerns.Two users can establish a common session key through a trusted server over an open communication channel using a three-party authenticated key agreement.Most of the early authenticated key agreement systems relied on pairing,hashing,or modular exponentiation processes that are computationally intensive and cost-prohibitive.In order to address this problem,this paper offers a new three-party authenticated key agreement technique based on fractional chaotic maps.The new scheme uses fractional chaotic maps and supports the dynamic sensing of HC-IoT devices in the network architecture without a password table.The projected security scheme utilized a hash function,which works well for the resource-limited HC-IoT architectures.Test results show that our new technique is resistant to password guessing attacks since it does not use a password.Furthermore,our approach provides users with comprehensive privacy protection,ensuring that a user forgery attack causes no harm.Finally,our new technique offers better security features than the techniques currently available in the literature.

Nuclear mass predictions based on a deep neural network and finite-range droplet model(2012)

A neural network with two hidden layers is developed for nuclear mass prediction,based on the finiterange droplet model(FRDM12).Different hyperparameters,including the number of hidden units,choice of activation functions,initializers,and learning rates,are adjusted explicitly and systematically.The resulting mass predictions are achieved by averaging the predictions given by several different sets of hyperparameters with different regularizers and seed numbers.This can provide not only the average values of mass predictions but also reliable estimations in the mass prediction uncertainties.The overall root-mean-square deviations of nuclear mass are reduced from 0.603 MeV for the FRDM12 model to 0.200 MeV and 0.232 MeV for the training and validation sets,respectively.

Selected Topics in Computational Mathematics

Computational mathematics is a discipline of mathematical research in areas of science where computation plays a central and essential role. Our everyday lives have been transformed by the impact of computation and communication.

质量超过0.98M_(TOV)的中子星的内核呈现奇异新物态

本文综合利用GW170817、PSR J0030+0451以及PSR J0740+6620的多信使数据及最新的手征有效场论和微扰量子色动力学计算信息,研究了中子星的状态方程.利用贝叶斯非参数推理中使用的单层前馈神经网络模型对各种状态方程结构进行采样,以非模型依赖的方式研究了中子星物质声速的结构.发现声速曲线中峰结构非常普遍,通常出现在2.4~4.8倍核饱和密度处,且声速平方在90%置信水平下超过真空中光速平方的1/3.这种非单调行为表明质量非常大的中子星中的物态偏离了纯强子物质.如果新的/奇异的物态比典型的强子模型甚至含有超子的模型都要软,作者发现引力质量在0.98M_(TOV)以上的中子星很可能存在一个超过10^(-3)M⊙的极可能由夸克物质组成的奇异核,这里的M_(TOV)=2.18_(-0.13)^(+0.27)M⊙(90%置信区间)是限制得到的慢转中子星的最大引力质量,它与GW170817/GRB 170817A/AT2017gfo的暂现超重中子星遗迹模型得到的2.17_(-0.12)^(+0.15)M⊙高度一致.对于迄今为止探测到的质量最大的中子星PSR J0740+6620,研究发现它含有一个奇异内核的概率约为36%.

Neural network representation of electronic structure from ab initio molecular dynamics

Despite their rich information content,electronic structure data amassed at high volumes in ab initio molecular dynamics simulations are generally under-utilized.We introduce a transferable high-fidelity neural network representation of such data in the form of tight-binding Hamiltonians for crystalline materials.This predictive representation of ab initio electronic structure,combined with machinelearning boosted molecular dynamics,enables efficient and accurate electronic evolution and sampling.When it is applied to a one-dimension charge-density wave material,carbyne,we are able to compute the spectral function and optical conductivity in the canonical ensemble.The spectral functions evaluated during soliton-antisoliton pair annihilation process reveal significant renormalization of low-energy edge modes due to retarded electron-lattice coupling beyond the Born-Oppenheimer limit.The availability of an efficient and reusable surrogate model for the electronic structure dynamical system will enable calculating many interesting physical properties,paving the way to previously inaccessible or challenging avenues in materials modeling.

Heterogeneous Multiscale Methods: A Review

This paper gives a systematic introduction to HMM,the heterogeneous multiscale methods,including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be overcome when using HMM for a particular problem.This is illustrated by examples from several application areas,including complex fluids,micro-fluidics,solids,interface problems,stochastic problems,and statistically self-similar problems.Emphasis is given to the technical tools,such as the various constrained molecular dynamics,that have been developed,in order to apply HMM to these problems.Examples of mathematical results on the error analysis of HMM are presented.The review ends with a discussion on some of the problems that have to be solved in order to make HMM a more powerful tool.

