Caesar Cipher , Substitution Cipher, PlayFair and Vigenere Cipher

Information Security

1. Information Security
Mamoona Jabbar

2. Information Security
Topic: Cryptology Techniques

3. Types of Cryptosystem
1.SymmetrickeyEncryption
2.AsymmetrickeyEncryption

4. Cryptographic Systems -History
Beforeproceedingfurther,youneedtoknowsomefactsabouthistorical
cryptosystems
•Allofthesesystemsarebasedonsymmetrickeyencryptionscheme.
•Theonlysecurityservicethesesystemsprovideisconfidentialityof
information.
•Unlikemodernsystemswhicharedigitalandtreatdataasbinarynumbers,
theearliersystemsworkedonalphabetsasbasicelement.
TheseearliercryptographicsystemsarealsoreferredtoasCiphers.Ingeneral,a
cipherissimplyjustasetofsteps(analgorithm)forperformingbothan
encryption,andthecorrespondingdecryption.

5. Caesar Cipher
Itisamono-alphabeticcipherwhereineachletteroftheplaintextissubstituted
byanotherlettertoformtheciphertext.Itisasimplestformofsubstitution
cipherscheme.
ThiscryptosystemisgenerallyreferredtoastheShiftCipher.Theconceptisto
replaceeachalphabetbyanotheralphabetwhichis‘shifted’bysomefixed
numberbetween0and25.
Forthistypeofscheme,bothsenderandreceiveragreeona‘secretshiftnumber’
forshiftingthealphabet.Thisnumberwhichisbetween0and25becomesthe
keyofencryption.
Thename‘CaesarCipher’isoccasionallyusedtodescribetheShiftCipherwhen
the‘shiftofthree’isused.

6. Process of Shift Cipher
•Inordertoencryptaplaintextletter,thesenderpositionstheslidingruler
underneaththefirstsetofplaintextlettersandslidesittoLEFTbythe
numberofpositionsofthesecretshift.
•Theplaintextletteristhenencryptedtotheciphertextletteronthesliding
rulerunderneath.Theresultofthisprocessisdepictedinthefollowing
illustrationforanagreedshiftofthreepositions.Inthiscase,theplaintext
‘tutorial’isencryptedtotheciphertext‘WXWRULDO’.Hereisthecipher
textalphabetforaShiftof3:

7. Process of Shift Cipher
•Onreceivingtheciphertext,thereceiverwhoalsoknowsthesecretshift,
positionshisslidingrulerunderneaththeciphertextalphabetandslidesitto
RIGHTbytheagreedshiftnumber,3inthiscase.
•Hethenreplacestheciphertextletterbytheplaintextletteronthesliding
rulerunderneath.Hencetheciphertext‘WXWRULDO’ isdecryptedto
‘tutorial’.TodecryptamessageencodedwithaShiftof3,generatethe
plaintextalphabetusingashiftof‘-3’asshownbelow:

8. Process of Shift Cipher
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CaesarCipherisnotasecurecryptosystembecausethereareonly
26possiblekeystotryout.Anattackercancarryoutanexhaustive
keysearchwithavailablelimitedcomputingresources.

9. Simple Substitution Cipher
ItisanimprovementtotheCaesarCipher.Insteadofshiftingthe
alphabetsbysomenumber,thisschemeusessomepermutationofthe
lettersinalphabet.
Forexample,A.B…..Y.ZandZ.Y……B.Aaretwoobviouspermutation
ofallthelettersinalphabet.Permutationisnothingbutajumbledupset
ofalphabets.
With26lettersinalphabet,thepossiblepermutationsare26!(Factorial
of26)whichisequalto4x10
26
.Thesenderandthereceivermaychoose
anyoneofthesepossiblepermutationasaciphertextalphabet.This
permutationisthesecretkeyofthescheme.

10. Process of Substitution Cipher
•WritethealphabetsA,B,C,...,Zinthenaturalorder.
•Thesenderandthereceiverdecideonarandomlyselectedpermutationof
thelettersofthealphabet.
•Underneaththenaturalorderalphabets,writeoutthechosenpermutationof
thelettersofthealphabet.Forencryption,senderreplaceseachplaintext
lettersbysubstitutingthepermutationletterthatisdirectlybeneathitinthe
table.Thisprocessisshowninthefollowingillustration.Inthisexample,the
chosenpermutationisK,D,G,...,O.Theplaintext‘point’isencryptedto
‘MJBXZ’.
HereisajumbledCiphertextalphabet,wheretheorderoftheciphertextletters
isakey.

