Log in

Relevant bibliographies by topics / Box polynomial / Journal articles

To see the other types of publications on this topic, follow the link: Box polynomial.

Journal articles on the topic 'Box polynomial'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Box polynomial.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Alamsyah, Alamsyah. "A Novel Construction of Perfect Strict Avalanche Criterion S-box using Simple Irreducible Polynomials." Scientific Journal of Informatics 7, no. 1 (May 30, 2020): 10–22. http://dx.doi.org/10.15294/sji.v7i1.24006.

Full text

Abstract:

An irreducible polynomial is one of the main components in building an S-box with an algebraic technique approach. The selection of the precise irreducible polynomial will determine the quality of the S-box produced. One method for determining good S-box quality is strict avalanche criterion will be perfect if it has a value of 0.5. Unfortunately, in previous studies, the strict avalanche criterion value of the S-box produced still did not reach perfect value. In this paper, we will discuss S-box construction using selected irreducible polynomials. This selection is based on the number of elements of the least amount of irreducible polynomials that make it easier to construct S-box construction. There are 17 irreducible polynomials that meet these criteria. The strict avalanche criterion test results show that the irreducible polynomial p17(x) =x8 + x7 + x6 + x + 1 is the best with a perfect SAC value of 0.5. One indicator that a robust S-box is an ideal strict avalanche criterion value of 0.5

APA, Harvard, Vancouver, ISO, and other styles

2

Goodman, T. N. T., and S. L. Lee. "Homogeneous polynomial splines." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 117, no. 1-2 (1991): 89–102. http://dx.doi.org/10.1017/s0308210500027621.

Full text

Abstract:

SynopsisWe construct functions which are piecewise homogeneous polynomials in the positive octant in three dimensions. These give a rich and elegant theory which combines properties of polynomial box splines see [6] and the references therein) with the explicit representation of simple exponential box splines [11], while enjoying complete symmetry in the three variables. By a linear transformation followed by a projection on suitable planes, one obtains piecewise polynomial functions of two variables on a mesh formed by three pencils of lines. The vertices of these pencils may be finite or one or two may be infinite, i.e. the corresponding pencils may comprise parallel lines. As a limiting case, all three vertices become infinite and one recovers polynomial box splines on a three-direction mesh.

APA, Harvard, Vancouver, ISO, and other styles

3

Encarnación, Mark J. "Black-box polynomial resultants." Information Processing Letters 61, no. 4 (February 1997): 201–4. http://dx.doi.org/10.1016/s0020-0190(97)00016-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Mahmood, Shahid, Shabieh Farwa, Muhammad Rafiq, Syed Muhammad Jawwad Riaz, Tariq Shah, and Sajjad Shaukat Jamal. "To Study the Effect of the Generating Polynomial on the Quality of Nonlinear Components in Block Ciphers." Security and Communication Networks 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/5823230.

Full text

Abstract:

Substitution box (S-box), being the only nonlinear component, contributes to the confusion creating capability of a cryptosystem. Keeping in view the predominant role of S-box, many design algorithms to synthesize cryptographically stronger S-boxes have gained pivotal attention. A quick review of these algorithms shows that all these ideas mainly concentrate on the choice of bijective Boolean functions, with nonobservance to the irreducible polynomial that generates the Galois field. In this paper, we propose that the selection of irreducible polynomial has a deep influence on the highly desirable features of an S-box such as nonlinearity, strict avalanche, bit independence, linear approximation probability, and differential approximation probability. We underpin our claim by investigating a detailed model, which deploys the same algorithm but different polynomials and produces unusual changes in the results regarding the performance parameters of S-box.

APA, Harvard, Vancouver, ISO, and other styles

5

Barlow, Angela T. "How Can a Box Help My Students with Multiplying Polynomials?" Mathematics Teaching in the Middle School 9, no. 9 (May 2004): 512–13. http://dx.doi.org/10.5951/mtms.9.9.0512.

Full text

Abstract:

For most of my students, multiplying polynomials is not a difficult procedure to understand. Students quickly grasp the idea that each term in the first polynomial must be multiplied by each term in the second polynomial. The difficulty, however, lies in the organization of the product's terms for ease in combining like terms and in the accuracy of having multiplied all of the appropriate subproducts. The purpose of this article is to demonstrate how a box can help students with both of these aspects.

APA, Harvard, Vancouver, ISO, and other styles

6

Dokken, Tor, Tom Lyche, and Kjell Fredrik Pettersen. "Polynomial splines over locally refined box-partitions." Computer Aided Geometric Design 30, no. 3 (March 2013): 331–56. http://dx.doi.org/10.1016/j.cagd.2012.12.005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Zahid, Amjad, and Muhammad Arshad. "An Innovative Design of Substitution-Boxes Using Cubic Polynomial Mapping." Symmetry 11, no. 3 (March 25, 2019): 437. http://dx.doi.org/10.3390/sym11030437.

Full text

Abstract:

In this paper, we propose to present a novel technique for designing cryptographically strong substitution-boxes using cubic polynomial mapping. The proposed cubic polynomial mapping is proficient to map the input sequence to a strong 8 × 8 S-box meeting the requirements of a bijective function. The use of cubic polynomial maintains the simplicity of S-box construction method and found consistent when compared with other existing S-box techniques used to construct S-boxes. An example proposed S-box is obtained which is analytically evaluated using standard performance criteria including nonlinearity, bijection, bit independence, strict avalanche effect, linear approximation probability, and differential uniformity. The performance results are equated with some recently scrutinized S-boxes to ascertain its cryptographic forte. The critical analyses endorse that the proposed S-box construction technique is considerably innovative and effective to generate cryptographic strong substitution-boxes.

