Buch, Englisch, Band 2369, 522 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1630 g
5th International Symposium, ANTS-V, Sydney, Australia, July 7-12, 2002. Proceedings
Buch, Englisch, Band 2369, 522 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1630 g
Reihe: Lecture Notes in Computer Science
ISBN: 978-3-540-43863-2
Verlag: Springer Berlin Heidelberg
. 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. 390 AlfredJ. vanderPoorten,XuanChuongTran DiscreteLogarithmsandFactoring FixedPointsandTwo-CyclesoftheDiscreteLogarithm. 405 JoshuaHolden RandomCayleyDigraphsandtheDiscreteLogarithm. 416 JeremyHorwitz,RamarathnamVenkatesan TheFunctionFieldSieveIsQuiteSpecial. 431 AntoineJoux,ReynaldLercier MPQSwithThreeLargePrimes. 446 PaulLeyland,ArjenLenstra,BruceDodson,AlecMu?ett,SamWagsta? AnImprovedBabyStepGiantStepAlgorithm forPointCountingofHyperellipticCurvesoverFiniteFields. 461 KazutoMatsuo,JinhuiChao,ShigeoTsujii 2 FactoringN=pq withtheEllipticCurveMethod. 475 PeterEbinger,EdlynTeske Gr¨obnerBases ANewSchemeforComputingwithAlgebraicallyClosedFields. 491 AllanSteel X TableofContents Complexity AdditiveComplexityandRootsofPolynomials overNumberFieldsandp-adicFields. 506 J. MauriceRojas AuthorIndex. 517 Gauss Composition and Generalizations ManjulBhargava Clay Mathematics Institute and Princeton University Abstract. We discuss several higher analogues of Gauss composition and consider their potential algorithmic applications.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
- Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
- Mathematik | Informatik Mathematik Algebra Zahlentheorie
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
Weitere Infos & Material
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.
