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Journal articles on the topic 'Extended Euclidean algorithm'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Okazaki, Hiroyuki, Yosiki Aoki, and Yasunari Shidama. "Extended Euclidean Algorithm and CRT Algorithm." Formalized Mathematics 20, no. 2 (2012): 175–79. http://dx.doi.org/10.2478/v10037-012-0020-2.

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Summary In this article we formalize some number theoretical algorithms, Euclidean Algorithm and Extended Euclidean Algorithm [9]. Besides the a gcd b, Extended Euclidean Algorithm can calculate a pair of two integers (x, y) that holds ax + by = a gcd b. In addition, we formalize an algorithm that can compute a solution of the Chinese remainder theorem by using Extended Euclidean Algorithm. Our aim is to support the implementation of number theoretic tools. Our formalization of those algorithms is based on the source code of the NZMATH, a number theory oriented calculation system developed by

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2

Levrie, Paul, and Rudi Penne. "The extended Euclidean Algorithm made easy." Mathematical Gazette 100, no. 547 (2016): 147–49. http://dx.doi.org/10.1017/mag.2016.25.

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3

Kim, Daehak, and Kwang Sik Oh. "Computer intensive method for extended Euclidean algorithm." Journal of the Korean Data and Information Science Society 25, no. 6 (2014): 1467–74. http://dx.doi.org/10.7465/jkdi.2014.25.6.1467.

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4

Diko, Ergin, and Mushab Ibraimi. "RSA & EXTENDED EUCLIDEAN ALGORITHM WITH EXAMPLES OF EXPONENTIAL RSA CIPHERS, RSA EXAMPLE SOLUTION WITH EXTENDED EUCLIDEAN ALGORITHM." Vision International Refereed Scientific Journal 8, no. 1 (2023): 161–75. http://dx.doi.org/10.55843/ivisum23810161d.

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5

Havas, George. "On the complexity of the extended euclidean algorithm (Extended Abstract)." Electronic Notes in Theoretical Computer Science 78 (April 2003): 1–4. http://dx.doi.org/10.1016/s1571-0661(04)81002-8.

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6

Luo, Zhikun, Huafei Sun, and Xiaomin Duan. "The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/693659.

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We use a second-order learning algorithm for numerically solving a class of the algebraic Riccati equations. Specifically, the extended Hamiltonian algorithm based on manifold of positive definite symmetric matrices is provided. Furthermore, this algorithm is compared with the Euclidean gradient algorithm, the Riemannian gradient algorithm, and the new subspace iteration method. Simulation examples show that the convergence speed of the extended Hamiltonian algorithm is the fastest one among these algorithms.

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Nguyen, Thi-Nhung. "Privacy preserving using extended euclidean – algorithm applied to RSA." Tạp chí Khoa học - Trường Đại học Sư phạm Hà Nội 2 1, no. 2 (2023): 53–63. http://dx.doi.org/10.56764/hpu2.jos.2023.1.2.53-63.

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RSA cryptography is a strong encryption method widely used in online transactions. Using the extended Euclidean algorithm is an important and efficient technique for finding the secret key in RSA cryptography. This study provides an implementation of the extended Euclidean algorithm to find secret keys based on RSA cryptography and hopes that it can be of help to experts in the field of information security.

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Aldaya, Alejandro Cabrera, Alejandro J. Cabrera Sarmiento, and Santiago Sánchez-Solano. "SPA vulnerabilities of the binary extended Euclidean algorithm." Journal of Cryptographic Engineering 7, no. 4 (2016): 273–85. http://dx.doi.org/10.1007/s13389-016-0135-4.

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9

Liu, Weihua, and Andrew Klapper. "AFSRs synthesis with the extended Euclidean rational approximation algorithm." Advances in Mathematics of Communications 11, no. 1 (2017): 139–50. http://dx.doi.org/10.3934/amc.2017008.

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Hechenberger, Ryan, Peter J. Stuckey, Pierre Le Bodic, and Daniel D. Harabor. "Dual Euclidean Shortest Path Search (Extended Abstract)." Proceedings of the International Symposium on Combinatorial Search 15, no. 1 (2022): 285–87. http://dx.doi.org/10.1609/socs.v15i1.21787.