APA, Harvard, Vancouver, ISO, and other styles

8

Sit, Atilla, Julie C. Mitchell, George N. Phillips, and Stephen J. Wright. "An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids." Computational and Mathematical Biophysics 1 (April 16, 2013): 75–89. http://dx.doi.org/10.2478/mlbmb-2013-0004.

Full text

Abstract:

AbstractZernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many expansion terms to describe object features along the edges and corners of the region. We overcome this problem by applying a Gram-Schmidt process to re-orthogonalize the Zernike polynomials so that they recover the orthonormality property over a specified box-shaped domain. We compare the shape retrieval performance of these new polynomial bases to that of the classical Zernike unit-ball polynomials.

APA, Harvard, Vancouver, ISO, and other styles

9

Juma, Ali, Valentine Kabanets, Charles Rackoff, and Amir Shpilka. "The Black-Box Query Complexity of Polynomial Summation." computational complexity 18, no. 1 (April 2009): 59–79. http://dx.doi.org/10.1007/s00037-009-0263-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Galatenko, Alexei V., Stepan A. Nersisyan, and Dmitriy N. Zhuk. "NP-Hardness of the Problem of Optimal Box Positioning." Mathematics 7, no. 8 (August 6, 2019): 711. http://dx.doi.org/10.3390/math7080711.

Full text

Abstract:

We consider the problem of finding a position of a d-dimensional box with given edge lengths that maximizes the number of enclosed points of the given finite set P ⊂ R d , i.e., the problem of optimal box positioning. We prove that while this problem is polynomial for fixed values of d, it is NP-hard in the general case. The proof is based on a polynomial reduction technique applied to the considered problem and the 3-CNF satisfiability problem.

APA, Harvard, Vancouver, ISO, and other styles

11

OH, SUNG-KWUN, DONG-WON KIM, and WITOLD PEDRYCZ. "HYBRID FUZZY POLYNOMIAL NEURAL NETWORKS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, no. 03 (June 2002): 257–80. http://dx.doi.org/10.1142/s0218488502001478.

Full text

Abstract:

We propose a hybrid architecture based on a combination of fuzzy systems and polynomial neural networks. The resulting Hybrid Fuzzy Polynomial Neural Networks (HFPNN) dwells on the ideas of fuzzy rule-based computing and polynomial neural networks. The structure of the network comprises of fuzzy polynomial neurons (FPNs) forming the nodes of the first (input) layer of the HFPNN and polynomial neurons (PNs) that are located in the consecutive layers of the network. In the FPN (that forms a fuzzy inference system), the generic rules assume the form "if A then y = P(x) " where A is fuzzy relation in the condition space while P(x) is a polynomial standing in the conclusion part of the rule. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as constant, linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are considered. Each PN of the network realizes a polynomial type of partial description (PD) of the mapping between input and out variables. HFPNN is a flexible neural architecture whose structure is based on the Group Method of Data Handling (GMDH) and developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated in a dynamic way. The experimental part of the study involves two representative numerical examples such as chaotic time series and Box-Jenkins gas furnace data.

APA, Harvard, Vancouver, ISO, and other styles

12

de Boor, Carl, Nira Dyn, and Amos Ron. "On two polynomial spaces associated with a box spline." Pacific Journal of Mathematics 147, no. 2 (February 1, 1991): 249–67. http://dx.doi.org/10.2140/pjm.1991.147.249.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Doerr, Benjamin, Carola Doerr, and Timo Kötzing. "The unbiased black-box complexity of partition is polynomial." Artificial Intelligence 216 (November 2014): 275–86. http://dx.doi.org/10.1016/j.artint.2014.07.009.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Jeyakumar, V., G. Li, and S. Srisatkunarajah. "Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations." Journal of Global Optimization 58, no. 1 (March 30, 2013): 31–50. http://dx.doi.org/10.1007/s10898-013-0058-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Nizam Chew, Liyana Chew, and Eddie Shahril Ismail. "S-box Construction Based on Linear Fractional Transformation and Permutation Function." Symmetry 12, no. 5 (May 17, 2020): 826. http://dx.doi.org/10.3390/sym12050826.

Full text

Abstract:

Substitution boxes (S-box) with strong and secure cryptographic properties are widely used for providing the key property of nonlinearity in block ciphers. This is critical to be resistant to a standard attack including linear and differential cryptanalysis. The ability to create a cryptographically strong S-box depends on its construction technique. This work aims to design and develop a cryptographically strong 8 × 8 S-box for block ciphers. In this work, the construction of the S-box is based on the linear fractional transformation and permutation function. Three steps involved in producing the S-box. In step one, an irreducible polynomial of degree eight is chosen, and all roots of the primitive irreducible polynomial are calculated. In step two, algebraic properties of linear fractional transformation are applied in Galois Field GF (28). Finally, the produced matrix is permuted to add randomness to the S-box. The strength of the S-box is measured by calculating its potency to create confusion. To analyze the security properties of the S-box, some well-known and commonly used algebraic attacks are used. The proposed S-box is analyzed by nonlinearity test, algebraic degree, differential uniformity, and strict avalanche criterion which are the avalanche effect test, completeness test, and strong S-box test. S-box analysis is done before and after the application of the permutation function and the analysis result shows that the S-box with permutation function has reached the optimal properties as a secure S-box.