11. Process of Substitution Cipher
•Onreceivingtheciphertext,thereceiver,whoalsoknowstherandomly
chosenpermutation,replaceseachciphertextletteronthebottomrowwith
thecorrespondingplaintextletterinthetoprow.Theciphertext‘MJBXZ’is
decryptedto‘point’.
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SimpleSubstitutionCipherisaconsiderableimprovementovertheCaesar
Cipher.Thepossiblenumberofkeysislarge(26!)andeventhemodern
computingsystemsarenotyetpowerfulenoughtocomfortablylaunchabrute
forceattacktobreakthesystem.However,theSimpleSubstitutionCipherhasa
simpledesignanditispronetodesignflaws,saychoosingobviouspermutation,
thiscryptosystemcanbeeasilybroken.

12. Monoalphabetic and Polyalphabetic Cipher
Monoalphabeticcipherisasubstitutioncipherinwhichforagivenkey,the
cipheralphabetforeachplainalphabetisfixedthroughouttheencryption
process.Forexample,if‘A’isencryptedas‘D’,foranynumberofoccurrencein
thatplaintext,‘A’willalwaysgetencryptedto‘D’.
PolyalphabeticCipherisasubstitutioncipherinwhichthecipheralphabetfor
theplainalphabetmaybedifferentatdifferentplacesduringtheencryption
process.Thenexttwoexamples,playfairandVigenereCipherare
polyalphabeticciphers.

13. PlayfairCipher
thisscheme,
•Pairsoflettersareencrypted,insteadofsinglelettersasinthecaseofsimple
substitutioncipher
•Initiallyakeytableiscreated
•Thekeytableisa5×5gridofalphabetsthatactsasthekeyforencrypting
theplaintext
•Eachofthe25alphabetsmustbeuniqueandoneletterofthealphabet
(usuallyJ)isomittedfromthetableasweneedonly25alphabetsinsteadof
26.IftheplaintextcontainsJ,thenitisreplacedbyI

14. PlayfairCipher
Thesenderandthereceiverdeicideonaparticularkey,say‘tutorials’.Inakey
table,thefirstcharacters(goinglefttoright)inthetableisthephrase,excluding
theduplicateletters.Therestofthetablewillbefilledwiththeremainingletters
ofthealphabet,innaturalorder.Thekeytableworksouttobe;

15. Process of PlayfairCipher
First,aplaintextmessageissplitintopairsoftwoletters(digraphs).Ifthereisan
oddnumberofletters,aZisaddedtothelastletter.Letussaywewantto
encryptthemessage“hidemoney”.Itwillbewrittenas−
HIDEMONEYZ
•Therulesofencryptionare−
•Ifboththelettersareinthesamecolumn,taketheletterbeloweachone
(goingbacktothetopifatthebottom)

16. Process of PlayfairCipher
•HIDEMONEYZ
•Ifbothlettersareinthesamerow,takethelettertotherightofeachone
(goingbacktotheleftifatthefarthestright)
•Ifneitheroftheprecedingtworulesaretrue,formarectanglewiththetwo
lettersandtakethelettersonthehorizontaloppositecorneroftherectangle.

17. Process of PlayfairCipher
Usingtheserules,theresultoftheencryptionof‘hidemoney’withthekeyof
‘tutorials’wouldbe−
QCEFNUMFZV
DecryptingthePlayfaircipherisassimpleasdoingthesameprocessinreverse.
Receiverhasthesamekeyandcancreatethesamekeytable,andthendecrypt
anymessagesmadeusingthatkey.
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Itisalsoasubstitutioncipherandisdifficulttobreakcomparedtothesimple
substitutioncipher.Asincaseofsubstitutioncipher,cryptanalysisispossibleon
thePlayfaircipheraswell,howeveritwouldbeagainst625possiblepairsof
letters(25x25alphabets)insteadof26differentpossiblealphabets.
ThePlayfaircipherwasusedmainlytoprotectimportant,yetnon-criticalsecrets,
asitisquicktouseandrequiresnospecialequipment.

