Domov technika Virginia Code

Virginia Code



Introduction

VirginiaCode(alsotranslatedasVergenalCode)istheuseofaseriesofCaesarcodestoformacodeTheencryptionalgorithmofthealphabetisasimpleformofmulti-tablecipher.

TheVirginiacipherhasbeeninventedmanytimes.ThismethodwasfirstrecordedinGiovanBattistaBellaso'sbook"TheCodeofMr.GiovanBattistaBellaso"(Italian:Lacifradel.Sig.GiovanBattistaBellaso).However,itwaslatermisrepresentedinthe19thcenturyasbeingcreatedbytheFrenchdiplomatBlaiseDeVigenère(BlaiseDeVigenère),soitisnowcalledthe"VirginiaCode".

TheVirginiacipherisknownforitssimplicityandeaseofuse,anditisusuallydifficultforbeginnerstocrack,soitisalsocalledthe"unbreakablecipher"(French:lechiffreindéchiffrable).ThisalsoallowsmanypeopletousetheVirginiaciphertoencryptitforthepurposeofcrackingit.

History

Themulti-tablepasswordwasfirstproposedbyLeonBattistaAlbertiaround1467.Heusedametalcipherdisctoswitchtheciphertable,butThissystemcanonlydosomelimitedconversions.Later,in1508,thetabularectainventedinJohannesTritmius'sSteganographia(Steganographia)becameakeypartoftheVirginiaCode.However,atthattime,thismethodcouldonlydosomesimpleandpredictableswitchingofthepasswordtable.ThisencryptiontechniqueisalsoknownastheTritmiuscipher.

Thismethodreallyappearedinthebook"GeovanBattistaBellaso'sArithmetic"writtenbyGeovanBattistaBellasoin1553.middle.HeisbasedonthetablemethodofTritmius,andatthesametimeintroducestheconceptofakey.

BrycedeVirginiainventedasimplerbutmoreeffectiveautokeycipherin1586duringHenryIII.Later,inthe19thcentury,Bellaso’smethodwasmistakenforbeingfirstinventedbyVirginia.DavidKahnexpressedregretaboutthisinTheCodebreakers,writingthat"historyignoredthisimportantcontributionandattributedittoVirginia,althoughhedidnotknowit".

Becauseofthedifficultyofdeciphering,theVirginiaCodehasgainedahighreputation.Thewell-knownauthorandmathematicianCharlesLutwigDodgson(pennameLouisCaro)describeditasundecipherableinTheAlphabetCipher(TheAlphabetCipher)editedbyhimin1868andcollectedinachildren’smagazine.of.In1917,"ScientificAmerican"referredtotheVirginiaCodeas"untransformable."However,theVirginiaCodeisnotworthyofsuchatitle.CharlesBabbagecompletedthedecipheringwork,buthedidnotpublishit.Later,FriedrichKasiskicompletelydecipheredandpublishedhismethodinthe19thcentury.Evenbeforethat,someseniorcryptanalystscouldoccasionallycrackitinthe16thcentury.

TheVirginiacipheriseasytouseenoughtomakeitabattlefieldcipher.Forexample,duringtheAmericanCivilWar,theConfederateArmyusedbrasscipherdiscstogenerateVirginiaciphers.TheNorthernArmywasoftenabletodeciphertheSouthernArmy’scode.Throughoutthewar,theSouthernArmymainlyusedthreekeys,namely"ManchesterBluff","CompleteVictory"and"ComeRetribution"attheendofthewar.

GilbertVernamtriedtopatchthecodethathadbeendeciphered(theVernam-Veniggiacodewascreatedin1918),butthiswastonoavail.However,Vernan'sinventioneventuallyledtothebirthoftheone-timepad,whichisatheoreticallyunbreakablepassword.

Description

InaCaesarcipher,eachletterinthealphabetwillbeoffset.Forexample,whentheoffsetis3,AwillbeconvertedtoDandBConvertedtoE...andtheVirginiacipheriscomposedofsomeCaesarcipherswithdifferentoffsets.

Inordertogenerateapassword,atablemethodisrequired.Thistable(showninFigure1)contains26rowsofthealphabet,eachrowisobtainedbyoffsettingthepreviousrowbyonebittotheleft.Whichlineofalphabetisusedtocompileisbasedonthekey,whichwillbeconstantlychangedintheprocess.

