Relevant bibliographies by topics / Extended Euclidean algorithm

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Extended Euclidean algorithm'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Extended Euclidean algorithm"

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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Extended Euclidean algorithm"

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Daneshbeh, Amir. "Bit Serial Systolic Architectures for Multiplicative Inversion and Division over GF(2m)." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/776.

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Systolic architectures are capable of achieving high throughput by maximizing pipelining and by eliminating global data interconnects. Recursive algorithms with regular data flows are suitable for systolization. The computation of multiplicative inversion using algorithms based on EEA (Extended Euclidean Algorithm) are particularly suitable for systolization. Implementations based on EEA present a high degree of parallelism and pipelinability at bit level which can be easily optimized to achieve local data flow and to eliminate the global interconnects which represent most important bot
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Abu-Mahfouz, Adnan Mohammed. "Elliptic curve cryptosystem over optimal extension fields for computationally constrained devices." Diss., University of Pretoria, 2004. http://hdl.handle.net/2263/25330.

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Data security will play a central role in the design of future IT systems. The PC has been a major driver of the digital economy. Recently, there has been a shift towards IT applications realized as embedded systems, because they have proved to be good solutions for many applications, especially those which require data processing in real time. Examples include security for wireless phones, wireless computing, pay-TV, and copy protection schemes for audio/video consumer products and digital cinemas. Most of these embedded applications will be wireless, which makes the communication channel vul
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Vestin, Albin, and Gustav Strandberg. "Evaluation of Target Tracking Using Multiple Sensors and Non-Causal Algorithms." Thesis, Linköpings universitet, Reglerteknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-160020.

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Today, the main research field for the automotive industry is to find solutions for active safety. In order to perceive the surrounding environment, tracking nearby traffic objects plays an important role. Validation of the tracking performance is often done in staged traffic scenarios, where additional sensors, mounted on the vehicles, are used to obtain their true positions and velocities. The difficulty of evaluating the tracking performance complicates its development. An alternative approach studied in this thesis, is to record sequences and use non-causal algorithms, such as smoothing, i
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Liu, Hsin-Yu, and 劉欣諭. "A Variation on Extended Euclidean Algorithm." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/19364081886415380592.

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碩士<br>國立中興大學<br>資訊科學研究所<br>93<br>Finite field arithmetic is more and more important in cryptography, such examples as in the RSA Cryptosystem [14], Digital Signature Algorithm and Elliptic Curve Cryptosystem [10][12] etc. Amount the basic operations; the multiplicative inversion is the most complex one. As we know, there are some methods to compute multiplicative inverses; such as Fermat’s little theorem, extended Euclid algorithm (EEA) and Mongromery algorithm[4][11][16]. In the software implement, EEA based scheme is the most efficiently and widely used algorithm for inversion in large numbe
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Hazmi, Ibrahim. "Systolic design space exploration of EEA-based inversion over binary and ternary fields." Thesis, 2018. https://dspace.library.uvic.ca//handle/1828/9981.

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Cryptographic protocols are implemented in hardware to ensure low-area, high speed and reduced power consumption especially for mobile devices. Elliptic Curve Cryptography (ECC) is the most commonly used public-key cryptosystem and its performance depends heavily on efficient finite field arithmetic hardware. Finding the multiplicative inverse (inversion) is the most expensive finite field operation in ECC. The two predominant algorithms for computing finite field inversion are Fermat’s Little Theorem (FLT) and Extended Euclidean Algorithm (EEA). EEA is reported to be the most efficient invers
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Book chapters on the topic "Extended Euclidean algorithm"

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Chi, Po-Wen, Yuan-Pang Lin, Ming-Hung Wang, and Yun-Hsin Chuang. "An Extended Euclidean Algorithm Implementation over Ciphertext Space." In Smart Innovation, Systems and Technologies. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-97-7786-0_42.

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Ito, Takehiro, Yuichiro Shibata, and Kiyoshi Oguri. "Implementation of the Extended Euclidean Algorithm for the Tate Pairing on FPGA." In Field Programmable Logic and Application. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-30117-2_98.

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Peinado, Alberto, and Andrés Ortiz. "Cryptanalysis of Multicast Protocols with Key Refreshment Based on the Extended Euclidean Algorithm." In Computational Intelligence in Security for Information Systems. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21323-6_22.

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Ramachandran, Parthasarathy. "Use of Extended Euclidean Algorithm in Solving a System of Linear Diophantine Equations with Bounded Variables." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11792086_14.

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Dai, Qionghai, and Yue Gao. "Neural Networks on Hypergraph." In Artificial Intelligence: Foundations, Theory, and Algorithms. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0185-2_7.

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AbstractWith the development of deep learning on high-order correlations, hypergraph neural networks have received much attention in recent years. Generally, the neural networks on hypergraph can be divided into two categories, including the spectral-based methods and the spatial-based methods. For the spectral-based methods, the convolution operation is formulated in the spectral domain of graph, and we introduce the typical spectral-based methods, including hypergraph neural networks (HGNN), hypergraph convolution with attention (Hyper-Atten), and hyperbolic hypergraph neural network (HHGNN)
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"Extended Euclidean Algorithm." In Encyclopedia of Cryptography and Security. Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_1073.

