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E-grāmata: Algorithmic Number Theory: 5th International Symposium, ANTS-V, Sydney, Australia, July 7-12, 2002. Proceedings

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  • Formāts: PDF+DRM
  • Sērija : Lecture Notes in Computer Science 2369
  • Izdošanas datums: 02-Aug-2003
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783540454557
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Algorithmic Number Theory: 5th International Symposium, ANTS-V, Sydney, Australia, July 7-12, 2002. ProceedingsPalielināt
  • Formāts: PDF+DRM
  • Sērija : Lecture Notes in Computer Science 2369
  • Izdošanas datums: 02-Aug-2003
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783540454557
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TheAlgorithmicNumberTheorySymposiabeganin1994atCornellUniversity inIthaca,NewYorktorecognizethegrowingimportanceofalgorithmicwork in the theory of numbers. The subject of the conference is broadly construed toencompassadiversebodyofmathematics,andtocoverboththetheoretical andpracticaladvancesinthe eld. Theyhavebeenheldeverytwoyearssince: inBordeaux(Universit'eBordeauxI)in1996,Portland(ReedCollege)in1998, Leiden(UniversiteitLeiden)in2000,andthepresentconferencehostedbythe MagmaComputationalAlgebraGroupattheUniversityofSydney. TheconferenceprogramincludedinvitedtalksbyManjulBhargava(Prin- ton),JohnCoates(Cambridge),AntoineJoux(DCSSICryptoLab),BjornP- nen(Berkeley),andTakakazuSatoh(Saitama),aswellas34contributedtalks invariousareasofnumbertheory. Inadditiontothemathematicalprogram,the conferenceincludedaspecialdinnertohonourAlfvanderPoortenofMacquarie University,ontheoccasionofhis60thbirthday. Eachpaperwasreviewedbyatleasttwoexpertsexternaltotheprogram committeeandtheselectionofpaperswasmadeonthebasisoftheserec- mendations. Weexpressourappreciationtothe66expertrefereeswhoprovided reportsonaverytightschedule. Refereeingofthesubmissionfromamemberof theMagmagroupwasorganizedbyJoeBuhler. Theprogramcommitteethanksthegenerousadvicefromorganizersofpre- ousANTSconferences,particularlyJoeBuhler,WiebBosma,HendrikLenstra, andBartdeSmit. TheconferencewasgenerouslysupportedbytheCollegeof ScienceandTechnology,theSchoolofMathematicsandStatistics(bothatthe UniversityofSydney),theAustralianDefenceScienceTechnologyOrganisation, andeSign. April2002 JohnCannon ClausFieker DavidKohel TableofContents InvitedTalks GaussCompositionandGeneralizations ...1 ManjulBhargava EllipticCurves-TheCrossroadsofTheoryandComputation...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...1 20 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'TheAlgorithmicNumberTheorySymposiabeganin 1994atCornellUniversity inIthaca,NewYorktorecognizethegrowingimportanceofalgorithmicwork in the theory of numbers. The subject of the conference is broadly construed toencompassadiversebodyofmathematics,andtocoverboththetheoretical andpracticaladvancesinthe eld. Theyhavebeenheldeverytwoyearssince: inBordeaux(Universit'eBordeauxI)in1996,Portland(ReedCollege)in1998, Leiden(UniversiteitLeiden)in2000,andthepresentconferencehostedbythe MagmaComputationalAlgebraGroupattheUniversityofSydney. TheconferenceprogramincludedinvitedtalksbyManjulBhargava(Prin- ton),JohnCoates(Cambridge),AntoineJoux(DCSSICryptoLab),BjornP- nen(Berkeley),andTakakazuSatoh(Saitama),aswellas34contributedtalks invariousareasofnumbertheory. Inadditiontothemathematicalprogram,the conferenceincludedaspecialdinnertohonourAlfvanderPoortenofMacquarie University,ontheoccasionofhis60thbirthday. Eachpaperwasreviewedbyatleasttwoexpertsexternaltotheprogram committeeandtheselectionofpaperswasmadeonthebasisoftheserec- mendations. Weexpressourappreciationtothe66expertrefereeswhoprovided reportsonaverytightschedule. Refereeingofthesubmissionfromamemberof theMagmagroupwasorganizedbyJoeBuhler. Theprogramcommitteethanksthegenerousadvicefromorganizersofpre- ousANTSconferences,particularlyJoeBuhler,WiebBosma,HendrikLenstra, andBartdeSmit. TheconferencewasgenerouslysupportedbytheCollegeof ScienceandTechnology,theSchoolofMathematicsandStatistics(bothatthe UniversityofSydney),theAustralianDefenceScienceTechnologyOrganisation, andeSign. April2002 JohnCannon ClausFieker DavidKohel TableofContents InvitedTalks GaussCompositionandGeneralizations ...1 ManjulBhargava EllipticCurves-TheCrossroadsofTheoryandComputation...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...1 89 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...3 49 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 GrobnerBases ANewSchemeforComputingwithAlgebraicallyClosedFields...491 AllanSteel X TableofContents Complexity AdditiveComplexityandRootsofPolynomials overNumberFieldsandp-adicFields...506 J. MauriceRojas AuthorIndex...5 17 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.

Recenzijas

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)

Papildus informācija

Springer Book Archives
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 Hilberts 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 Kroneckers
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
Kedlayas 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.
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