APA, Harvard, Vancouver, ISO, and other styles

16

Dadush, Dan, László A. Végh, and Giacomo Zambelli. "Geometric Rescaling Algorithms for Submodular Function Minimization." Mathematics of Operations Research 46, no. 3 (August 2021): 1081–108. http://dx.doi.org/10.1287/moor.2020.1064.

Full text

Abstract:

We present a new class of polynomial-time algorithms for submodular function minimization (SFM) as well as a unified framework to obtain strongly polynomial SFM algorithms. Our algorithms are based on simple iterative methods for the minimum-norm problem, such as the conditional gradient and Fujishige–Wolfe algorithms. We exhibit two techniques to turn simple iterative methods into polynomial-time algorithms. First, we adapt the geometric rescaling technique, which has recently gained attention in linear programming, to SFM and obtain a weakly polynomial bound [Formula: see text]. Second, we exhibit a general combinatorial black box approach to turn [Formula: see text]-approximate SFM oracles into strongly polynomial exact SFM algorithms. This framework can be applied to a wide range of combinatorial and continuous algorithms, including pseudo-polynomial ones. In particular, we can obtain strongly polynomial algorithms by a repeated application of the conditional gradient or of the Fujishige–Wolfe algorithm. Combined with the geometric rescaling technique, the black box approach provides an [Formula: see text] algorithm. Finally, we show that one of the techniques we develop in the paper can also be combined with the cutting-plane method of Lee et al., yielding a simplified variant of their [Formula: see text] algorithm.

APA, Harvard, Vancouver, ISO, and other styles

17

Crespo, Luis G., Sean P. Kenny, and Daniel P. Giesy. "Reliability analysis of polynomial systems subject to p-box uncertainties." Mechanical Systems and Signal Processing 37, no. 1-2 (May 2013): 121–36. http://dx.doi.org/10.1016/j.ymssp.2012.08.012.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Chuong, Thai Doan. "Semidefinite Program Duals for Separable Polynomial Programs Involving Box Constraints." Journal of Optimization Theory and Applications 185, no. 1 (March 4, 2020): 289–99. http://dx.doi.org/10.1007/s10957-020-01646-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

ROSENTHAL, JOACHIM. "A POLYNOMIAL DESCRIPTION OF THE RIJNDAEL ADVANCED ENCRYPTION STANDARD." Journal of Algebra and Its Applications 02, no. 02 (June 2003): 223–36. http://dx.doi.org/10.1142/s0219498803000532.

Full text

Abstract:

The paper gives a polynomial description of the Rijndael Advanced Encryption Standard recently adopted by the National Institute of Standards and Technology. Special attention is given to the structure of the S-Box.

APA, Harvard, Vancouver, ISO, and other styles

20

Brooksbank, Peter A. "Fast Constructive Recognition of Black-Box Unitary Groups." LMS Journal of Computation and Mathematics 6 (2003): 162–97. http://dx.doi.org/10.1112/s1461157000000437.

Full text

Abstract:

AbstractIn this paper, the author presents a new algorithm to recognise, constructively, when a given black-box group is a homomorphic image of the unitary group SU(d, q) for known d and q. The algorithm runs in polynomial time, assuming the existence of oracles for handling SL(2, q) subgroups, and for computing discrete logarithms in cyclic groups of order q ± 1.

APA, Harvard, Vancouver, ISO, and other styles

21

Kane, Daniel M., and Samuel A. Kutin. "Quantum interpolation of polynomials." Quantum Information and Computation 11, no. 1&2 (January 2011): 95–103. http://dx.doi.org/10.26421/qic11.1-2-7.

Full text

Abstract:

Can a quantum computer efficiently interpolate polynomials? We consider black-box algorithms that seek to learn information about a polynomial $f$ from input/output pairs $(x_i, f(x_i))$. We define a more general class of \emph{$(d,S)$-independent} function properties, where, outside of a set $S$ of exceptions, knowing $d$ input values does not help one predict the answer. There are essentially two strategies to computing such a function: query $d+1$ random input values, or search for one of the $|S|$ exceptions. We show that, up to constant factors, we cannot beat these two approaches.

APA, Harvard, Vancouver, ISO, and other styles

22

Silveira, Daniel D., Thiago V. N. Coelho, and Alexandre Bessa dos Santos. "Evolution of Black-Box Models Based on Volterra Series." Journal of Applied Mathematics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/638978.

Full text

Abstract:

This paper presents a historical review of the many behavioral models actually used to model radio frequency power amplifiers and a new classification of these behavioral models. It also discusses the evolution of these models, from a single polynomial to multirate Volterra models, presenting equations and estimation methods. New trends in RF power amplifier behavioral modeling are suggested.

APA, Harvard, Vancouver, ISO, and other styles

23

Kieslich, Chris A., Fani Boukouvala, and Christodoulos A. Floudas. "Optimization of black-box problems using Smolyak grids and polynomial approximations." Journal of Global Optimization 71, no. 4 (May 3, 2018): 845–69. http://dx.doi.org/10.1007/s10898-018-0643-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Sweatha, A. Anjalin, and K. Mohaideen Pitchai. "Construction of Cryptographically Secure AES S-Box using Second-order Reversible Cellular Automata." Journal of Intelligent & Fuzzy Systems 39, no. 3 (October 7, 2020): 4313–18. http://dx.doi.org/10.3233/jifs-200326.

