stein w elementary number theory, a computational approach (march 2007)(166s)外语英文电子书

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1、ThisispageiPrinter:OpaquethisElementaryNumberTheory,AComputationalApproachWilliamSteinMarch2007iiTomywifeClaritaLefthand.ThisispageiiiPrinter:OpaquethisContentsPreface31PrimeNumbers51.1PrimeFactorization......................51.2TheSequenceofPrimeNumbers...............141.3Exercises

2、............................222TheRingofIntegersModulon252.1CongruencesModulon.....................252.2TheChineseRemainderTheorem...............322.3QuicklyComputingInversesandHugePowers........352.4PrimalityTesting........................402.5TheStructureof(Z/pZ)∗.................

3、..432.6Exercises............................483Public-KeyCryptography513.1TheDiffie-HellmanKeyExchange..............543.2TheRSACryptosystem....................603.3AttackingRSA.........................643.4Exercises............................704QuadraticReciprocity734.1Statementofthe

4、QuadraticReciprocityLaw........744.2Euler’sCriterion........................77Contents14.3FirstProofofQuadraticReciprocity.............794.4AProofofQuadraticReciprocityUsingGaussSums....854.5FindingSquareRoots.....................904.6Exercises............................925Continue

5、dFractions955.1FiniteContinuedFractions..................965.2InfiniteContinuedFractions..................1035.3TheContinuedFractionofe..................1095.4QuadraticIrrationals......................1125.5RecognizingRationalNumbersFromTheirDecimalExpansion1165.6SumsofTwoSquares....

6、.................1185.7Exercises............................1216EllipticCurves1256.1TheDefinition.........................1256.2TheGroupStructureonanEllipticCurve..........1266.3IntegerFactorizationUsingEllipticCurves.........1296.4EllipticCurveCryptography.................1356.5Elli

7、pticCurvesOvertheRationalNumbers.........1396.6Exercises............................144AnswersandHints147References153Index1582ContentsThisispage3Printer:OpaquethisPrefaceThisisatextbookaboutprimenumbers,congruences,basicpublic-keycryptography,quadraticreciprocity,continuedfractions

8、,ellipticcurves,and