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Caesar cipher

Caesar cipher, is one of the simplest and most widely known encryption techniques. The transformation can be represented by aligning two alphabets, the cipher alphabet is the plain alphabet rotated left or right by some number of positions.

When encrypting, a person looks up each letter of the message in the 'plain' line and writes down the corresponding letter in the 'cipher' line. Deciphering is done in reverse.
The encryption can also be represented using modular arithmetic by first transforming the letters into numbers, according to the scheme, A = 0, B = 1,..., Z = 25. Encryption of a letter x by a shift n can be described mathematically as

Plaintext: caputi
cipher variations:
dbqvuj ecrwvk fdsxwl getyxm hfuzyn
igvazo jhwbap kixcbq ljydcr mkzeds
nlafet ombgfu pnchgv qodihw rpejix
sqfkjy trglkz ushmla vtinmb wujonc
xvkpod ywlqpe zxmrqf aynsrg bzotsh

Decryption is performed similarly,

(There are different definitions for the modulo operation. In the above, the result is in the range 0...25. I.e., if x+n or x-n are not in the range 0...25, we have to subtract or add 26.)
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Atbash Cipher

Atbash is an ancient encryption system created in the Middle East. It was originally used in the Hebrew language.
The Atbash cipher is a simple substitution cipher that relies on transposing all the letters in the alphabet such that the resulting alphabet is backwards.
The first letter is replaced with the last letter, the second with the second-last, and so on.
An example plaintext to ciphertext using Atbash:
Plain: caputi
Cipher: xzkfgr

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Baconian Cipher

To encode a message, each letter of the plaintext is replaced by a group of five of the letters 'A' or 'B'. This replacement is done according to the alphabet of the Baconian cipher, shown below.
a   AAAAA   g    AABBA     m    ABABB   s    BAAAB     y    BABBA
b   AAAAB   h    AABBB     n    ABBAA   t    BAABA     z    BABBB
c   AAABA   i    ABAAA     o    ABBAB   u    BAABB 
d   AAABB   j    BBBAA     p    ABBBA   v    BBBAB
e   AABAA   k    ABAAB     q    ABBBB   w    BABAA
f   AABAB   l    ABABA     r    BAAAA   x    BABAB

Plain: caputi

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Affine Cipher
In the affine cipher the letters of an alphabet of size m are first mapped to the integers in the range 0..m - 1. It then uses modular arithmetic to transform the integer that each plaintext letter corresponds to into another integer that correspond to a ciphertext letter. The encryption function for a single letter is

where modulus m is the size of the alphabet and a and b are the key of the cipher. The value a must be chosen such that a and m are coprime.
Considering the specific case of encrypting messages in English (i.e. m = 26), there are a total of 286 non-trivial affine ciphers, not counting the 26 trivial Caesar ciphers. This number comes from the fact there are 12 numbers that are coprime with 26 that are less than 26 (these are the possible values of a). Each value of a can have 26 different addition shifts (the b value) ; therefore, there are 12*26 or 312 possible keys.
Plaintext: caputi
cipher variations:

The decryption function is

where a - 1 is the modular multiplicative inverse of a modulo m. I.e., it satisfies the equation

The multiplicative inverse of a only exists if a and m are coprime. Hence without the restriction on a decryption might not be possible. It can be shown as follows that decryption function is the inverse of the encryption function,

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ROT13 Cipher
Applying ROT13 to a piece of text merely requires examining its alphabetic characters and replacing each one by the letter 13 places further along in the alphabet, wrapping back to the beginning if necessary. A becomes N, B becomes O, and so on up to M, which becomes Z, then the sequence continues at the beginning of the alphabet: N becomes A, O becomes B, and so on to Z, which becomes M. Only those letters which occur in the English alphabet are affected; numbers, symbols, whitespace, and all other characters are left unchanged. Because there are 26 letters in the English alphabet and 26 = 2 * 13, the ROT13 function is its own inverse:

ROT13(ROT13(x)) = x for any basic Latin-alphabet text x

An example plaintext to ciphertext using ROT13:

Plain: caputi
Cipher: pnchgv

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Polybius Square

A Polybius Square is a table that allows someone to translate letters into numbers. To give a small level of encryption, this table can be randomized and shared with the recipient. In order to fit the 26 letters of the alphabet into the 25 spots created by the table, the letters i and j are usually combined.
1 2 3 4 5
1 A B C D E
2 F G H I/J K
3 L M N O P
4 Q R S T U
5 V W X Y Z