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The Euclidean Shortest Path Problem (ESPP) asks us to find a minimum length path between two points on a 2D plane while avoiding a set of polygonal obstacles. Existing approaches for ESPP, based on Dijkstra or A* search, are primal methods that gradually build up longer and longer valid paths until they reach the target. In this paper we define an alternative algorithm for ESPP which can avoid this problem. Our approach starts from a path that ignores all obstacles, and generates longer and longer paths, each avoiding more obstacles, until eventually the search finds an optimal valid path.

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Tynymbaev, Sakhybai, Zhanyerke Temirbekova, Tolganai Chinibayeva, and Mirzakul Myrzakul. "IMPLEMENTATION OF THE EL-GAMAL CRYPTOSYSTEM ON A MICROCONTROLLER." Вестник Алматинского университета энергетики и связи 1, no. 64 (2021): 47–56. http://dx.doi.org/10.51775/2790-0886_2024_64_1_47.

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To ensure the security of the Internet of Things, a microcontroller is used due to its small size, simple architecture, etc. Microcontrollers have limited resources compared to more powerful computers. Decryption time plays an important role when choosing cryptographic algorithms for microcontrollers, especially if they operate in real-time systems or process data in idle mode. The article is devoted to the development of an effective digital scheme for decryption in the El- Gamal cryptosystem using the extended Euclidean algorithm to solve the linear diophant equation. Based on the problem of

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Neda Fatma, M. R. Hassan, Dilshad Akhtar, J. K. M. S. Zaman. "Diminution of Extended Euclidean Algorithm for Finding Multiplicative Inverse in Galois Field." Proceeding International Conference on Science and Engineering 11, no. 1 (2023): 1222–40. http://dx.doi.org/10.52783/cienceng.v11i1.267.

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This manuscript deals with the theorem on diminution of the Extended Euclidean Algorithm for finding the multiplicative inverse of non-zero elemental polynomials of Galois field with respect to a monic irreducible polynomial over , where is a prime and is any positive integer. This method became successful in finding the multiplicative inverse of all those non-zero polynomials for which the Extended Euclidean Algorithm fails. We find the inverse of all 342 non-zero elemental polynomials of using an irreducible polynomial We also used Cayley Hamilton’s theorem for finding the multiplicative inv

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Al-Hiaja, Qasem Abu, Abdullah AlShuaibi, and Ahmad Al Badawi. "Frequency Analysis of 32-bit Modular Divider Based on Extended GCD Algorithm for Different FPGA chips." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 17, no. 1 (2018): 7133–39. http://dx.doi.org/10.24297/ijct.v17i1.6992.

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Modular inversion with large integers and modulus is a fundamental operation in many public-key cryptosystems. Extended Euclidean algorithm (XGCD) is an extension of Euclidean algorithm (GCD) used to compute the modular multiplicative inverse of two coprime numbers. In this paper, we propose a Frequency Analysis study of 32-bit modular divider based on extended-GCD algorithm targeting different chips of field-programmable gate array (FPGA). The experimental results showed that the design recorded the best performance results when implemented using Kintex7 (xc7k70t-2-fbg676) FPGA kit with a min

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14

KAIHARA, M. E. "A Hardware Algorithm for Modular Multiplication/Division Based on the Extended Euclidean Algorithm." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E88-A, no. 12 (2005): 3610–17. http://dx.doi.org/10.1093/ietfec/e88-a.12.3610.

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Ratseev, S. M., A. D. Lavrinenko, and E. A. Stepanova. "ON THE BERLEKAMP — MASSEY ALGORITHM AND ITS APPLICATION FOR DECODING ALGORITHMS." Vestnik of Samara University. Natural Science Series 27, no. 1 (2021): 44–61. http://dx.doi.org/10.18287/2541-7525-2021-27-1-44-61.

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The paper is devoted to the Berlekamp Masssey algorithm and its equivalent version based on the extended Euclidean algorithm. An optimized Berlekamp Massey algorithm is also given for the case ofa field of characteristic 2. The Berlekamp Massey algorithm has a quadratic complexity and is used, for example, to solve systems of linear equations in which the matrix of the system is the Toeplitz matrix. In particular, such systems of equations appear in algorithms for the syndrome decoding of BCH codes, Reed Solomon codes, generalized Reed Solomon codes, and Goppa codes. Algorithms for decoding th

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Yi, Jin, Shiqiang Zhang, Yueqi Cao, Erchuan Zhang, and Huafei Sun. "Rigid Shape Registration Based on Extended Hamiltonian Learning." Entropy 22, no. 5 (2020): 539. http://dx.doi.org/10.3390/e22050539.