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"Extended Euclidean Algorithm." In Encyclopedia of Cryptography, Security and Privacy. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-030-71522-9_300347.

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Prajapat, Gopal Krishan, and Rakesh Kumar. "A Hybrid Approach for Facial Expression Recognition Using Extended Local Binary Patterns and Principal Component Analysis." In Research Anthology on Rehabilitation Practices and Therapy. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-3432-8.ch026.

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Facial feature extraction and recognition plays a prominent role in human non-verbal interaction and it is one of the crucial factors among pose, speech, facial expression, behaviour and actions which are used in conveying information about the intentions and emotions of a human being. In this article an extended local binary pattern is used for the feature extraction process and a principal component analysis (PCA) is used for dimensionality reduction. The projections of the sample and model images are calculated and compared by Euclidean distance method. The combination of extended local bin
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Conference papers on the topic "Extended Euclidean algorithm"

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Fournaris, Apostolos P., and Odysseas Koufopavlou. "One Dimensional Systolic Inversion Architecture Based on Modified GF(2^k) Extended Euclidean Algorithm." In 2009 12th Euromicro Conference on Digital System Design, Architectures, Methods and Tools (DSD). IEEE, 2009. http://dx.doi.org/10.1109/dsd.2009.161.

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Fournaris, A. P., and O. Koufopavlou. "A Systolic Inversion Architecture Based on Modified Extended Euclidean Algorithm for GF(2K) Fields." In 2006 13th IEEE International Conference on Electronics, Circuits and Systems. IEEE, 2006. http://dx.doi.org/10.1109/icecs.2006.379626.

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Phiamphu, Dongmuanthang, and Prabir Saha. "Redesigned the Architecture of Extended-Euclidean Algorithm for Modular Multiplicative Inverse and Jacobi Symbol." In 2018 2nd International Conference on Trends in Electronics and Informatics (ICOEI). IEEE, 2018. http://dx.doi.org/10.1109/icoei.2018.8553922.

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Muhammad, Khairun Nisak, та Hailiza Kamarulhaili. "On the sequences ri, si, ti ∈ ℤ related to extended Euclidean algorithm and continued fractions". У INNOVATIONS THROUGH MATHEMATICAL AND STATISTICAL RESEARCH: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4952482.

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Kampf, Sabine, and Martin Bossert. "A fast Generalized Minimum Distance decoder for Reed-Solomon codes based on the extended Euclidean algorithm." In 2010 IEEE International Symposium on Information Theory - ISIT. IEEE, 2010. http://dx.doi.org/10.1109/isit.2010.5513705.

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Xu, Xiaoqiang, Shikui Chen, Xianfeng David Gu, and Michael Yu Wang. "Conformal Topology Optimization of Heat Conduction Problems on Manifolds Using an Extended Level Set Method (X-LSM)." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-67819.

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Abstract In this paper, the authors propose a new dimension reduction method for level-set-based topology optimization of conforming thermal structures on free-form surfaces. Both the Hamilton-Jacobi equation and the Laplace equation, which are the two governing PDEs for boundary evolution and thermal conduction, are transformed from the 3D manifold to the 2D rectangular domain using conformal parameterization. The new method can significantly simplify the computation of topology optimization on a manifold without loss of accuracy. This is achieved due to the fact that the covariant derivative
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Gasiorek, Marcin, Daniel Simson, and Katarzyna Zajac. "On Corank Two Edge-Bipartite Graphs and Simply Extended Euclidean Diagrams." In 2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2014. http://dx.doi.org/10.1109/synasc.2014.17.

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Khan, Nadeem S., Jami J. Shah, and Joseph K. Davidson. "Probability Tolerance Maps: A New Statistical Model for Non-Linear Tolerance Analysis Applied to Rectangular Faces." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28937.

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A new statistical model for the tolerance analysis based upon joint probability distribution of the trivariate normal distributed variables involved in the construction of Tolerance-maps (T-Maps) for rectangular face is presented. Central to the new model is a Tolerance-Map (T-Map) (Patent No. 69638242). It is the range of points resulting from a one-to-one mapping from all the variational possibilities of a perfect-form feature, within its tolerance-zone, to a specially designed Euclidean point-space. The model is fully compatible with the ASME/ANSI/ISO Standard for geometric tolerances. In t
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Benger, Werner. "Illustrating Geometric Algebra and Differential Geometry in 5D Color Space." In WSCG 2023 – 31. International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision. University of West Bohemia, Czech Republic, 2023. http://dx.doi.org/10.24132/csrn.3301.1.

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Geometric Algebra (GA) is popular for its immediate geometric interpretations of algebraic objects and operations. It is based on Clifford Algebra on vector spaces and extends linear algebra of vectors by operations such as an invertible product, i.e. divisions by vectors. This formalism allows for a complete algebra on vectors same as for scalar or complex numbers. It is particularly suitable for rotations in arbitrary dimensions. In Euclidean 3D space quaternions are known to be numerically superior to rotation matrices and already widely used in computer graphics. However, their meaning bey
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