Full text

Abstract:

In cryptography the block ciphers are the mostly used symmetric algorithms. In the existing system the standard S-Box of Advanced Encryption Standard(AES) is performed using the irreducible polynomial equation in table form known as look-up tables(LUTs). For more security purposes, second-order reversible cellular automata based S-box is created. The security aspects of the S-Box used in the AES algorithm are evaluated using cryptographic properties like Strict Avalanche Criteria, Non-Linearity, Entropy, and Common Immunity Bias. The design of S-Box using second-order reversible Cellular Automata is better concerning security and dynamic aspect as compared to the classical S-boxes used Advanced Encryption Standard.

APA, Harvard, Vancouver, ISO, and other styles

25

González-Castaño, Catalina, Leandro L. Lorente-Leyva, Javier Muñoz, Carlos Restrepo, and Diego H. Peluffo-Ordóñez. "An MPPT Strategy Based on a Surface-Based Polynomial Fitting for Solar Photovoltaic Systems Using Real-Time Hardware." Electronics 10, no. 2 (January 17, 2021): 206. http://dx.doi.org/10.3390/electronics10020206.

Full text

Abstract:

This paper presents an optimal design of a surface-based polynomial fitting for tracking the maximum power point (MPPT) of a photovoltaic (PV) system, here named surface-based polynomial fitting (MPPT-SPF). The procedure of the proposed MPPT-SPF strategy is based on a polynomial model to characterize data from the PV module with a global fit. The advantage of using polynomials is that they provide a good fit within a predefined data range even though they can diverge greatly from that range. The MPPT-SPF strategy is integrated with a DC-DC boost converter to verify its performance and its interaction with different control loops. Therefore, the MPPT strategy is applied to the reference outer PI control loop, which in turn provides the current reference to the inner current loop based on a discrete-time sliding current control. A real-time and high-speed simulator (PLECS RT Box 1) and a digital signal controller (DSC) are used to implement the hardware-in-the-loop system to obtain the results. The proposed strategy does not have a high computational cost and can be implemented in a commercial low-cost DSC (TI 28069M). The proposed MPPT strategy is compared with a conventional perturb and observe method to prove its effectiveness under demanding tests.

APA, Harvard, Vancouver, ISO, and other styles

26

Shaukat Jamal, Sajjad, Dawood Shah, Abdulaziz Deajim, and Tariq Shah. "The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers." Security and Communication Networks 2020 (September 24, 2020): 1–14. http://dx.doi.org/10.1155/2020/8883884.

Full text

Abstract:

Substitution boxes are the only nonlinear component of the symmetric key cryptography and play a key role in the cryptosystem. In block ciphers, the S-boxes create confusion and add valuable strength. The majority of the substitution boxes algorithms focus on bijective Boolean functions and primitive irreducible polynomial that generates the Galois field. For binary field F2, there are exactly 16 primitive irreducible polynomials of degree 8 and it prompts us to construct 16 Galois field extensions of order 256. Conventionally, construction of affine power affine S-box is based on Galois field of order 256, depending on a single degree 8 primitive irreducible polynomial over ℤ2. In this manuscript, we study affine power affine S-boxes for all the 16 distinct degree 8 primitive irreducible polynomials over ℤ2 to propose 16 different 8×8 substitution boxes. To perform this idea, we introduce 16 affine power affine transformations and, for fixed parameters, we obtained 16 distinct S-boxes. Here, we thoroughly study S-boxes with all possible primitive irreducible polynomials and their algebraic properties. All of these boxes are evaluated with the help of nonlinearity test, strict avalanche criterion, bit independent criterion, and linear and differential approximation probability analyses to measure the algebraic and statistical strength of the proposed substitution boxes. Majority logic criterion results indicate that the proposed substitution boxes are well suited for the techniques of secure communication.

APA, Harvard, Vancouver, ISO, and other styles

27

Hedger, Richard D., François Martin, Julian J. Dodson, Daniel Hatin, François Caron, and Fred G. Whoriskey. "The optimized interpolation of fish positions and speeds in an array of fixed acoustic receivers." ICES Journal of Marine Science 65, no. 7 (June 30, 2008): 1248–59. http://dx.doi.org/10.1093/icesjms/fsn109.

Full text

Abstract:

Abstract Hedger, R. D., Martin, F., Dodson, J, J., Hatin, D., Caron, F., and Whoriskey, F. G. 2008. The optimized interpolation of fish positions and speeds in an array of fixed acoustic receivers. – ICES Journal of Marine Science, 65: 1248–1259. The principal method for interpolating the positions and speeds of tagged fish within an array of fixed acoustic receivers is the weighted-mean method, which uses a box-kernel estimator, one of the simplest smoothing options available. This study aimed to determine the relative error of alternative, non-parametric regression methods for estimating these parameters. It was achieved by predicting the positions and speeds of three paths made through a dense array of fixed acoustic receivers within a coastal embayment (Gaspé Bay, Québec, Canada) by a boat with a GPS trailing an ultrasonic transmitter. Transmitter positions and speeds were estimated from the receiver data using kernel estimators, with box and normal kernels and the kernel size determined arbitrarily, and by several non-parametric methods, i.e. a kernel estimator, a smoothing spline, and local polynomial regression, with the kernel size or smoothing span determined by cross-validation. Prediction error of the kernel estimator was highly dependent upon kernel size, and a normal kernel produced less error than the box kernel. Of the methods using cross-validation, local polynomial regression produced least error, suggesting it as the optimal method for interpolation. Prediction error was also strongly dependent on array density. The local polynomial regression method was used to determine the movement patterns of a sample of tagged Atlantic salmon (Salmo salar) smolt and kelt, and American eel (Anguilla rostrata). Analysis of the estimates from local polynomial regression suggested that this was a suitable method for monitoring patterns of fish movement.