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Shape registration, finding the correct alignment of two sets of data, plays a significant role in computer vision such as objection recognition and image analysis. The iterative closest point (ICP) algorithm is one of well known and widely used algorithms in this area. The main purpose of this paper is to incorporate ICP with the fast convergent extended Hamiltonian learning (EHL), so called EHL-ICP algorithm, to perform planar and spatial rigid shape registration. By treating the registration error as the potential for the extended Hamiltonian system, the rigid shape registration is modelled

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Ibrahim, A. A., Abubakar S.I., Zaid I., Shehu S., and Rufa'i A. "GCD OF AUNU BINARY POLYNOMIALS OF CARDINALITY SEVEN USING EXTENDED EUCLIDEAN ALGORITHM." GCD OF AUNU BINARY POLYNOMIALS OF CARDINALITY SEVEN USING EXTENDED EUCLIDEAN ALGORITHM 09, no. 09 (2021): 2381–89. https://doi.org/10.47191/ijmcr/v9i9.02.

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Finite fields is considered to be the most widely used algebraic structures today due to its applications in cryptography, coding theory, error correcting codes among others. This paper reports the use of extended Euclidean algorithm in computing the greatest common divisor (gcd) of Aunu binary polynomials of cardinality seven. Each class of the polynomial is permuted into pairs until all the succeeding classes are exhausted. The findings of this research reveals that the gcd of most of the pairs of the permuted classes are relatively prime. This results can be used further in constructing som

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Adamu, Abubakar, Grace Nnennaya Ogwo, Chibueze Christain Okeke, and Bertin Zinsou. "A Two-Step Inertial CQ Method for Split Feasibility Problems with Applications." Bangmod International Journal of Mathematical and Computational Science 11 (March 7, 2025): 23–50. https://doi.org/10.58715/bangmodjmcs.2025.11.2.

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This paper introduces an algorithm for approximating solutions of split feasibility problems by employing a two-step inertial acceleration strategy along with a self-adaptive step size. This combination enhances the convergence rate and reduces computational complexity of the proposed algorithm. The nonasymptotic O(1/t) convergence rate and global convergence of the proposed method are established within the context of Euclidean spaces. The algorithm is extended to handle multiple set split feasibility problems, and a sensitivity analysis is conducted to identify optimal inertial parameter cho

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19

Rangel, Irepan, Daniel-Eduardo Vázquez, Eduardo Vázquez, Gonzalo Duchen, Juan-Gerardo Avalos, and Giovanny Sanchez. "First ElGamal Encryption/Decryption Scheme Based on Spiking Neural P Systems with Communication on Request, Weights on Synapses, and Delays in Rules." Mathematics 13, no. 9 (2025): 1366. https://doi.org/10.3390/math13091366.

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During the last five years, spiking neural P (SN P) systems have attracted a lot of attention in the field of cryptography since these systems can more efficiently support advanced and complex cryptographic algorithms due to their high computational capabilities. Specifically, these systems can be seen as a potential solution to efficiently performing asymmetric algorithms, which are more demanding than symmetric systems. This factor becomes critical, especially in resource-constrained single-board computer systems, since many of these systems are currently used to ensure the security of IoT a

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20

Achuthan, P., and S. Sundar. "A new application of the extended Euclidean algorithm for matrix padé approximants." Computers & Mathematics with Applications 16, no. 4 (1988): 287–96. http://dx.doi.org/10.1016/0898-1221(88)90145-9.

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21

Mielke, Paul W., and Kenneth J. Berry. "Multivariate Multiple Regression Prediction Models: A Euclidean Distance Approach." Psychological Reports 92, no. 3 (2003): 763–69. http://dx.doi.org/10.2466/pr0.2003.92.3.763.

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An extension of a multiple regression prediction model to multiple response variables is presented. An algorithm using least sum of Euclidean distances between the multivariate observed and model-predicted response values provides regression coefficients, a measure of effect size, and inferential procedures for evaluating the extended multivariate multiple regression prediction model.