18. VigenereCipher
Thisschemeofcipherusesatextstring(say,aword)asakey,whichisthenused
fordoinganumberofshiftsontheplaintext.
Forexample,let’sassumethekeyis‘math’.Eachalphabetofthekeyis
convertedtoitsrespectivenumericvalue:Inthiscase,

19. Process of VigenereCipher
Forexample,let’sassumethekeyis‘point’.Eachalphabetofthekeyis
convertedtoitsrespectivenumericvalue:Inthiscase,
p→16,o→15,i→9,n→14,andt→20.
Thus,thekeyis:161591420.
ProcessofVigenereCipher
•Thesenderandthereceiverdecideonakey.Say‘point’isthekey.Numeric
representationofthiskeyis‘161591420’.
•Thesenderwantstoencryptthemessage,say‘attackfromsoutheast’.He
willarrangeplaintextandnumerickeyasfollows−
•Henowshiftseachplaintextalphabetbythenumberwrittenbelowitto
createciphertextasshownbelow−

20. Process of VigenereCipher
•Here,eachplaintextcharacterhasbeenshiftedbyadifferentamount–and
thatamountisdeterminedbythekey.Thekeymustbelessthanorequalto
thesizeofthemessage.
•Fordecryption,thereceiverusesthesamekeyandshiftsreceivedciphertext
inreverseordertoobtaintheplaintext.
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VigenereCipherwasdesignedbytweakingthestandardCaesarciphertoreduce
theeffectivenessofcryptanalysisontheciphertextandmakeacryptosystem
morerobust.ItissignificantlymoresecurethanaregularCaesarCipher.
Inthehistory,itwasregularlyusedforprotectingsensitivepoliticalandmilitary
information.Itwasreferredtoastheunbreakablecipherduetothedifficultyit
posedtothecryptanalysis.

21. Variants of VigenereCipher
SpecialcasesofVigenerecipher−
•Thekeywordlengthissameasplaintextmessage.Thiscaseiscalled
VernamCipher.ItismoresecurethantypicalVigenerecipher.
•Vigenerecipherbecomesacryptosystemwithperfectsecrecy,whichis
calledOne-timepad.

22. One-Time Pad
Thecircumstancesare:
•Thelengthofthekeywordissameasthelengthoftheplaintext.
•Thekeywordisarandomlygeneratedstringofalphabets.
•Thekeywordisusedonlyonce.
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LetuscompareShiftcipherwithone-timepad.
•ShiftCipher−EasytoBreak
•One-timePad−ImpossibletoBreak

23. One-Time Pad VS. Shift Cipher
Shift Cipher One-time Pad
EasytoBreak ImpossibletoBreak
Theentiremessagecouldhavehadashift
between1and25
Possiblekeysaredependonencryption
key,weencryptthename“point”witha
one-timepad.Itisa5lettertext
Itisaverysmallsize Longermessage
Itisveryeasytobruteforce Tobreaktheciphertextbybruteforce,
youneedtotryallpossibilitiesofkeys
andconductcomputationfor(26x26x
26x26x26)=26
5
=11881376times
However,witheachcharacternowhaving
itsownindividualshiftbetween1and26,
thepossiblekeysgrowexponentiallyfor
themessage.
thecomputationgrowsexponentially
witheveryadditionalalphabet.This
makesitcomputationallyimpossibleto
breaktheciphertextbybruteforce.

24. Substitution Technique
1.SubstitutionCipher
2.FairPlayCipher
SubstitutionCipher:
C=(p+k)mod26(Encryption)
C=(p-k)mod26(Decryption)
Where,
kisakey,Cisaletter,Xisencryptmessageletter,andmode26meanstotal
alphabets(0to25)
Theorem:
1<(lessthenequalto)k<(lessthenequalto)26
Example:Encryptthemessage“KHAN”whereCiphershiftkeyis19

25. Substitution Technique
FairPlay/PlayfairCipher:
Ablockof5*5
Instructions:
1.Divideplaintextinpairofletters.
2.Replacerepeatedletterinthepairwithdummyletter.
3.IfPairofplaintextareinsamerowthenreplacethemwithrightmostletter.
4.Iftheplaintextletterareinsamecolumnreplacethemwithbeneathletter.
5.Ifplaintextletterareindifferentrowandcolumnreplacethemdiagonally.