Basic Form:
Plain: caputi
Cipher: 311153544442

Extended Methods:
Method #1

Plaintext: caputi
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
c a p u t i 
3 1 5 5 4 4 
1 1 3 4 4 2 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: caputi
Cipher: cztasi

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Method #3

Plaintext: caputi
method variations:
avxttm vxttma xttmav
ttmavx tmavxt mavxtt

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Permutation Cipher
In classical cryptography, a permutation cipher is a transposition cipher in which the key is a permutation. To apply a cipher, a random permutation of size E is generated (the larger the value of E the more secure the cipher). The plaintext is then broken into segments of size E and the letters within that segment are permuted according to this key.
In theory, any transposition cipher can be viewed as a permutation cipher where E is equal to the length of the plaintext; this is too cumbersome a generalisation to use in actual practice, however.
The idea behind a permutation cipher is to keep the plaintext characters unchanged, butalter their positions by rearrangement using a permutation
This cipher is defined as:
Let m be a positive integer, and K consist of all permutations of {1,...,m}
For a key (permutation) , define:
The encryption function
The decryption function
A small example, assuming m = 6, and the key is the permutation :

The first row is the value of i, and the second row is the corresponding value of (i)
The inverse permutation, is constructed by interchanging the two rows, andrearranging the columns so that the first row is in increasing order, Therefore, is:

Total variation formula:

