Public key

Introduction

Publickeysarealsocalledasymmetrickeys.Everyonehasapairofuniquekeys:publickey(referredtoaspublickey)andprivatekey(referredtoasPrivatekey),thepublickeyisdisclosedtotheoutsideworld,andtheprivatekeyiskeptsecretbytheindividual;ifoneofthekeysisusedforencryption,theotherkeycanonlybeusedfordecryption.ThetypicalrepresentativeofasymmetrickeyencryptionalgorithmisRSA.Thepublickeyisusuallyusedtoencryptsessionkeys,verifydigitalsignatures,orencryptdatathatcanbedecryptedwiththecorrespondingprivatekey.Thekeypairobtainedthroughthisalgorithmcanbeguaranteedtobeuniqueintheworld.Whenusingthiskeypair,ifoneofthekeysisusedtoencryptapieceofdata,theotherkeymustbeusedtodecryptit.Forexample,ifyouuseapublickeytoencryptdata,youmustusetheprivatekeytodecryptit.Ifyouusetheprivatekeytoencryptdata,youmustalsousethepublickeytodecryptit,otherwisethedecryptionwillnotsucceed.

Proposed

1976.Atthattime,DiffieandHellmanatStanfordUniversityintheUnitedStatesproposedthenewideaof​​publickeycryptography(thesis"NewDirectioninCryptography").Notonlytheencryptionalgorithmitselfcanbedisclosed,butalsotheencryptionusedThekeycanalsobemadepublic.Butthisdoesnotmeanareductioninconfidentiality.Becausetheencryptionkeyandthedecryptionkeyarenotthesame.Thisisthefamouspublickeycryptosystem.Alsoknownasasymmetriccryptosystem.Itisdifferentfromsymmetricalcryptographyinthatitsencryptionkeyisonlyapplicabletoasingleuser.

Including

Aprivatekeythatonlytheuserhas.

Apublickeycanbeissuedanddistributedpublicly,anditcanbeobtainedaslongasthereisarequest.

Eachkeygeneratesafunctionthatisusedtochangeattributes.Aprivatekeyproducesaprivatepropertychangefunction,andapublickeyproducesapublicpropertychangefunction.Thesefunctionsareinverselyrelated.Forexample,ifonefunctionisusedtoencryptamessage,anotherfunctionisusedtodecryptthemessage.Itdoesn'tmatterwhattheorderofthisattributechangefunctionis.Theadvantageoftheopenkeysystemisthattwouserscancommunicatesecurelywithoutexchangingsecretkeys.Forexample,supposeasenderneedstosendamessagetoarecipient,andtheconfidentialityoftheinformationisnecessary.Thesenderusestherecipient’spublickeytoencrypt,andonlytherecipient’sprivatekeycandecrypttheinformation..Publickeycryptographyisverysuitableforprovidingauthentication,completeandundeniableservices.Alltheseservicesareknownasdigitalsignatures.

RSA

TheRSApublickeysystemwasinventedoneyearafterthenewideawasputforward.AtMIT,RonaldRivest,AdiShamirandAdiShamirLenAdlemanproposedthefirstrelativelycompletepublickeycryptosystem-theRSAsystem,namedbytheinitialsofthelastnamesofthethreeinventors.Thisisanalgorithmbasedonfactorizationoflargenumbers.Itisthefirstmatureandtheoreticallymostsuccessfulpublickeycryptosystemtodate.Itssecurityisbasedonthefactorizationoflargeintegersinnumbertheory.Thisproblemisadifficultprobleminnumbertheory,andthereisnoeffectivealgorithmsofar(thatis,thefactorizationoflargeintegerscannotbecompletedinpolynomialtime),whichmakesthissystemhighlyconfidential.Andithasbeenwidelyused.Whatisnotknownisthatasearlyas1970insecretresearch,themathematicianJamesH.EllisoftheBritishintelligenceagencyGCHQhadinventedasymmetrickeycryptography,andDiffie-HellmanandRSAwerebothusedbyMalcolmJ.WilliamsonandClifford.Cockswereinventedbefore.Thesetwoearliestpublickeysystemsprovideagoodfoundationforencryption,andarethereforewidelyused.OtherpublickeysystemsincludeCramer-Shoup,Elgamal,andellipticcurvecryptography.Theseeventswerenotknowntothepublicuntilthedeclassificationofhistoricaldocumentsin1997.

Contribution

Inadditiontoencryption,themostsignificantachievementofpublickeycryptographyistherealizationofdigitalsignatures.Digitalsignatures,asthenamesuggests,aretodigitizeordinarysignatures.Theircharacteristicisthatonecaneasilycreateasignature,butitisdifficultforotherstocounterfeit.Thedigitalsignaturecanbepermanentlycombinedwiththesignedinformationandcannotberemovedfromtheinformation.Digitalsignatureroughlyincludestwoalgorithms:oneissigning,whichusesaprivatekeytoprocessinformationorthehashvalueoftheinformationtogenerateasignature;theotherisverification,whichusesapublickeytoverifytheauthenticityofthesignature.RSAandDSAarethetwomostpopulardigitalsignaturemechanisms.Digitalsignaturesarethebasisofpublickeyinfranstructures(PKI)andmanynetworksecuritymechanisms(SSL/TLS,VPNs,etc.).

Publickeyalgorithmsaremostlybasedonthedifficultyofcomputationalcomplexity,usuallyfromnumbertheory.Forexample,RSAcomesfromtheintegerfactorizationproblem;DSAcomesfromthediscretelogarithmproblem.Thefast-developingellipticcurvecryptographyisbasedonmathematicalproblemsrelatedtoellipticcurves,whichareequivalenttodiscretelogarithms.Sincetheseunderlyingproblemsmostlyinvolvemodulusmultiplicationorexponentialoperations,theyrequiremorecomputingresourcesthanblockciphers.Therefore,thepublickeysystemisusuallyacompositetype,whichcontainsahigh-efficiencysymmetrickeyalgorithmtoencryptinformation,andthenthepublickeyisusedtoencryptthekeysusedbythesymmetrickeysystemtoimproveefficiency.