23959.有限素域上的全同態(tài)加密方案及其應用研究

1、分類號一UDC密級餐開暑哦≯產(chǎn)篝。碩士研究生學位論文有限素域上的全同態(tài)加密方案及其應用研究申請人：岳秋玲學號：2111082培養(yǎng)單位：數(shù)學科學學院學科專業(yè)：應用數(shù)學研究方向：密碼學指導教師：張龍副教授完成日期：2014年3月lOEtAbstractWiththedevelopmentofinformationtechnology，ontheonehand，peoplegrad—uallyrealizetheimportanceofinf

2、ormationsecurity，andalsopaymoreandmoreattentiontoprivacyinformationOntheotherhand，alongwiththedevelopmentoftechnologyInordertoachievemoreefficient，moreconvenient，thewayofin—formationstoragehasbeengraduallychangedintothew

3、ayofcentralizedstorageApracticalquestionishowtoimplementtrustedstorageonuntrustedthirdpartyFullyhomomorphicencryptionhasthefollowingproperty：TheresultofoperatingcipertextsistheciphertextoftheresultofoperatingplaintextSot

4、heproblemcanbesolvedbyfullyhomomorphicencryptionAlthoughfullyhomomorphicencryptionWasputforwardearlyithasbeenlittleprogressUntil2009，thefirstonewaspresentedbyGentrywhichbringitintotheneweraThispaperismainlyontheresearcho

5、ffullyhomomorphicencryptionoverfiniteprimefieldanditsapplicationSpecificworkisasfollows：1Thispaperintroducesthekeytechnologyoffullyhomomorphicencryption，andthetechnologyofdecryptioncircuitcompression，reerypttechnologyand

6、securitywereanalyzedandstudiedsystematically2TheexistingfullyhomomorphicencryptionschemebasedOilintegersisintroducedFortheproblemofplaintextspaceistoosmall，respectivelyputforwardtwofullyhomomorphicencryptionschemeswhosep

7、laintextspacesarefiniteprimefield昂and咒dimensionalvectorspace曰over懇Baseonthetwoschemes，afullyhomomorphicencryptionschemewhoseplaintextspaceis聰isproposedInaddi—tiontoourschemeandoriginalschemesareanalyzedandcompared，thecip

8、hertextoftheproposedschemeisquitesmallinthispaper，andthetimeofencryptionanddecryptionisshort3ThispaperpresentsafullyhomomorphicencryptionschemeonmatrixoverfiniteprimefieldRApplytoimageencryption，andputforwardafullyhomomo

9、rphicencryptionschemewhichissuitableforimageencryptionWithsecretelementsdiscardprocessingmethod，afastfullyhomomorphicencryptionschemeonmatrixisputforwardFinallythefullyhomomorphicencryptionoftheimageisonthedisplayKeyword