Algorithmic Number Theory

Claus Fieker

ISBN 10: 3540438637 / ISBN 13: 9783540438632

Published by Springer, Springer Jun 2002, 2002

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -Invited Talks.- Gauss Composition and Generalizations.- Elliptic Curves - The Crossroads of Theory and Computation.- The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems.- Using Elliptic Curves of Rank One towards the Undecidability of Hilbert's Tenth Problem over Rings of Algebraic Integers.- On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields.- Number Theory.- On Arithmetically Equivalent Number Fields of Small Degree.- A Survey of Discriminant Counting.- A Higher-Rank Mersenne Problem.- An Application of Siegel Modular Functions to Kronecker's Limit Formula.- Computational Aspects of NUCOMP.- Efficient Computation of Class Numbers of Real Abelian Number Fields.- An Accelerated Buchmann Algorithm for Regulator Computation in Real Quadratic Fields.- Arithmetic Geometry.- Some Genus 3 Curves with Many Points.- Trinomials ax 7 + bx + c and ax 8 + bx + c with Galois Groups of Order 168 and 8 168.- Computations on Modular Jacobian Surfaces.- Integral Points on Punctured Abelian Surfaces.- Genus 2 Curves with (3, 3)-Split Jacobian and Large Automorphism Group.- Transportable Modular Symbols and the Intersection Pairing.- Elliptic Curves and CM.- Action of Modular Correspondences around CM Points.- Curves Dy 2 = x 3 - x of Odd Analytic Rank.- Comparing Invariants for Class Fields of Imaginary Quadratic Fields.- A Database of Elliptic Curves - First Report.- Point Counting.- Isogeny Volcanoes and the SEA Algorithm.- Fast Elliptic Curve Point Counting Using Gaussian Normal Basis.- An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2.- Cryptography.- Implementing the Tate Pairing.- Smooth Orders and Cryptographic Applications.- Chinese Remaindering for Algebraic Numbers in a Hidden Field.-Function Fields.- An Algorithm for Computing Weierstrass Points.- New Optimal Tame Towers of Function Fields over Small Finite Fields.- Periodic Continued Fractions in Elliptic Function Fields.- Discrete Logarithms and Factoring.- Fixed Points and Two-Cycles of the Discrete Logarithm.- Random Cayley Digraphs and the Discrete Logarithm.- The Function Field Sieve Is Quite Special.- MPQS with Three Large Primes.- An Improved Baby Step Giant Step Algorithm for Point Counting of Hyperelliptic Curves over Finite Fields.- Factoring N = pq 2 with the Elliptic Curve Method.- Gröbner Bases.- A New Scheme for Computing with Algebraically Closed Fields.- Complexity.- Additive Complexity and Roots of Polynomials over Number Fields and -adic Fields.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 532 pp. Englisch.

Seller Inventory # 9783540438632

Bibliographic Details

• Title: Algorithmic Number Theory
• Publisher: Springer, Springer Jun 2002
• Publication Date: 2002
• Language: English
• ISBN 10: 3540438637
• ISBN 13: 9783540438632
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 29D millimeters 235 millimeters width by 155 millimeters height by 29 millimeters depth
• Weight: 797 grams

