多變量公鑰密碼的設計與分析.pdf

1、西安電子科技大學博士學位論文多變量公鑰密碼的設計與分析姓名：袁峰申請學位級別：博士專業(yè)：密碼學指導教師：胡予濮201009AbstractThespeedsoftraditionalpublickeycryptographicalgorithmsarerelativelylowwhichhampertheirfurtherapplicationsWiththedevelopmentofquantumcomputation，thedesi

2、gnsofnewandfastpublickeycryptographicalgorithmsaremotivatedinthecryptographiccommunityThemultivariatepublickeycryptosystemisanewandfastpublickeycryptosystem，anditssecurityassumptionisbasedonthedifficultyofsolvingasetofmu

3、ltivariatepolynomialequationsoverafinitefieldMoreovercomparedwithtraditionalpublickeycryptosystemsbasedonlargeintegerfactorizationanddiscretelogarithmproblems，themultivariatepublickeycryptosystemiSnotonlymorecomputationa

4、llyefficient，butalsesistanttothequantumalgorithmThispaperinvestigatesthedesignandanalysisofmultivariatepublickeycryptosystem，andtheauthorobtainsthefollowingmainresults：1Wepresentallalgebraicmethodtoattackthecandidatedrag

5、onsignaturealgorithmThebasicideaoftheattackistoutilizetheunderlyingalgebraicstructureofthecandidatedragonsignaturealgorithmovertheextensionfieldtoderiveawaytoenablethevariableYbeviewedasafixedvalueWhentheparametersofthec

6、andidatedragonsignaturealgorithmaresmallenough，theattackCanrecovertheprivatekeys2WeproposeanalgebraicmethodtoattacktheprojectedC—schemeThebasicideaoftheattackistoapplytheaffinepartsoftheprivatekeysandtheweaknesscausedbvm

7、estructuresoftheprivatekeystofindalargenumberoflinearequationsMeanwhile，theweakkeysoftheschemearefoundandtheprivatekeyscanberecoveredoncetheweakkeysareusedWealsopresentanewmodificationofC～scheme，whichisnotonlyasefficient

8、asoriginalprojectedC一scheme，butalsesistanttothedifferentialattackandtheattackproposedinthispaper3WeproposeanimprovedRMPKCschemeThebasicideaoftheimprovementisthatthedegreeofthefunctionofthefirstrationalmappingischangedtot