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Algorithmic Number Theory: 5th International Symposium, ANTS-V, Sydney, Australia, July 7-12, 2002. Proceedings - Lecture Notes in Computer Science 2369 (Paperback)
  • Algorithmic Number Theory: 5th International Symposium, ANTS-V, Sydney, Australia, July 7-12, 2002. Proceedings - Lecture Notes in Computer Science 2369 (Paperback)
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Algorithmic Number Theory: 5th International Symposium, ANTS-V, Sydney, Australia, July 7-12, 2002. Proceedings - Lecture Notes in Computer Science 2369 (Paperback)

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Paperback 522 Pages / Published: 26/06/2002
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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'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...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.

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN: 9783540438632
Number of pages: 522
Weight: 1630 g
Dimensions: 235 x 155 x 27 mm
Edition: 2002 ed.


MEDIA REVIEWS

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)

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