Solving Exponential Diophantine Equations Using Lattice Basis Reduction Algorithms

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Lattice Basis Reduction

Author : Murray R. Bremner
Publisher : CRC Press
ISBN 13 : 1439807027
Total Pages : 336 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Lattice Basis Reduction by : Murray R. Bremner

Download or read book Lattice Basis Reduction written by Murray R. Bremner and published by CRC Press. This book was released on 2011-08-12 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: First developed in the early 1980s by Lenstra, Lenstra, and Lovász, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial factorization, and matrix canonical forms.

Arithmetic Geometry, Number Theory, and Computation

Author : Jennifer S. Balakrishnan
Publisher : Springer Nature
ISBN 13 : 3030809145
Total Pages : 587 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Arithmetic Geometry, Number Theory, and Computation by : Jennifer S. Balakrishnan

Download or read book Arithmetic Geometry, Number Theory, and Computation written by Jennifer S. Balakrishnan and published by Springer Nature. This book was released on 2022-03-15 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.

Algorithms for Diophantine Equations

Author : Benne M. M. De Weger
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Algorithms for Diophantine Equations by : Benne M. M. De Weger

Download or read book Algorithms for Diophantine Equations written by Benne M. M. De Weger and published by . This book was released on 1989 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Number Theory

Author : Henri Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 038749894X
Total Pages : 619 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis Number Theory by : Henri Cohen

Download or read book Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2008-12-17 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.

Number Theory and Cryptography

Author : J. H. Loxton
Publisher : Cambridge University Press
ISBN 13 : 0521398770
Total Pages : 249 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Number Theory and Cryptography by : J. H. Loxton

Download or read book Number Theory and Cryptography written by J. H. Loxton and published by Cambridge University Press. This book was released on 1990-04-19 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers presented by prominent contributors at a workshop on Number Theory and Cryptography, and the annual meeting of the Australian Mathematical Society.

Number Theory

Author : Richard Mollin
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110848635
Total Pages : 676 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Number Theory by : Richard Mollin

Download or read book Number Theory written by Richard Mollin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-12-19 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Unsolved Problems in Number Theory

Author : Richard Guy
Publisher : Springer Science & Business Media
ISBN 13 : 1489935851
Total Pages : 303 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Unsolved Problems in Number Theory by : Richard Guy

Download or read book Unsolved Problems in Number Theory written by Richard Guy and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.

A Panorama of Number Theory Or The View from Baker's Garden

Author : Gisbert Wüstholz
Publisher : Cambridge University Press
ISBN 13 : 9780521807999
Total Pages : 378 pages
Book Rating : 4.8/5 (79 download)

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Book Synopsis A Panorama of Number Theory Or The View from Baker's Garden by : Gisbert Wüstholz

Download or read book A Panorama of Number Theory Or The View from Baker's Garden written by Gisbert Wüstholz and published by Cambridge University Press. This book was released on 2002-09-26 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a selection of high quality articles on number theory by leading figures.

Advances in Cryptology - EUROCRYPT 2006

Author : Serge Vaudenay
Publisher : Springer Science & Business Media
ISBN 13 : 3540345469
Total Pages : 624 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Advances in Cryptology - EUROCRYPT 2006 by : Serge Vaudenay

Download or read book Advances in Cryptology - EUROCRYPT 2006 written by Serge Vaudenay and published by Springer Science & Business Media. This book was released on 2006-05-26 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 25th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2006. 33 revised full papers are presented together with 2 invited talks. The papers are organized in topical sections on cryptanalysis, cryptography meets humans, stream ciphers, hash functions, oblivious transfer, numbers and lattices, foundations, block ciphers, cryptography without random oracles, multiparty computation, and cryptography for groups.

Solving $S$-Unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture

Author : Rafael von Känel
Publisher : American Mathematical Society
ISBN 13 : 1470464160
Total Pages : 154 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Solving $S$-Unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture by : Rafael von Känel

Download or read book Solving $S$-Unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture written by Rafael von Känel and published by American Mathematical Society. This book was released on 2023-06-22 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Computability and Complexity in Analysis

Author : Jens Blanck
Publisher : Springer
ISBN 13 : 3540453350
Total Pages : 403 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Computability and Complexity in Analysis by : Jens Blanck

Download or read book Computability and Complexity in Analysis written by Jens Blanck and published by Springer. This book was released on 2003-06-29 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: The workshop on Computability and Complexity in Analysis, CCA 2000, was hosted by the Department of Computer Science of the University of Wales Swansea, September 17{19, 2000. It was the fourth workshop in a successful series of workshops: CCA’95 in Hagen, Germany, CCA’96 in Trier, Germany, and CCA’98 in Brno, Czech Republic. About 40 participants from the countries United Kingdom, Germany, Japan, Italy, Russia, France, Denmark, Greece, and Ireland contributed to the success of this meeting. Altogether, 28 talkswere p- sented in Swansea. These proceedings include 23 papers which represent a cro- section through recent research on computability and complexity in analysis. The workshop succeeded in bringing together people interested in computability and complexity aspects of analysis and in exploring connections with nume- cal methods, physics and, of course, computer science. It was rounded o by a number of talks and papers on exact computer arithmetic and by a competition of v e implemented systems. A report on this competition has been included in these proceedings. We would like to thank the authors for their contributions and the referees for their careful work, and we hope for further inspiring and constructive meetings of the same kind. April 2001 Jens Blanck Vasco Brattka Peter Hertling Organization CCA2000was hosted by the Department of Computer Science of the University of Wales Swansea and took place on September 17{19, 2000.