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22

Dilshad Akhtar et al. "Computation of Multiplicative Inverses of non-zero Polynomials of GF(73) by Gauss-Jordan method." Proceeding International Conference on Science and Engineering 11, no. 1 (2023): 1183–98. http://dx.doi.org/10.52783/cienceng.v11i1.260.

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The present manuscript deals with the derivation of multiplicative inverses of all non-zero elemental polynomials of the Galois field with respect to the monic irreducible polynomials of degree 3 over the prime field by Gauss-Jordan method as the Extended Euclidean Algorithm (EEA) is not always successful over the prime field , when prime .

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de la Fe, Sadiel, Han-Byeol Park, Bo-Yeon Sim, Dong-Guk Han, and Carles Ferrer. "Profiling Attack against RSA Key Generation Based on a Euclidean Algorithm." Information 12, no. 11 (2021): 462. http://dx.doi.org/10.3390/info12110462.

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A profiling attack is a powerful variant among the noninvasive side channel attacks. In this work, we target RSA key generation relying on the binary version of the extended Euclidean algorithm for modular inverse and GCD computations. To date, this algorithm has only been exploited by simple power analysis; therefore, the countermeasures described in the literature are focused on mitigating only this kind of attack. We demonstrate that one of those countermeasures is not effective in preventing profiling attacks. The feasibility of our approach relies on the extraction of several leakage vect

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Rospotniuk, Volodymyr, and Rupert Small. "Optimal Any-Angle Pathfinding on a Sphere." Journal of Artificial Intelligence Research 72 (October 21, 2021): 475–505. http://dx.doi.org/10.1613/jair.1.12483.

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    Pathfinding in Euclidean space is a common problem faced in robotics and computer games. For long-distance navigation on the surface of the earth or in outer space however, approximating the geometry as Euclidean can be insufficient for real-world applications such as the navigation of spacecraft, aeroplanes, drones and ships. This article describes an any-angle pathfinding algorithm for calculating the shortest path between point pairs over the surface of a sphere. Introducing several novel adaptations, it is shown that Anya as described by Harabor & Grastien f

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Hou, Jie, and William W. Symes. "Accelerating extended least-squares migration with weighted conjugate gradient iteration." GEOPHYSICS 81, no. 4 (2016): S165—S179. http://dx.doi.org/10.1190/geo2015-0499.1.

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Least-squares migration (LSM) iteratively achieves a mean-square best fit to seismic reflection data, provided that a kinematically accurate velocity model is available. The subsurface offset extension adds extra degrees of freedom to the model, thereby allowing LSM to fit the data even in the event of significant velocity error. This type of extension also implies additional computational expense per iteration from crosscorrelating source and receiver wavefields over the subsurface offset, and therefore places a premium on rapid convergence. We have accelerated the convergence of extended lea

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Zhou, Qiang, Chengliang Tian, Hanlin Zhang, Jia Yu, and Fengjun Li. "How to securely outsource the extended euclidean algorithm for large-scale polynomials over finite fields." Information Sciences 512 (February 2020): 641–60. http://dx.doi.org/10.1016/j.ins.2019.10.007.

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Palwinder, Kaur. "A Comparative Study and Performance Analysis of Kernelized Fuzzy C- means based Methods for Segmentation of Brain Magnetic Resonance Images." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 6, no. 7 (2019): 146–55. https://doi.org/10.5281/zenodo.3356905.

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In spite of being an effective image segmentation algorithm, the standard fuzzy c-means (FCM) is very sensitive to Rician noise and outliers in images. Thus, segmentation with FCM becomes problematic for brain magnetic resonance (MR) images where we need to segment tissues such as cerebrospinal fluid (CSF), gray matter (GM) and white matter (WM) from these images. Various FCM algorithms have been extended to their kernelized versions to make them enough robust to noise, outliers and other imaging artifacts and to reveal non-Euclidean structure of input data.  This paper presents a compara

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Kaye, P. R. "Optimized quantum implementation of elliptic curve arithmetic over binary fields." Quantum Information and Computation 5, no. 6 (2005): 474–91. http://dx.doi.org/10.26421/qic5.6-6.