Forexample,supposetheplaintextis:

ATTACKATDAWN

Selectakeywordandrepeatittoobtainthekey.Forexample,whenthekeywordisLEMON,thekeyis:

LEMONLEMONLE

ForthefirstletterAoftheplaintext,itcorrespondstothefirstletterLofthekey,sousetheLlinealphabetinthetabletoencrypt,gettheciphertextAletterL.Similarly,thesecondletteroftheplaintextisT,andthecorrespondingrowEisusedforencryptioninthetabletoobtainthesecondletterXoftheciphertext.Byanalogy,youcanget:

Plaintext:ATTACKATDAWNKey:LEMONLEMONLEciphertext:LXFOPVEFRNHR

Thedecryptionprocessistheoppositeofencryption.Forexample:AccordingtotheLrowalphabetcorrespondingtothefirstletterLofthekey,itisfoundthatthefirstletterLoftheciphertextislocatedintheAcolumn,sothefirstletteroftheplaintextisA.ThesecondletterEofthekeycorrespondstothealphabetofrowE,andthesecondletterXoftheciphertextislocatedincolumnTofthisrow,sothesecondletteroftheplaintextisT.Byanalogy,theplaintextcanbeobtained.

Usingthenumbers0-25insteadofthelettersAZ,theencryptiongrammaroftheVirginiapasswordcanbewrittenintheformofcongruence:

Thedecryptionmethodcanbewrittenas:

PasswordDeciphering

ForallkindsofThedecipheringoftablecodesisbasedonletterfrequency,butdirectfrequencyanalysisisnotapplicable.Forexample,ifPisthemostfrequentletterintheciphertext,thenPislikelytocorrespondtoE(providedthatthelanguageoftheplaintextisEnglish).ThereasonisthatEisthemostfrequentlyusedletterinEnglish.However,sinceEcanbeencryptedintodifferentciphertextsintheVirginiacipher,simplefrequencyanalysisisnotusefulhere.

ThekeytodecipheringtheVirginiacipheristhatitskeyisrepeatedcyclically.Ifweknowthelengthofthekey,theciphertextcanbeseenasanintertwinedCaesarcipher,andeachofthemcanbecrackedseparately.UsetheKasiskitestandFriedmantesttogetthelengthofthekey.

TheKasiskiTest

FriedrichCassisfirstpublishedacompletemethodofdecipheringtheVirginiacodebasedon1863,calledKasiskiTest(Kasiskiexamination).Someoftheearlierdecipheringswerebasedontheknowledgeofplaintext,ortheuseofrecognizablewordsaskeys.However,Kasiski'smethoddoesnothavetheselimitations.However,beforethis,somepeoplehaverealizedthismethod.In1854,CharlesBabbagewasinspiredbyJohnHallBrockThwaites'sclaimintheJournaloftheSocietyoftheArtstohaveinventedthe"newcode",thusdecipheringVigieNiapassword.BabbagediscoveredthatSvetis’scipherwasjustavariantoftheVirginiacipher,andSvetischallengeditandaskedhimtotrytodeciphertheciphertextencryptedwithtwokeysofdifferentlengths.Babbagesuccessfullydeciphered,andtheplaintextobtainedwasthepoem"TheVisionofSin"writtenbyTennyson,andthekeyusedwasTennyson’swife’snameEmily..Babbageneverexplainedhismethod.InthestudyofBabbage'snotesduringhislifetime,itwasfoundthatBabbageusedthismethodasearlyas1846,whichisthesameasthemethodpublishedbyKasiskilater.

TheKasiskitestisbasedonthepossibilitythatcommonwordslikethemaybeencryptedbythesamekeyletter,andthusappearrepeatedlyintheciphertext.Forexample,differentCRYPTOsintheplaintextmaybeencryptedintodifferentciphertextsbythekeyABCDEF:

Key:ABCDEFABCDEFABCDEFABCDEFABCD

Plaintext:CRYPTOISSHORTFORCRYPTOGRAPHY

p>

Ciphertext:CSASXTITUKSWTGQUGWYQVRKWAQJB

Atthistime,therepeatedelementsintheplaintextarenotrepeatedintheciphertext.However,ifthekeysarethesame,theresultmaybe(usingthekeyABCD):

Key:ABCDABCDABCDABCDABCDABCDABCD

Plaintext:CRYPTOISSHORTFORCRYPTOGRAPHY

p>

Ciphertext:CSASTPKVSIQUTGQUCSASTPIUAQJB

Atthistime,theCassistestcanproduceresults.Thismethodismoreeffectiveforlongerparagraphs,becauseusuallytherearemorerepeatedsegmentsintheciphertext.Forexample,thelengthofthekeycanbedecipheredbythefollowingciphertext:

Ciphertext:DYDUXRMHTVDVNQDQNWDYDUXRMHARTJGWNQD

Amongthem,thetwoDYDUXRMHappear18lettersapart.Therefore,itcanbeassumedthatthelengthofthekeyisadivisorof18,thatis,thelengthis18,9,6,3,or2.ThetwoNQDsare20lettersapart,whichmeansthatthekeylengthshouldbe20,10,5,4,or2.Takingtheintersectionofthetwo,youcanbasicallydeterminethatthekeylengthis2.

