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

. 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. . . . . . . . . .

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)