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Shor's quantum algorithm for discrete logarithms applied to elliptic curve groups forms the basis of a ``quantum attack'' of elliptic curve cryptosystems. To implement this algorithm on a quantum computer requires the efficient implementation of the elliptic curve group operation. Such an implementation requires we be able to compute inverses in the underlying field. In \cite{PZ03}, Proos and Zalka show how to implement the extended Euclidean algorithm to compute inverses in the prime field $\GF(p)$. They employ a number of optimizations to achieve a running time of $O(n^2)$, and a space-requi

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Shalileh, Soroosh, and Boris Mirkin. "Community Partitioning over Feature-Rich Networks Using an Extended K-Means Method." Entropy 24, no. 5 (2022): 626. http://dx.doi.org/10.3390/e24050626.

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This paper proposes a meaningful and effective extension of the celebrated K-means algorithm to detect communities in feature-rich networks, due to our assumption of non-summability mode. We least-squares approximate given matrices of inter-node links and feature values, leading to a straightforward extension of the conventional K-means clustering method as an alternating minimization strategy for the criterion. This works in a two-fold space, embracing both the network nodes and features. The metric used is a weighted sum of the squared Euclidean distances in the feature and network spaces. T

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Dong, Shuda, and Heng Wang. "A Robust Tri-Electromagnet-Based 6-DoF Pose Tracking System Using an Error-State Kalman Filter." Sensors 24, no. 18 (2024): 5956. http://dx.doi.org/10.3390/s24185956.

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Magnetic pose tracking is a non-contact, accurate, and occlusion-free method that has been increasingly employed to track intra-corporeal medical devices such as endoscopes in computer-assisted medical interventions. In magnetic pose-tracking systems, a nonlinear estimation algorithm is needed to recover the pose information from magnetic measurements. In existing pose estimation algorithms such as the extended Kalman filter (EKF), the 3-DoF orientation in the S<sup>3</sup> manifold is normally parametrized as unit quaternions and simply treated as a vector in the Euclidean space,

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Bufalo, Michele, Daniele Bufalo, and Giuseppe Orlando. "A Note on the Computation of the Modular Inverse for Cryptography." Axioms 10, no. 2 (2021): 116. http://dx.doi.org/10.3390/axioms10020116.

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In literature, there are a number of cryptographic algorithms (RSA, ElGamal, NTRU, etc.) that require multiple computations of modulo multiplicative inverses. In this paper, we describe the modulo operation and we recollect the main approaches to computing the modulus. Then, given a and n positive integers, we present the sequence (zj)j≥0, where zj=zj−1+aβj−n, a<n and GCD(a,n)=1. Regarding the above sequence, we show that it is bounded and admits a simple explicit, periodic solution. The main result is that the inverse of a modulo n is given by a−1=⌊im⌋+1 with m=n/a. The computational cost

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GISBRECHT, ANDREJ, BASSAM MOKBEL, FRANK-MICHAEL SCHLEIF, XIBIN ZHU, and BARBARA HAMMER. "LINEAR TIME RELATIONAL PROTOTYPE BASED LEARNING." International Journal of Neural Systems 22, no. 05 (2012): 1250021. http://dx.doi.org/10.1142/s0129065712500219.

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Prototype based learning offers an intuitive interface to inspect large quantities of electronic data in supervised or unsupervised settings. Recently, many techniques have been extended to data described by general dissimilarities rather than Euclidean vectors, so-called relational data settings. Unlike the Euclidean counterparts, the techniques have quadratic time complexity due to the underlying quadratic dissimilarity matrix. Thus, they are infeasible already for medium sized data sets. The contribution of this article is twofold: On the one hand we propose a novel supervised prototype bas

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Pilarczyk, Rafał, and Władysław Skarbek. "On Intra-Class Variance for Deep Learning of Classifiers." Foundations of Computing and Decision Sciences 44, no. 3 (2019): 285–301. http://dx.doi.org/10.2478/fcds-2019-0015.