About this title

Synopsis

. 9 JohnCoates TheWeilandTatePairingsasBuildingBlocks forPublicKeyCryptosystems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 AntoineJoux UsingEllipticCurvesofRankOnetowardstheUndecidability ofHilbert’sTenthProblemoverRingsofAlgebraicIntegers. . . . . . . . . . . . . 33 BjornPoonen Onp-adicPointCountingAlgorithmsforEllipticCurves overFiniteFields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 TakakazuSatoh NumberTheory OnArithmeticallyEquivalentNumberFieldsofSmallDegree . . . . . . . . . . . 67 WiebBosma,BartdeSmit ASurveyofDiscriminantCounting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 HenriCohen,FranciscoDiazyDiaz,MichelOlivier AHigher-RankMersenneProblem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 GrahamEverest,PeterRogers,ThomasWard AnApplicationofSiegelModularFunctions toKronecker’sLimitFormula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 TakashiFukuda,KeiichiKomatsu ComputationalAspectsofNUCOMP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 MichaelJ. Jacobson,Jr. ,AlfredJ. vanderPoorten E?cientComputationofClassNumbersofRealAbelianNumberFields. . 134 St´ephaneR. Louboutin AnAcceleratedBuchmannAlgorithmforRegulatorComputation inRealQuadraticFields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 UlrichVollmer VIII TableofContents ArithmeticGeometry SomeGenus3CurveswithManyPoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 RolandAuer,JaapTop 7 8 Trinomialsax +bx+candax +bx+c withGaloisGroupsofOrder168and8·168. . . . . . . . . . . . . . . . . . . . . . . . . . . 172 NilsBruin,NoamD. Elkies ComputationsonModularJacobianSurfaces. . . . . . . . . . . . . . . . . . . . . . . . . . 189 EnriqueGonz´alez-Jim´enez,JosepGonz´alez,JordiGu`ardia IntegralPointsonPuncturedAbelianSurfaces. . . . . . . . . . . . . . . . . . . . . . . . . 198 AndrewKresch,YuriTschinkel Genus2Curveswith(3,3)-SplitJacobian andLargeAutomorphismGroup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 TonyShaska TransportableModularSymbolsandtheIntersectionPairing. . . . . . . . . . . . 219 HelenaA. Verrill EllipticCurvesandCM ActionofModularCorrespondencesaroundCMPoints. . . . . . . . . . . . . . . . . 234 Jean-MarcCouveignes,ThierryHenocq 2 3 CurvesDy =x ?xofOddAnalyticRank. . . . . . . . . . . . . . . . . . . . . . . . . . . 244 NoamD. Elkies ComparingInvariantsforClassFieldsofImaginaryQuadraticFields. . . . . 252 AndreasEnge,Fran¸coisMorain ADatabaseofEllipticCurves–FirstReport. . . . . . . . . . . . . . . . . . . . . . . . . . 267 WilliamA. Stein,MarkWatkins PointCounting IsogenyVolcanoesandtheSEAAlgorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 MireilleFouquet,Fran¸coisMorain FastEllipticCurvePointCountingUsingGaussianNormalBasis. . . . . . . . 292 HaeYoungKim,JungYoulPark,JungHeeCheon,JeHongPark, JaeHeonKim,SangGeunHahn AnExtensionofKedlaya’sAlgorithmtoArtin-SchreierCurves inCharacteristic2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 JanDenef,FrederikVercauteren TableofContents IX Cryptography ImplementingtheTatePairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 StevenD. Galbraith,KeithHarrison,DavidSoldera SmoothOrdersandCryptographicApplications. . . . . . . . . . . . . . . . . . . . . . . 338 CarlPomerance,IgorE. Shparlinski ChineseRemainderingforAlgebraicNumbersinaHiddenField. . . . . . . . . 349 IgorE. Shparlinski,RonSteinfeld FunctionFields AnAlgorithmforComputingWeierstrassPoints. . . . . . . . . . . . . . . . . . . . . . . 357 FlorianHess NewOptimalTameTowersofFunctionFieldsoverSmallFiniteFields . . . 372 Wen-ChingW. Li,HirenMaharaj,HenningStichtenoth, NoamD. Elkies PeriodicContinuedFractionsinEllipticFunctionFields. . . . . . . . . .

Review

From the reviews:

"The book contains 39 articles about computational algebraic number theory, arithmetic geometry and cryptography. ... The articles in this book reflect the broad interest of the organizing committee and the participants. The emphasis lies on the mathematical theory as well as on computational results. We recommend the book to students and researchers who want to read about current research in number theory and arithmetic geometry and its applications." (R. Carls, Nieuw Archief voor Wiskunde, Vol. 6 (3), 2005)