e = 2,718281828 , n - plaintext length

Plaintext: caputi

all 720 cipher variations:
caputi capuit captui captiu capitu capiut caupti caupit cautpi cautip cauitp
cauipt catupi catuip catpui catpiu catipu catiup caiutp caiupt caitup caitpu
caiptu caiput cpauti cpauit cpatui cpatiu cpaitu cpaiut cpuati cpuait cputai
cputia cpuita cpuiat cptuai cptuia cptaui cptaiu cptiau cptiua cpiuta cpiuat
cpitua cpitau cpiatu cpiaut cupati cupait cuptai cuptia cupita cupiat cuapti
cuapit cuatpi cuatip cuaitp cuaipt cutapi cutaip cutpai cutpia cutipa cutiap
cuiatp cuiapt cuitap cuitpa cuipta cuipat ctpuai ctpuia ctpaui ctpaiu ctpiau
ctpiua ctupai ctupia ctuapi ctuaip ctuiap ctuipa ctaupi ctauip ctapui ctapiu
ctaipu ctaiup ctiuap ctiupa ctiaup ctiapu ctipau ctipua ciputa cipuat ciptua
ciptau cipatu cipaut ciupta ciupat ciutpa ciutap ciuatp ciuapt citupa cituap
citpua citpau citapu citaup ciautp ciaupt ciatup ciatpu ciaptu ciaput acputi
acpuit acptui acptiu acpitu acpiut acupti acupit acutpi acutip acuitp acuipt
actupi actuip actpui actpiu actipu actiup aciutp aciupt acitup acitpu aciptu
aciput apcuti apcuit apctui apctiu apcitu apciut apucti apucit aputci aputic
apuitc apuict aptuci aptuic aptcui aptciu apticu aptiuc apiutc apiuct apituc
apitcu apictu apicut aupcti aupcit auptci auptic aupitc aupict aucpti aucpit
auctpi auctip aucitp aucipt autcpi autcip autpci autpic autipc auticp auictp
auicpt auitcp auitpc auiptc auipct atpuci atpuic atpcui atpciu atpicu atpiuc
atupci atupic atucpi atucip atuicp atuipc atcupi atcuip atcpui atcpiu atcipu
atciup atiucp atiupc aticup aticpu atipcu atipuc aiputc aipuct aiptuc aiptcu
aipctu aipcut aiuptc aiupct aiutpc aiutcp aiuctp aiucpt aitupc aitucp aitpuc
aitpcu aitcpu aitcup aicutp aicupt aictup aictpu aicptu aicput pacuti pacuit
pactui pactiu pacitu paciut paucti paucit pautci pautic pauitc pauict patuci
patuic patcui patciu paticu patiuc paiutc paiuct paituc paitcu paictu paicut
pcauti pcauit pcatui pcatiu pcaitu pcaiut pcuati pcuait pcutai pcutia pcuita
pcuiat pctuai pctuia pctaui pctaiu pctiau pctiua pciuta pciuat pcitua pcitau
pciatu pciaut pucati pucait puctai puctia pucita puciat puacti puacit puatci
puatic puaitc puaict putaci putaic putcai putcia putica putiac puiatc puiact
puitac puitca puicta puicat ptcuai ptcuia ptcaui ptcaiu ptciau ptciua ptucai
ptucia ptuaci ptuaic ptuiac ptuica ptauci ptauic ptacui ptaciu ptaicu ptaiuc
ptiuac ptiuca ptiauc ptiacu pticau pticua picuta picuat pictua pictau picatu
picaut piucta piucat piutca piutac piuatc piuact pituca pituac pitcua pitcau
pitacu pitauc piautc piauct piatuc piatcu piactu piacut uapcti uapcit uaptci
uaptic uapitc uapict uacpti uacpit uactpi uactip uacitp uacipt uatcpi uatcip
uatpci uatpic uatipc uaticp uaictp uaicpt uaitcp uaitpc uaiptc uaipct upacti
upacit upatci upatic upaitc upaict upcati upcait upctai upctia upcita upciat
uptcai uptcia uptaci uptaic uptiac uptica upicta upicat upitca upitac upiatc
upiact ucpati ucpait ucptai ucptia ucpita ucpiat ucapti ucapit ucatpi ucatip
ucaitp ucaipt uctapi uctaip uctpai uctpia uctipa uctiap uciatp uciapt ucitap
ucitpa ucipta ucipat utpcai utpcia utpaci utpaic utpiac utpica utcpai utcpia
utcapi utcaip utciap utcipa utacpi utacip utapci utapic utaipc utaicp uticap
uticpa utiacp utiapc utipac utipca uipcta uipcat uiptca uiptac uipatc uipact
uicpta uicpat uictpa uictap uicatp uicapt uitcpa uitcap uitpca uitpac uitapc
uitacp uiactp uiacpt uiatcp uiatpc uiaptc uiapct tapuci tapuic tapcui tapciu
tapicu tapiuc taupci taupic taucpi taucip tauicp tauipc tacupi tacuip tacpui
tacpiu tacipu taciup taiucp taiupc taicup taicpu taipcu taipuc tpauci tpauic
tpacui tpaciu tpaicu tpaiuc tpuaci tpuaic tpucai tpucia tpuica tpuiac tpcuai
tpcuia tpcaui tpcaiu tpciau tpciua tpiuca tpiuac tpicua tpicau tpiacu tpiauc
tupaci tupaic tupcai tupcia tupica tupiac tuapci tuapic tuacpi tuacip tuaicp
tuaipc tucapi tucaip tucpai tucpia tucipa tuciap tuiacp tuiapc tuicap tuicpa
tuipca tuipac tcpuai tcpuia tcpaui tcpaiu tcpiau tcpiua tcupai tcupia tcuapi
tcuaip tcuiap tcuipa tcaupi tcauip tcapui tcapiu tcaipu tcaiup tciuap tciupa
tciaup tciapu tcipau tcipua tipuca tipuac tipcua tipcau tipacu tipauc tiupca
tiupac tiucpa tiucap tiuacp tiuapc ticupa ticuap ticpua ticpau ticapu ticaup
tiaucp tiaupc tiacup tiacpu tiapcu tiapuc iaputc iapuct iaptuc iaptcu iapctu
iapcut iauptc iaupct iautpc iautcp iauctp iaucpt iatupc iatucp iatpuc iatpcu
iatcpu iatcup iacutp iacupt iactup iactpu iacptu iacput ipautc ipauct ipatuc
ipatcu ipactu ipacut ipuatc ipuact iputac iputca ipucta ipucat iptuac iptuca
iptauc iptacu iptcau iptcua ipcuta ipcuat ipctua ipctau ipcatu ipcaut iupatc
iupact iuptac iuptca iupcta iupcat iuaptc iuapct iuatpc iuatcp iuactp iuacpt
iutapc iutacp iutpac iutpca iutcpa iutcap iucatp iucapt iuctap iuctpa iucpta
iucpat itpuac itpuca itpauc itpacu itpcau itpcua itupac itupca ituapc ituacp
itucap itucpa itaupc itaucp itapuc itapcu itacpu itacup itcuap itcupa itcaup
itcapu itcpau itcpua icputa icpuat icptua icptau icpatu icpaut icupta icupat
icutpa icutap icuatp icuapt ictupa ictuap ictpua ictpau ictapu ictaup icautp
icaupt icatup icatpu icaptu icaput

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History of cryptography
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