APA, Harvard, Vancouver, ISO, and other styles

28

Agarwal, Praveen, Amandeep Singh, and Adem Kilicman. "Development of key-dependent dynamic S-Boxes with dynamic irreducible polynomial and affine constant." Advances in Mechanical Engineering 10, no. 7 (July 2018): 168781401878163. http://dx.doi.org/10.1177/1687814018781638.

Full text

Abstract:

In recent years, the need to develop advanced information technology systems in the area of mechanical engineering has been growing continuously to deliver better product quality at reduced cost. Embedding the electronics and software with machines transform them into smart machines sophistically called mechatronic. These software-oriented machines collect big data using sensors and other electronics and share among other smart machines, which further helps them in controlling the manufacturing processes, decision-making, and even in maintenance. Machine-to-machine sharing of data involves the risk of data stealing or modification, which may further disrupt the working of manufacturing process and leads to poor quality product. For data security, block ciphers like advanced encryption standard are needed. Advanced encryption standard is an encryption algorithm which is widely used to provide security to sensitive information by organizations. The main core of advanced encryption standard is its non-liner component that is S-Box, which is also called substitution table. The S-Box provides confusion capabilities in algorithm. The point of interest for cryptanalysis and hackers is S-Box, which is fixed in case of advanced encryption standard. Cryptanalysis and hackers exploit this weakness of advanced encryption standard. Many researchers tried to modify S-Box using different techniques. In this article, we tried to create dynamic S-Boxes which are key-dependent and, at the same time, they are using dynamic irreducible polynomial and affine constant.

APA, Harvard, Vancouver, ISO, and other styles

29

Decker, T., J. Draisma, and P. Wocjan. "Efficient quantum algorithm for identifying hidden polynomials." Quantum Information and Computation 9, no. 3&4 (March 2009): 215–30. http://dx.doi.org/10.26421/qic9.3-4-3.

Full text

Abstract:

We consider a natural generalization of an abelian Hidden Subgroup Problem where the subgroups and their cosets correspond to graphs of linear functions over a finite field $\F$ with $d$ elements. The hidden functions of the generalized problem are not restricted to be linear but can also be $m$-variate polynomial functions of total degree $n\geq 2$. The problem of identifying hidden $m$-variate polynomials of degree less or equal to $n$ for fixed $n$ and $m$ is hard on a classical computer since $\Omega(\sqrt{d})$ black-box queries are required to guarantee a constant success probability. In contrast, we present a quantum algorithm that correctly identifies such hidden polynomials for all but a finite number of values of $d$ with constant probability and that has a running time that is only polylogarithmic in $d$.

APA, Harvard, Vancouver, ISO, and other styles

30

Xiao, Jin-ke, Wei-min Li, Wei Li, and Xin-rong Xiao. "Optimization on Black Box Function Optimization Problem." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/647234.

Full text

Abstract:

There are a large number of engineering optimization problems in real world, whose input-output relationships are vague and indistinct. Here, they are called black box function optimization problem (BBFOP). Then, inspired by the mechanism of neuroendocrine system regulating immune system, BP neural network modified immune optimization algorithm (NN-MIA) is proposed. NN-MIA consists of two phases: the first phase is training BP neural network with expected precision to confirm input-output relationship and the other phase is immune optimization phase, whose aim is to search global optima. BP neural network fitting without expected fitting precision could be replaced with polynomial fitting or other fitting methods within expected fitting precision. Experimental simulation confirms global optimization capability of MIA and the practical application of BBFOP optimization method.

APA, Harvard, Vancouver, ISO, and other styles

31

de Boor, Carl, and Amos Ron. "On polynomial ideals of finite codimension with applications to box spline theory." Journal of Mathematical Analysis and Applications 158, no. 1 (June 1991): 168–93. http://dx.doi.org/10.1016/0022-247x(91)90275-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Zahid, Amjad Hussain, Hamza Rashid, Mian Muhammad Umar Shaban, Soban Ahmad, Ehtezaz Ahmed, Muhammad Tallal Amjad, Muhammad Azfar Tariq Baig, et al. "Dynamic S-Box Design Using a Novel Square Polynomial Transformation and Permutation." IEEE Access 9 (2021): 82390–401. http://dx.doi.org/10.1109/access.2021.3086717.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Hammi, Oualid. "Augmented Twin-Nonlinear Two-Box Behavioral Models for Multicarrier LTE Power Amplifiers." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/762534.