TheFriedmanTest

TheFriedmanTestwasinventedbyWilliamF.Friedmaninthe1920s.Heusedtheindexofcoincidencetodescribetheunevennessoftheciphertextletterfrequency,therebydecipheringthecode.referstotheprobabilitythattwoarbitrarylettersinthetargetlanguagearethesame(0.067inEnglish),andreferstotheprobabilityofthisoccurrenceinthealphabet(1/26=inEnglish)0.0385),sothekeylengthcanbeestimatedas:

where,theobservationprobabilityis

where,creferstothelengthofthealphabet(26inEnglish),Nreferstothelengthofthetext,n1toncreferstotheletterfrequencyoftheciphertext,whichisaninteger.

Thismethodisonlyanestimateandwillbecomemoreaccurateasthelengthofthetextincreases.Inpractice,attemptsaremadetoapproachthisestimatedmultiplekeylength.Abettermethodistowritetheciphertextinmatrixform,wherethenumberofcolumnsisconsistentwiththeassumedkeylength,calculatethecoincidenceindexofeachcolumnseparately,andobtaintheaveragecoincidenceindex.Forallpossiblekeylengths,thehighestaveragecoincidenceindexismostlikelytobethetruekeylength.SuchatestcanbeusedasasupplementtotheKasiskitest.

Frequencyanalysis

Oncethelengthofthekeycanbedetermined,theciphertextcanberewrittenintomultiplecolumns,andthenumberofcolumnscorrespondstothelengthofthekey.Inthisway,eachcolumnisactuallyaCaesarcipher,andthekey(offset)ofthisciphercorrespondstothecorrespondingletteroftheVirginiacipherkey.TheciphertextcanbedecipheredbyamethodsimilartodecipheringtheCaesarcipher.

TheKirckhoffmethodwasproposedbyAugusteKerckhoffsasanimprovementoftheKasiskitest.Itcorrespondstheletterfrequencyofeachcolumnwiththeconvertedplaintextfrequencytoobtainthekeyletterofeachcolumn.Onceeachletterinthekeycanbedetermined,theciphertextcanbeeasilydecipheredtoobtaintheplaintext.IftheVirginiaalphabettableitselfismessyinsteadofintheusualalphabeticalorder,theKirkhoffmethodwillbeinvalid,buttheKasiskitestandrepetitionindexarestillvalidfordeterminingthekeylength.

Variants

VariationsoftheVirginiacipher,therollingkeycipher,wasonceconsideredundecipherable.Thekeyofthisvariantisconsistentwiththelengthoftheciphertext,sotheKasiskitestandFriedmantestbecomeinvalid.In1920,Friedmanfirstdiscoveredtheweaknessofthismethod.Sincethekeyoftherollingkeycipherisapieceofreallanguage,thedecipherercanunderstandthestatisticalinformationofthekeytext,andthisinformationwillalsobereflectedintheciphertext.

Ifthekeyiscompletelyrandom,consistentwiththelengthoftheplaintextandusedonlyonce,theVirginiacipheristheoreticallyundecipherable.However,inthiscase,thekeyitselfratherthantheciphertextbecomesthekey,whichiscalledaone-timepad.

VirginiaherselfindeedinventedastrongervariantofVirginiacipher-automatickeycipher.WhatBabbagedeciphersisactuallythiskindofautomatickeycipher,andKasiskiisusuallyconsideredtobethefirsttopublishamethodofdecipheringfixed-keymulti-tableciphers.

ThereisalsoasimplevariantthatusesVirginia'sdecodingmethodforencryption,whileusingVirginia'sencryptionmethodfordecryption,whichiscalledavariantBeaufortcipher.ThismethodisdifferentfromtheBeaufortciphercreatedbyFrancisBeaufort.AlthoughthelatterissimilartotheVirginiacipher,itusesamodifiedencryptionmethodandform,whichisakindofpeer-to-peerencryption.

TheapparentstrengthoftheVirginiacipherdidnotmakeitwidelyusedinEurope.TheGronsfeldciphercreatedbytheEarlofGronsfeldisbasicallythesameastheVirginiacipher,butitonlyuses10differentcipheralphabets(correspondingtoletters0to9).ThestrengthoftheGronsfeldcipherisveryhigh,becauseitskeyisnotaword,butthedisadvantageisthatthenumberofalphabetsistoosmall.Nevertheless,theGronsfeldcodeisstillwidelyusedinGermanyandthroughoutEurope.

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