William_Stein_-_Elementary_Number_Theory

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

2、.141.3Exercises............................222TheRingofIntegersModulon252.1CongruencesModulon.....................252.2TheChineseRemainderTheorem...............322.3QuicklyComputingInversesandHugePowers........352.4PrimalityTesting........................402.5TheStruc

3、tureof(Z/pZ)∗...................432.6Exercises............................483Public-KeyCryptography513.1TheDiffie-HellmanKeyExchange..............543.2TheRSACryptosystem....................603.3AttackingRSA.........................643.4Exercises.........................

4、...704QuadraticReciprocity734.1StatementoftheQuadraticReciprocityLaw........744.2Euler’sCriterion........................77Contents14.3FirstProofofQuadraticReciprocity.............794.4AProofofQuadraticReciprocityUsingGaussSums....854.5FindingSquareRoots..............

5、.......904.6Exercises............................925ContinuedFractions955.1FiniteContinuedFractions..................965.2InfiniteContinuedFractions..................1035.3TheContinuedFractionofe..................1095.4QuadraticIrrationals......................1125.5Re

6、cognizingRationalNumbersFromTheirDecimalExpansion1165.6SumsofTwoSquares.....................1185.7Exercises............................1216EllipticCurves1256.1TheDefinition.........................1256.2TheGroupStructureonanEllipticCurve..........1266.3IntegerFactoriza

7、tionUsingEllipticCurves.........1296.4EllipticCurveCryptography.................1356.5EllipticCurvesOvertheRationalNumbers.........1396.6Exercises............................144AnswersandHints147References153Index1582ContentsThisispage3Printer:OpaquethisPrefaceThisisa

8、textbookaboutprimenumbers,congruences,basicpublic-keycryptography,quadraticreciprocity,continuedfractions,ellipticcurves,and