Full text

Abstract:

A novel class of behavioral models is proposed for LTE-driven Doherty power amplifiers with strong memory effects. The proposed models, labeled augmented twin-nonlinear two-box models, are built by cascading a highly nonlinear memoryless function with a mildly nonlinear memory polynomial with cross terms. Experimental validation on gallium nitride based Doherty power amplifiers illustrates the accuracy enhancement and complexity reduction achieved by the proposed models. When strong memory effects are observed, the augmented twin-nonlinear two-box models can improve the normalized mean square error by up to 3 dB for the same number of coefficients when compared to state-of-the-art twin-nonlinear two-box models. Furthermore, the augmented twin-nonlinear two-box models lead to the same performance as previously reported twin-nonlinear two-box models while requiring up to 80% less coefficients.

APA, Harvard, Vancouver, ISO, and other styles

34

Sharma, Vijay K., Saurabh Kumar, and K. K. Mahapatra. "Iterative and Fully Pipelined High Throughput Efficient Architectures of AES in FPGA and ASIC." Journal of Circuits, Systems and Computers 25, no. 05 (February 25, 2016): 1650049. http://dx.doi.org/10.1142/s0218126616500493.

Full text

Abstract:

This paper presents high throughput iterative and pipelined VLSI architectures of the Advanced encryption standard (AES) algorithm based on composite field arithmetic in polynomial basis. A logical rearrangement has been performed in the byte substitution (S-box) module to reduce the number of gates in the critical path. Also, inversion in GF(24) module has been separately optimized. ASIC implementation of our S-box has comparatively low power and low energy consumption. The iterative and pipelined implementations of AES in field programmable gate array (FPGA) and ASIC using proposed S-box have high hardware efficiency in terms of throughput per unit area (slices in FPGA).

APA, Harvard, Vancouver, ISO, and other styles

35

Porta, J. M., L. Ros, T. Creemers, and F. Thomas. "Box Approximations of Planar Linkage Configuration Spaces." Journal of Mechanical Design 129, no. 4 (April 18, 2006): 397–405. http://dx.doi.org/10.1115/1.2437808.

Full text

Abstract:

This paper presents a numerical method able to compute all possible configurations of planar linkages. The procedure is applicable to rigid linkages (i.e., those that can only adopt a finite number of configurations) and to mobile ones (i.e., those that exhibit a continuum of possible configurations). The method is based on the fact that this problem can be reduced to finding the roots of a polynomial system of linear, quadratic, and hyperbolic equations, which is here tackled with a new strategy exploiting its structure. The method is conceptually simple and easy to implement, yet it provides solutions of the desired accuracy in short computation times. Experiments are included that show its performance on the double butterfly linkage and on larger linkages formed by the concatenation of basic patterns.

APA, Harvard, Vancouver, ISO, and other styles

36

Pitarch, José, Antonio Sala, and César de Prada. "A Systematic Grey-Box Modeling Methodology via Data Reconciliation and SOS Constrained Regression." Processes 7, no. 3 (March 23, 2019): 170. http://dx.doi.org/10.3390/pr7030170.

Full text

Abstract:

Developing the so-called grey box or hybrid models of limited complexity for process systems is the cornerstone in advanced control and real-time optimization routines. These models must be based on fundamental principles and customized with sub-models obtained from process experimental data. This allows the engineer to transfer the available process knowledge into a model. However, there is still a lack of a flexible but systematic methodology for grey-box modeling which ensures certain coherence of the experimental sub-models with the process physics. This paper proposes such a methodology based in data reconciliation (DR) and polynomial constrained regression. A nonlinear optimization of limited complexity is to be solved in the DR stage, whereas the proposed constrained regression is based in sum-of-squares (SOS) convex programming. It is shown how several desirable features on the polynomial regressors can be naturally enforced in this optimization framework. The goodnesses of the proposed methodology are illustrated through: (1) an academic example and (2) an industrial evaporation plant with real experimental data.

APA, Harvard, Vancouver, ISO, and other styles

37

Zhang, Shenggui. "A sufficient condition of Euclidean rings given by polynomial optimization over a box." Numerical Algebra, Control & Optimization 4, no. 2 (2014): 93–101. http://dx.doi.org/10.3934/naco.2014.4.93.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Geerts, Floris. "Expressing the box cone radius in the relational calculus with real polynomial constraints." Discrete and Computational Geometry 30, no. 4 (October 1, 2003): 607–22. http://dx.doi.org/10.1007/s00454-003-0770-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Liu, Chunli, and Jianjun Gao. "A polynomial case of convex integer quadratic programming problems with box integer constraints." Journal of Global Optimization 62, no. 4 (January 7, 2015): 661–74. http://dx.doi.org/10.1007/s10898-014-0263-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Xiao, Liang, Ming Feng, Yang Ge, and Wei Wang. "Multi-Objective Optimization of the FOFAS Based on the Workbench/Exploration." Advanced Materials Research 889-890 (February 2014): 101–6. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.101.

Full text

Abstract:

A certain FOFAS (framework of feeding ammunition system) has extremely important function such as fixing, supporting and leading orientation, etc. Optimization design for FOFAS is the focal point under meeting such criterions as stiffness, strength and safety. Using Workbench, this article mainly carried out parametric design to optimize feeding ammunition box under Multi-objective Genetic Algorithm (MOGA). Pareto solutions from optimization simulation showed that minimum mass of ammunition box was decreased by 6.17%, displacement deformation had little influence on the FOFAS and equivalent stress was increased by 0.35%. The optimizing results satisfied the strength, stiffness and polynomial response requirements.