Truncated Gaussian RBF Differences are Always Inferior to Finite Differences of the Same Stencil Width

Radial basis functions(RBFs)can be used to approximate derivatives and solve differential equations in several ways.Here,we compare one important scheme to ordinary finite differences by a mixture of numerical experiments and theoretical Fourier analysis,that is,by deriving and discussing analytical formulas for the error in differentiating exp(ikx)for arbitrary k.‘Truncated RBF differences”are derived from the same strategy as Fourier and Chebyshev pseudospectral methods:Differentiation of the Fourier,Chebyshev or RBF interpolant generates a differentiation matrix that maps the grid point values or samples of a function u(x)into the values of its derivative on the grid.For Fourier and Chebyshev interpolants,the action of the differentiation matrix can be computed indirectly but efficiently by the Fast Fourier Transform(FFT).For RBF functions,alas,the FFT is inapplicable and direct use of the dense differentiation matrix on a grid of N points is prohibitively expensive(O(N2))unless N is tiny.However,for Gaussian RBFs,which are exponentially localized,there is another option,which is to truncate the dense matrix to a banded matrix,yielding“truncated RBF differences”.The resulting formulas are identical in form to finite differences except for the difference weights.On a grid of spacing h with the RBF asφ(x)=exp(−α^(2)(x/h)^(2)),d f dx(0)≈∑^(∞)_(m)=1 wm{f(mh)−f(−mh)},where without approximation wm=(−1)m+12α^(2)/sinh(mα^(2)).We derive explicit formula for the differentiation of the linear function,f(X)≡X,and the errors therein.We show that Gaussian radial basis functions(GARBF),when truncated to give differentiation formulas of stencil width(2M+1),are significantly less accurate than(2M)-th order finite differences of the same stencil width.The error of the infinite series(M=∞)decreases exponentially asα→0.However,truncated GARBF series have a second error(truncation error)that grows exponentially asα→0.Even forα∼O(1)where the sum of these two errors is minimized,it is shown that the finite difference formulas are always superior.We explain,less rigorously,why these arguments extend to more general species of RBFs and to an irregular grid.There are,however,a variety of alternative differentiation strategies which will be analyzed in future work,so it is far too soon to dismiss RBFs as a tool for solving differential equations.

Deep potentials for materials science

To fill the gap between accurate(and expensive)ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials,a new class of descriptions of atomic interactions has emerged and been widely applied;i.e.machine learning potentials(MLPs).One recently developed type of MLP is the deep potential(DP)method.In this review,we provide an introduction to DP methods in computational materials science.The theory underlying the DP method is presented along with a step-by-step introduction to their development and use.We also review materials applications of DPs in a wide range of materials systems.The DP Library provides a platform for the development of DPs and a database of extant DPs.We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

Lattice quantum chromodynamics and baryon-baryon interactions

After briefly reviewing the theoretical concepts and numerical methods in lattice QCD, recent sireulation results of the hadron masses and hadron interactions with nearly physical quark masses are presented. Special emphasis is placed on the baryon-baryon interactions on the basis of the HAL QCD method where the integro-differential equation for the equal-time Nambu-Bethe-Salpeter amplitude plays a key role to bridge a gap between the multi-baryon correlation and the scattering observable such as the phase shift.

The Elastic Continuum Limit of the Tight Binding Model

The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.

Simulation of Impurity Diffusion in a Strained Nanowire Using Off-Lattice KMC

Kinetic Monte Carlo(KMC)is a stochastic model used to simulate crystal growth.However,most KMC models rely on a pre-defined lattice that neglects dislocations,lattice mismatch and strain effects.In this paper,we investigate the use of a 3D off-lattice KMC algorithm.We test this method by investigating impurity diffusion in a strained FCC nanowire.While faster than a molecular dynamics simulation,the most general implementation of off-lattice KMC is much slower than a lattice-based algorithm.An improved procedure is achieved for weakly strained systems by precomputing approximate saddle point locations based on unstrained lattice structures.In this way,one gives up some of the flexibility of the general method to restore some of the computational speed of lattice-based KMC.In addition to providing an alternative approach to nano-materials simulation,this type of simulation will be useful for testing and calibrating methods that seek to parameterize the variation in the transition rates for lattice-based KMC using continuum modeling.

Effective Maxwell Equations from Time-dependent Density Functional Theory

The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting from time-dependent density functional theory. Effective permittivity and permeability coefficients are obtained.

Optimization-Based String Method for Finding Minimum Energy Path

We present an efficient algorithm for calculating the minimum energy path(MEP)and energy barriers between local minima on a multidimensional potential energy surface(PES).Such paths play a central role in the understanding of transition pathways between metastable states.Our method relies on the original formulation of the string method[Phys.Rev.B,66,052301(2002)],i.e.to evolve a smooth curve along a direction normal to the curve.The algorithm works by performing minimization steps on hyperplanes normal to the curve.Therefore the problem of finding MEP on the PES is remodeled as a set of constrained minimization problems.This provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method[J.Chem.Phys.,126(16),164103(2007)].At the same time,it provides a more direct analog of the finite temperature string method.The applicability of the algorithm is demonstrated using various examples.