Unit Equations in Diophantine Number Theory

Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
ISBN 13 : 1316432351
Total Pages : 381 pages
Book Rating : 4.3/5 (164 download)

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Book Synopsis Unit Equations in Diophantine Number Theory by : Jan-Hendrik Evertse

Download or read book Unit Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2015-12-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.

Some Tapas of Computer Algebra

Author : Arjeh M. Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 3662038919
Total Pages : 365 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Some Tapas of Computer Algebra by : Arjeh M. Cohen

Download or read book Some Tapas of Computer Algebra written by Arjeh M. Cohen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.

Information Security

Author : Colin Boyd
Publisher : Springer Science & Business Media
ISBN 13 : 3540201769
Total Pages : 453 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Information Security by : Colin Boyd

Download or read book Information Security written by Colin Boyd and published by Springer Science & Business Media. This book was released on 2003-09-24 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 6th International Conference on Information Security, ISC 2003, held in Bristol, UK in October 2003. The 31 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 133 submissions. The papers are organized in topical sections on network security, public key algorithms, cryptographic protocols, protocol attacks, attacks on public key cryptosystems, block ciphers, authorization, water marking, software security, and codes and related issues.

Number Theory

Author : Jean-Marie De Koninck
Publisher : Walter de Gruyter
ISBN 13 : 9783110117912
Total Pages : 1038 pages
Book Rating : 4.1/5 (179 download)

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Book Synopsis Number Theory by : Jean-Marie De Koninck

Download or read book Number Theory written by Jean-Marie De Koninck and published by Walter de Gruyter. This book was released on 1989 with total page 1038 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monumental proceedings (very handsomely produced) of a major international conference. The book contains 74 refereed articles which, apart from a few survey papers of peculiar interest, are mostly research papers (63 in English, 11 in French). The topics covered reflect the full diversity of the current trends and activities in modern number theory: elementary, algebraic and analytic number theory; constructive (computational) number theory; elliptic curves and modular forms; arithmetical geometry; transcendence; quadratic forms; coding theory. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Information Security Applications

Author : Jooseok Song
Publisher : Springer
ISBN 13 : 3540331530
Total Pages : 388 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Information Security Applications by : Jooseok Song

Download or read book Information Security Applications written by Jooseok Song and published by Springer. This book was released on 2006-02-02 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 6th International Workshop on Information Security Applications, WISA 2005, held in Jeju Island, Korea, in August 2005. The 29 revised full papers presented were carefully selected during two rounds of reviewing and improvement from 168 submissions. The papers are organized in topical sections on security analysis and attacks, systems security, network security, DRM/software security, efficient HW implementation, side-channel attacks, privacy/anonymity, and efficient implementation.

International Symposium in Memory of Hua Loo Keng

Author : Sheng Gong
Publisher : Springer
ISBN 13 : 366207981X
Total Pages : 356 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis International Symposium in Memory of Hua Loo Keng by : Sheng Gong

Download or read book International Symposium in Memory of Hua Loo Keng written by Sheng Gong and published by Springer. This book was released on 2013-12-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The international symposium on number theory and analysis in memory of the late famous Chinese mathematician Professor Hua Loo Keng took place in August 1988 at the Tsinghua University in Beijing. Excellent survey lectures and expositions of the most recent results in number theory and analysis were given by experts from all over the world. While Volume I focuses on number theory, Volume II deals mainly with several complex variables, differential geometry and classical complex analysis. Both volumes also include two fascinating accounts of Professor Hua Loo Keng's life and work by Professor S. Iyanaga and Professor Wang Yuan. Highlights in Volume I: D.A. Hejhal: Eigenvalues of the Laplacian for PSL (2 Z): Some new Results and Computational Techniques.- A.A. Karatsuba: On the Zeros of Riemann's Zeta-Function on the Critical Line.- H.E. Richert: Aspects of the Small Sieve.- W.M. Schmidt: On the Number of Good Simultaneous Approximations to Algebraic Numbers.- M.V. Subbarao, Wang Yuan: On a Generalized Waring's Problem in Algebraic Number Fields.- G. WA1/4stholz: From Baker to Mordell. Highlights in Volume II: F. Capocasa, F. Catanese: Periodic Meroporphic Functions and Lefschetz Type Theorems on Quasi-Abelian Varieties.- S.S. Chern: Families of Hypersurfaces Under Contact Transformations in Rn.- G. Dethloff, H. Grauert: On the Infinitesimal Deformation of Simply Connected Domains in One Complex Variable.- D. Drasin: Asymptotic Periods of Entire and Meromorphic Functions.- D. Gaier: On the Convergence of the Bieberbach Polynomials in Regions With Corners.- Gong Sheng, Zheng Xuena: Distortion Theorem for Biholomorphic Mappings in Transitive Domains (I).- C.O. Kiselman: Tangents of Plurisubharmonic Functions.- A. KorAnyi: Hua-Type Integrals, Hypergeometric Functions and Symmetric Polynomials.- J. Mitchell: Two-Sided L1-Estimates for SzegA Kernels on Classical Domains.- I. Satake: On the Rational Structures of Symmetric Domains, I.- Y.-T. Siu: Some Problems of Rigidity in Several Complex Variables.- S.-T. Yau, F. Zheng: On Projective Manifolds Covered by Space in Cn.