APA, Harvard, Vancouver, ISO, and other styles

41

Khalfi, Jaouad, Najib Boumaaz, Abdallah Soulmani, and El Mehdi Laadissi. "Box–Jenkins Black-Box Modeling of a Lithium-Ion Battery Cell Based on Automotive Drive Cycle Data." World Electric Vehicle Journal 12, no. 3 (July 28, 2021): 102. http://dx.doi.org/10.3390/wevj12030102.

Full text

Abstract:

The Box–Jenkins model is a polynomial model that uses transfer functions to express relationships between input, output, and noise for a given system. In this article, we present a Box–Jenkins linear model for a lithium-ion battery cell for use in electric vehicles. The model parameter identifications are based on automotive drive-cycle measurements. The proposed model prediction performance is evaluated using the goodness-of-fit criteria and the mean squared error between the Box–Jenkins model and the measured battery cell output. A simulation confirmed that the proposed Box–Jenkins model could adequately capture the battery cell dynamics for different automotive drive cycles and reasonably predict the actual battery cell output. The goodness-of-fit value shows that the Box–Jenkins model matches the battery cell data by 86.85% in the identification phase, and 90.83% in the validation phase for the LA-92 driving cycle. This work demonstrates the potential of using a simple and linear model to predict the battery cell behavior based on a complex identification dataset that represents the actual use of the battery cell in an electric vehicle.

APA, Harvard, Vancouver, ISO, and other styles

42

Dey, Sankhanil, and Ranjan Ghosh. "Mathematical Method to Search for Monic Irreducible Polynomials with Decimal Equivalents of Polynomials over Galois Field GF(pq)." Circulation in Computer Science 2, no. 11 (December 20, 2017): 17–22. http://dx.doi.org/10.22632/ccs-2017-252-68.

Full text

Abstract:

Substitution boxes or S-boxes play a significant role in encryption and decryption of bit level plaintext and cipher-text respectively. Irreducible Polynomials (IPs) have been used to construct 4-bit or 8-bit substitution boxes in many cryptographic block ciphers. In Advance Encryption Standard the 8-bit the elements S-box have been obtained from the Multiplicative Inverse (MI) of elemental polynomials (EPs) of the 1st IP over Galois field GF(28) by adding an additive element. In this paper a mathematical method and the algorithm of the said method with the discussion of the execution time of the algorithm, to obtain monic IPs over Galois field GF(pq) have been illustrated with example. The method is very similar to polynomial multiplication of two polynomials over Galois field GF(pq) but has a difference in execution. The decimal equivalents of polynomials have been used to identify Basic Polynomials (BPs), EPs, IPs and Reducible polynomials (RPs). The monic RPs have been determined by this method and have been cancelled out to produce monic IPs. The non-monic IPs have been obtained with multiplication of α where α GF(pq) and assume values from 2 to (p-1) to monic IPs.

APA, Harvard, Vancouver, ISO, and other styles

43

Nooraziah, Ahmad, and V. Janahiraman Tiagrajah. "A Study on Regression Model Using Response Surface Methodology." Applied Mechanics and Materials 666 (October 2014): 235–39. http://dx.doi.org/10.4028/www.scientific.net/amm.666.235.

Full text

Abstract:

Response Surface Methodology (RSM) mostly employs statistical regression method as it is practical, economical and relatively easy to use. The first and second order polynomial equation was developed using RSM. This polynomial model usually refers as a regression model. In this research, the objective is to find the best response surface method to model three factors and three levels parameters in machining. From the study, the Box-Behnken Design can develop a good regression model rather than Central Composite Design or Full Factorial Design. While, the second order regression model has proved to be more effective in predicting the performance of the given data set.

APA, Harvard, Vancouver, ISO, and other styles

44

Boufleur, Rodrigo Carlos, Marcelo Emilio, Eduardo Janot Pacheco, Jorge Ramiro de La Reza, and José Carlos da Rocha. "Eliminating Noise at the Box-fitting Spectrum." Proceedings of the International Astronomical Union 8, S293 (August 2012): 410–12. http://dx.doi.org/10.1017/s1743921313013288.

Full text

Abstract:

AbstractNon gaussian sources of erros need to be taken into consideration when searching for planetary transits. Such phenomena are mostly caused by the impact of high energetic particles on the detector (Pinheiro da Silva et al. 2008). The detection efficiency of transits, therefor, depend significantly on the data quality and the algorithms utilized to deal with these errors sources. In this work we show that a modified detrend algorithm CDA (CoRoT Detrend Algorithm; Mislis et al. 2010) using a robust statistics and an empirical fit, instead of a polynomial one, can eliminate more efficiently gaps in the data and other long-term trends from the light-curve. Using this algorithm enables us to obtain a reconstructed light-curve with better signal-to-noise ratio that allows to improve the detection of exoplanet transits, although long term signals are destroyed. The results show that these modifications lead to an improved BLS (Box-fitting Least Squares; Kovács, Zucker & Mazeh 2002) algorithm spectrum. At the end we have compared our planetary search results with CoRoT (Convection, Rotation and planetary Transits) satellite chromatic light-curves available in the literature.

APA, Harvard, Vancouver, ISO, and other styles

45

Doerr, Benjamin, Carola Doerr, and Timo Kötzing. "Unbiased Black-Box Complexities of Jump Functions." Evolutionary Computation 23, no. 4 (December 2015): 641–70. http://dx.doi.org/10.1162/evco_a_00158.

