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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-KeyCryptography513.1TheDi?e-HellmanKeyExchange..............543.2TheRSACryptosystem....................603.3AttackingRSA.........................643.4Exercises.........................
4、...704QuadraticReciprocity734.1StatementoftheQuadraticReciprocityLaw........744.2Euler’sCriterion........................77Contents14.3FirstProofofQuadraticReciprocity.............794.4AProofofQuadraticReciprocityUsingGaussSums....854.5FindingSquareRoots..............
5、.......904.6Exercises............................925ContinuedFractions955.1FiniteContinuedFractions..................965.2In?niteContinuedFractions..................1035.3TheContinuedFractionofe..................1095.4QuadraticIrrationals......................1125.5Re
6、cognizingRationalNumbersFromTheirDecimalExpansion1165.6SumsofTwoSquares.....................1185.7Exercises............................1216EllipticCurves1256.1TheDe?nition.........................1256.2TheGroupStructureonanEllipticCurve..........1266.3IntegerFactoriza
7、tionUsingEllipticCurves.........1296.4EllipticCurveCryptography.................1356.5EllipticCurvesOvertheRationalNumbers.........1396.6Exercises............................144AnswersandHints147References153Index1582ContentsThisispage3Printer:OpaquethisPrefaceThisisa
8、textbookaboutprimenumbers,congruences,basicpublic-keycryptography,quadraticreciprocity,continuedfractions,ellipticcurves,and