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Abstract A novel technique for deep learning of image classifiers is presented. The learned CNN models higher offer better separation of deep features (also known as embedded vectors) measured by Euclidean proximity and also no deterioration of the classification results by class membership probability. The latter feature can be used for enhancing image classifiers having the classes at the model’s exploiting stage different from from classes during the training stage. While the Shannon information of SoftMax probability for target class is extended for mini-batch by the intra-class variance,

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Wang, Juxiang, Si Li, and Xiangyu Zhou. "A Novel GDMD-PROMETHEE Algorithm Based on the Maximizing Deviation Method and Social Media Data Mining for Large Group Decision Making." Symmetry 15, no. 2 (2023): 387. http://dx.doi.org/10.3390/sym15020387.

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Multi-attribute group decision making is widely used in the real world, and many scholars have done a lot of research on it. The public’s focus on emergencies can provide an important reference for emergency handling decision making in the social media big data environment. Due to the complexity of emergency handling decision making, the asymmetry of user evaluation information is easy to cause the loss of important information. It is very important to mine valuable information for decision making through online reviews. Then, a generalized extended hybrid distance measure method between the p

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Ivanchuk, Y., Y. Horobets, and K. Koval. "Method for increasing the degree of protection of message encryption based on an algorithm for a constant component in time." System technologies 2, no. 139 (2022): 3–13. http://dx.doi.org/10.34185/1562-9945-2-139-2022-01.

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Currently, asymmetric cryptosystems are used everywhere, in document management for cryptocurrencies, providing a high level of protection to end users, relying on the mathematical complexity of calculating a discrete algorithm. But, it is possible to make a cryptocurrency attack on the so-called ephemeral key, which is an auxiliary key when creating a signature. Recent works have shown examples of cryptocurrencies on the random number generator, processor cache, timing attacks. However, these attacks do not work when the numerical value of the bits is unknown. Also, recent work shows the main

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Fournaris, Apostolos P., and O. Koufopavlou. "Applying systolic multiplication–inversion architectures based on modified extended Euclidean algorithm for GF(2k) in elliptic curve cryptography." Computers & Electrical Engineering 33, no. 5-6 (2007): 333–48. http://dx.doi.org/10.1016/j.compeleceng.2007.05.001.

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Volkov, Dmitrii Yu, and Kseniia V. Galunova. "Metric invariants of a second-order hypersurface in an n-dimensional Euclidean space." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9, no. 2 (2022): 219–28. http://dx.doi.org/10.21638/spbu01.2022.204.

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The article is devoted to the classical problem of analytic geometry in n-dimensional Euclidean space: finding the canonical equation of a quadric. The canonical equation is determined by the invariants of the second-order surface equation. Invariants are quantities that do not change under an affine change of space coordinates. S. L. Pevsner found a convenient system of the following invariants: q is the rank of the extended matrix of the system for determining the center of symmetry of the surface; the roots of the characteristic polynomial of the matrix of quadratic terms of the surface equ

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Grošek, Otokar, and Tomáš Fabšič. "Computing multiplicative inverses in finite fields by long division." Journal of Electrical Engineering 69, no. 5 (2018): 400–402. http://dx.doi.org/10.2478/jee-2018-0059.

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Abstract We study a method of computing multiplicative inverses in finite fields using long division. In the case of fields of a prime order p, we construct one fixed integer d(p) with the property that for any nonzero field element a, we can compute its inverse by dividing d(p) by a and by reducing the result modulo p. We show how to construct the smallest d(p) with this property. We demonstrate that a similar approach works in finite fields of a non-prime order, as well. However, we demonstrate that the studied method (in both cases) has worse asymptotic complexity than the extended Euclidea

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Wu, Chuan-Kun, and Bin Zhao. "On the Existence of Multiple RSA Private Keys." Security and Communication Networks 2022 (September 14, 2022): 1–6. http://dx.doi.org/10.1155/2022/4997392.

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It is known that, given an RSA modulus, n = p q , the public key e and the corresponding private key d satisfy the modulo congruence e d ≡ 1 mod ϕ n , where ϕ n = p − 1 q − 1 . Usually, the private key d can be computed efficiently using the extended Euclidean algorithm, and it is common knowledge that the private key is unique in the sense of modular ϕ n . This paper shows that there exist multiple private keys d ; they all satisfy that d < ϕ n . This paper also presents the exact relationship between an RSA public key and a corresponding private key.

