23549.大數(shù)分解的若干歷史問題研究

1、4V坐縣?Ji?密級：無UDC=單位代碼：10118山西師范大學(xué)研究生碩士學(xué)位論文大數(shù)分解的若干歷史問題研究楊莉莉指導(dǎo)教師姓名楊浩菊副教授學(xué)院山西師范大學(xué)數(shù)學(xué)與計(jì)算機(jī)科學(xué)學(xué)院申請學(xué)位級別理學(xué)碩士專業(yè)名稱基拙數(shù)學(xué)論文提交日期2014年月日論文答辯日期2014年月日學(xué)位授予單位山西師范大學(xué)學(xué)位授予日期2014年月日答辯委員會(huì)主席.評閱人_2014年3月28日Title:Aresearchoncertainquestionsrelatedto

2、factizationoflargeNumbersinhistyMajor:PureMathematicsName:LiliYangSupervisor:ProfessHaojuYangSignature:Signature:AbstractPrimalitytestingandintegerfactorizationareofgreatvaluenotonlyintheorybutalsoinpractice.Thisthesisis

3、mainlybasedontheformerresearchesandsystematicallysummarizesthedevelopmentoftheprimalitytestingandintegerfactorization.Furtherthisthesisalsobrieflyintroducestheapplicationofintegerfactorizationinthecryptography.Themaincon

4、tentofthethesisislistedasfollows:ThefirstpartexpoundsthesystematicalresearchoftheintegerprobleminancientChinawhichmainlyincludesthetwoaspects:Chineseremaindertheoryandgreatestcommondivis.Thesecondpartexpoundstheoriginoft

5、henumbertheoryinwesternmath.ThischapternotonlyincludesthenumbertheoryresearchesconductedbyPythagorasandEuclidbutalsoincludesthebriefintroductionofGausssbasictheoremofarithmetic.Thethirdpartdetailedinvestigatesthebasicthe

6、oryofprimeNumbers.CombingsomemethodfordeterminationofprimeNumbersandshowshowtoimplementoncomputerprimenumberdetermination.Thefourthpartnotonlyelaboratestheevolutionoftheintegerfactorizationsinceancienttimesbutalsointrodu

7、cessomeofthetypicalandhisticdecompositionmethodsindetails.Thelastpartresearchesthecryptographyandintegerfactorization.ThischapternotonlyexpoundseveryphaseofthecryptographysinceancienttimesbutalsointroducestheRSApublickey