Full text

Abstract:

We analyze the unbiased black-box complexities of jump functions with small, medium, and large sizes of the fitness plateau surrounding the optimal solution. Among other results, we show that when the jump size is [Formula: see text], that is, when only a small constant fraction of the fitness values is visible, then the unbiased black-box complexities for arities 3 and higher are of the same order as those for the simple OneMax function. Even for the extreme jump function, in which all but the two fitness values [Formula: see text] and n are blanked out, polynomial time mutation-based (i.e., unary unbiased) black-box optimization algorithms exist. This is quite surprising given that for the extreme jump function almost the whole search space (all but a [Formula: see text] fraction) is a plateau of constant fitness. To prove these results, we introduce new tools for the analysis of unbiased black-box complexities, for example, selecting the new parent individual not only by comparing the fitnesses of the competing search points but also by taking into account the (empirical) expected fitnesses of their offspring.

APA, Harvard, Vancouver, ISO, and other styles

46

Leonhardt, Karsten, Norbert Peyerimhoff, Martin Tautenhahn, and Ivan Veselić. "Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials." Reviews in Mathematical Physics 27, no. 04 (May 2015): 1550007. http://dx.doi.org/10.1142/s0129055x15500075.

Full text

Abstract:

We study Schrödinger operators on L2(ℝd) and ℓ2(ℤd) with a random potential of alloy-type. The single-site potential is assumed to be exponentially decaying but not necessarily of fixed sign. In the continuum setting, we require a generalized step-function shape. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. In the described situation, a Wegner estimate, which is polynomial in the volume of the box and linear in the size of the energy interval, holds. We apply the established Wegner estimate as an ingredient for a localization proof via multiscale analysis.

APA, Harvard, Vancouver, ISO, and other styles

47

Liu, H. B., C. Jiang, and Z. Xiao. "Efficient uncertainty propagation for parameterized p-box using sparse-decomposition-based polynomial chaos expansion." Mechanical Systems and Signal Processing 138 (April 2020): 106589. http://dx.doi.org/10.1016/j.ymssp.2019.106589.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Vellanki, Pratibha, Santu Rana, Sunil Gupta, David Rubin de Celis Leal, Alessandra Sutti, Murray Height, and Svetha Venkatesh. "Bayesian Functional Optimisation with Shape Prior." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1617–24. http://dx.doi.org/10.1609/aaai.v33i01.33011617.

Full text

Abstract:

Real world experiments are expensive, and thus it is important to reach a target in a minimum number of experiments. Experimental processes often involve control variables that change over time. Such problems can be formulated as functional optimisation problem. We develop a novel Bayesian optimisation framework for such functional optimisation of expensive black-box processes. We represent the control function using Bernstein polynomial basis and optimise in the coefficient space. We derive the theory and practice required to dynamically adjust the order of the polynomial degree, and show how prior information about shape can be integrated. We demonstrate the effectiveness of our approach for short polymer fibre design and optimising learning rate schedules for deep networks.

APA, Harvard, Vancouver, ISO, and other styles

49

Razaq, Abdul, Awais Yousaf, Umer Shuaib, Nasir Siddiqui, Atta Ullah, and Adil Waheed. "A Novel Construction of Substitution Box Involving Coset Diagram and a Bijective Map." Security and Communication Networks 2017 (2017): 1–16. http://dx.doi.org/10.1155/2017/5101934.

Full text

Abstract:

The substitution box is a basic tool to convert the plaintext into an enciphered format. In this paper, we use coset diagram for the action of PSL(2,Z) on projective line over the finite field GF29 to construct proposed S-box. The vertices of the cost diagram are elements of GF29 which can be represented by powers of α, where α is the root of irreducible polynomial px=x9+x4+1 over Z2. Let GF⁎29 denote the elements of GF29 which are of the form of even powers of α. In the first step, we construct a 16×16 matrix with the elements of GF⁎29 in a specific order, determined by the coset diagram. Next, we consider h:GF⁎29⟶GF28 defined by hα2n=ωn to destroy the structure of GF28. In the last step, we apply a bijective map g on each element of the matrix to evolve proposed S-box. The ability of the proposed S-box is examined by different available algebraic and statistical analyses. The results are then compared with the familiar S-boxes. We get encouraging statistics of the proposed box after comparison.

APA, Harvard, Vancouver, ISO, and other styles

50

Huang, Jinyu. "Parallel algorithms for matroid intersection and matroid parity." Discrete Mathematics, Algorithms and Applications 07, no. 02 (May 25, 2015): 1550019. http://dx.doi.org/10.1142/s1793830915500196.

Full text

Abstract:

A maximum linear matroid parity set is called a basic matroid parity set, if its size is the rank of the matroid. We show that determining the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity) is in NC2, provided that there are polynomial number of common bases (basic matroid parity sets). For graphic matroids, we show that finding a common base for matroid intersection is in NC2, if the number of common bases is polynomial bounded. To our knowledge, these algorithms are the first deterministic NC algorithms for matroid intersection and matroid parity. We also give a new RNC2 algorithm that finds a common base for graphic matroid intersection. We prove that if there is a black-box NC algorithm for Polynomial Identity Testing (PIT), then there is an NC algorithm to determine the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity).

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!