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Francisco, Amyr Edmar, Angelo Lance Seraspi, Jamillah Guialil, and Khatalyn Mata. "An enhancement of the Eigenface algorithm using weber local descriptor applied in attendance management system." International Student Research Review 2, no. 1 (2025): 139–73. https://doi.org/10.53378/isrr.164.

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This study presents an improved face recognition system tackling the Eigenface algorithm's limitations regarding lighting variance, class separability, and classification. The proposed method incorporates Weber Local Descriptor (WLD) for illumination normalization during training and recognition. Further improvements include Kernel Principal Component Analysis (KPCA) for non-linear feature transformation, Linear Discriminant Analysis (LDA) to maximize class separability, and Ridge classification for noise-resistant recognition, replacing Euclidean distance. Testing on the extended Yale B datas

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ElSheikh, Muhammad, İrem Keskinkurt Paksoy, Murat Cenk, and M. Anwar Hasan. "Accelerating EdDSA Signature Verification with Faster Scalar Size Halving." IACR Transactions on Cryptographic Hardware and Embedded Systems 2025, no. 3 (2025): 493–515. https://doi.org/10.46586/tches.v2025.i3.493-515.

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This paper establishes that the extended Euclidean algorithm (EEA) implemented in a division-free manner is faster than the Lagrange algorithm with a similar level of optimization when it comes to halving the size of scalars found in the equations of elliptic curve signature verification. Our implementation results show that our EEA based method achieves roughly 4x speed-up for generating half- size scalars used in EdDSA. For the first time ever, EEA generated half-size scalars are used for verification of individual Ed25519 signatures yielding timing results that outperform ed25519-donna, a h

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Wu, Bingjian, Fan Zhang, Yi Wang, Min Hu, and Xue Bai. "Anomaly Detection Algorithm for Urban Infrastructure Construction Equipment Based on Multidimensional Time Series." Sustainability 16, no. 8 (2024): 3335. http://dx.doi.org/10.3390/su16083335.

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Safety is the foundation of urban sustainable development. The urban construction and operation process involves a large amount of multidimensional time series data. By detecting anomalies in these multidimensional time subsequences (MTSs), decision support can be provided for early warning of urban construction and operation risks. Considering the complexity of urban infrastructure, there is an urgent need for fast and accurate anomaly detection. This paper proposes a real-time anomaly detection algorithm based on improved distance measurement (RADIM). RADIM retains the relationships between

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Sghaier, Anissa, Medien Zeghid, Chiraz Massoud, Hassan Yousif Ahmed, Abdellah Chehri, and Mohsen Machhout. "Fast Constant-Time Modular Inversion over Fp Resistant to Simple Power Analysis Attacks for IoT Applications." Sensors 22, no. 7 (2022): 2535. http://dx.doi.org/10.3390/s22072535.

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The advent of the Internet of Things (IoT) has enabled millions of potential new uses for consumers and businesses. However, with these new uses emerge some of the more pronounced risks in the connected object domain. Finite fields play a crucial role in many public-key cryptographic algorithms (PKCs), which are used extensively for the security and privacy of IoT devices, consumer electronic equipment, and software systems. Given that inversion is the most sensitive and costly finite field arithmetic operation in PKCs, this paper proposes a new, fast, constant-time inverter over prime fields

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Singh, Arjun, Surbhi Chauhan, Shashi Kant Dargar, et al. "Blockchain enabled security mechanism for preventing data forgery in IoT-based smart homes." Journal of Discrete Mathematical Sciences and Cryptography 26, no. 5 (2023): 1437–46. http://dx.doi.org/10.47974/jdmsc-1769.

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Conventional homes have grown to be smart homes (SM) with the assistance of the Internet of Things (IoT). A unified gateway connects all Internet-enabled devices. Those gateways need to be secured by the usage of a sturdy safety method due to the fact safety is very vital. In order to conquer those problems, this observation shows employing Blockchain Technology (BC) for secured houses to make certain information private and safe. To cope with the safety problem with SH gateways, this paper proposes a solution. A reliable Q-learning algorithm with Blockchain assistance is proposed for the SH g

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NASRAOUI, OLFA, HICHEM FRIGUI, RAGHU KRISHNAPURAM, and ANUPAM JOSHI. "EXTRACTING WEB USER PROFILES USING RELATIONAL COMPETITIVE FUZZY CLUSTERING." International Journal on Artificial Intelligence Tools 09, no. 04 (2000): 509–26. http://dx.doi.org/10.1142/s021821300000032x.

