一類可逆變換的分支數(shù)分析.pdf

1、青島大學(xué)碩士學(xué)位論文一類可逆變換的分支數(shù)分析姓名：田英倩申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：徐克艦20100601AbstractInthispaper，resultsonanalysisofbranchnumbersofRijndaelalgorithmandSMS4algorithmforspecialinvertiblelineartransformationsaregeneralizedtothoseforarbitrar

2、yinvertiblelineartransformationsFirstlyapplyingmatrixtheoryandrecursivemethod，acriteriontheoremisgivenforanyinvertiblelin—eartransformationon碟4todeterminelinearbranchnumbersanddifferencebranchnumbersFromthistheorem，theli

3、nearbranchnumberandthedifferencebranchnumbercanbecompletelydetermined，whileinpastworks，bylinearcodetheoryonecanonlyknowwhetherthetwonumbersaremaximumornotAsaconsequence，theresultsonbranchnumbersinreference【2】arerecovered

4、Secondlyitisknownthatforaninvertiblelineartransformationon堿4itsdifferencebranchnumberisequaltoitslinearbranchnumberwhenitismaximum，sayitis5Inthispaper，theresultisfurtherimprovedasthatthedifferencebranchnumberisequaltoits

5、linearbranchnumber，whenitismorethan3Furthermore，fortheSMS4algorithm，basedontheintrinsicproper—tiesofitsmatrixofthecyclicshiftplusonF2，asimplifiedformoftheabovecriteriontheoremisgivenAsacorollaryitisprovedtheoreticallytha

6、tthebranchnumbersofSMS4aremaximum，whileinthepastthisresultWasonlyconfirmedthroughenumerationbycomputerInaddition，usingtheknowledgeoflocalrings，asufficientandnecessaryconditionofwhetherthecyclicshiftplusonF2isinvertibleis

7、achieved，preciselyitisprovedthatthecyclicshiftplusonF2isinvertibleifandonlyifthenumberofnontrivialtermsisoddFinallythecriteriontheoremon嚷則aboutthebranchnumbersisextendedtotheoneon吩mKeywords：Rijndaelnumber；linearbranchalg