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The proliferation of information on the World Wide Web has made the personalization of this information space a necessity. An important component of Web personalization is to mine typical user profiles from the vast amount of historical data stored in access logs. In the absence of any a priori knowledge, unsupervised classification or clustering methods seem to be ideally suited to analyze the semi-structured log data of user accesses. In this paper, we define the notion of a "user session" as being a temporally compact sequence of Web accesses by a user. We also define a new distance measure

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Alqwaifly, Nawaf A. "Peak-Shift Control Codes for the $L_1$ Metric." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5873. https://doi.org/10.29020/nybg.ejpam.v18i2.5873.

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This paper gives some theory and efficient design of $q$-ary block codes capable of controlling the single peak-shifts of one direction (left or right shift) of size $l$. This problem of controlling $l_{L}(l_{R})$-peak-shift is shown to be equivalent to the efficient design of some $L_{1}$ metric asymmetric error control codes over the natural alphabet, $\inat$. From the relations with the $L_{1}$ distance error control codes and constant weight codes, new improved upper and lower bounds on the size of the optimal single $l_{L}(l_{R})$-peak-shifts error correcting codes are given. Furthermore,

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Gallardo-Alvarado, Jaime, Mario Garcia-Murillo, Juan Tabares-Martinez, and X. Sandoval-Castro. "Symbolic Computation of the Lie Algebra se(3) of the Euclidean Group SE(3): An Application to the Infinitesimal Kinematics of Robot Manipulators." Mathematics 12, no. 16 (2024): 2538. http://dx.doi.org/10.3390/math12162538.

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This paper reports an application of the Lie algebra se(3) of the Euclidean group SE(3), which is isomorphic to the theory of screws in the velocity and acceleration analyses of serial manipulators. The symbolic computation of the infinitesimal kinematics allows one to obtain algebraic expressions related to the kinematic characteristics of the end effector of the serial manipulator, while in the case of complex manipulators, numerical computations are preferred owing to the emergence of long terms. The algorithm presented enables the symbolic computation of the velocity and acceleration chara

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Ushakov, Andrey L. "Investigation of the problem of representation of a linear functional in the form of a scoal product." Yugra State University Bulletin 18, no. 3 (2022): 152–62. http://dx.doi.org/10.18822/byusu202203152-162.

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Subject of research: the problem of representing a linear functional in the form of a scalar product in the Hilbert space. For example, this may be the Dirichlet problem for a second-order elliptic equation in variational form. Purpose of research: to present a general scheme of the method of iterative extensions for solving elliptic boundary value problems with Dirichlet conditions. Methods and objects of research: the object of study in such a problem can be the deformation of the membrane. A continuation of the considered problem in the Hilbert space is given. The extended probl

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Du, Mo, Shu Li, and Qiang Li. "A Novel Method of Efficient Max-min Metric for Classification." Journal of Physics: Conference Series 2449, no. 1 (2023): 012014. http://dx.doi.org/10.1088/1742-6596/2449/1/012014.

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Abstract Distance metric learning is an important method to study distance metrics that reflect the interaction between features and labels. Because of the high computational complexity and the fact that existing studies on algorithms that measure the similarities with Euclidean distances cannot reflect the real correlations between pairs of samples, learning a suitable distance metric is quite demanding for many data mining tasks. This paper innovatively proposes an extended efficient max-min metric (EMM) that maximizes the total distance between different pairs and minimizes the total distan

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Madasu, Sairam. "A Research to Study Concerns Regarding the Security of Cloud Computing." International Journal of Research 10, no. 8 (2023): 270–74. https://doi.org/10.5281/zenodo.8265734.

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<em>Concerning the safety of data stored in the cloud is the focus of this article.   The most recent advancements in computing have caused a sea shift in how people see the architecture and development of IT systems.   As the dangers and threats to sensitive information continue to grow, this article will discuss the many methods now in use throughout the world to keep it safe. In addition, the concept of an encryption/decryption algorithm-based, simple, safe, and privacy-preserving system for inter-cloud data exchange against unauthorised access is presented. Si

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