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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: toiles
cipher variations:
upjmft vqkngu wrlohv xsmpiw ytnqjx
zuorky avpslz bwqtma cxrunb dysvoc
eztwpd fauxqe gbvyrf hcwzsg idxath
jeybui kfzcvj lgadwk mhbexl nicfym
ojdgzn pkehao qlfibp rmgjcq snhkdr

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: toiles
Cipher: glrovh

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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: toiles

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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: toiles
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: toiles
Cipher: gbvyrf

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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: toiles
Cipher: 444342135134

Extended Methods:
Method #1

Plaintext: toiles
method variations:

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

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Method #3

Plaintext: toiles
method variations:
tsbxlt sbxltt bxltts
xlttsb lttsbx ttsbxl

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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: toiles

all 720 cipher variations:
toiles toilse toiels toiesl toisel toisle tolies tolise toleis tolesi tolsei
tolsie toelis toelsi toeils toeisl toesil toesli toslei toslie toseli toseil
tosiel tosile tioles tiolse tioels tioesl tiosel tiosle tiloes tilose tileos
tileso tilseo tilsoe tielos tielso tieols tieosl tiesol tieslo tisleo tisloe
tiselo tiseol tisoel tisole tlioes tliose tlieos tlieso tliseo tlisoe tloies
tloise tloeis tloesi tlosei tlosie tleois tleosi tleios tleiso tlesio tlesoi
tlsoei tlsoie tlseoi tlseio tlsieo tlsioe teilos teilso teiols teiosl teisol
teislo telios teliso telois telosi telsoi telsio teolis teolsi teoils teoisl
teosil teosli tesloi teslio tesoli tesoil tesiol tesilo tsileo tsiloe tsielo
tsieol tsioel tsiole tslieo tslioe tsleio tsleoi tsloei tsloie tselio tseloi
tseilo tseiol tseoil tseoli tsolei tsolie tsoeli tsoeil tsoiel tsoile otiles
otilse otiels otiesl otisel otisle otlies otlise otleis otlesi otlsei otlsie
otelis otelsi oteils oteisl otesil otesli otslei otslie otseli otseil otsiel
otsile oitles oitlse oitels oitesl oitsel oitsle oiltes oiltse oilets oilest
oilset oilste oielts oielst oietls oietsl oiestl oieslt oislet oislte oiselt
oisetl oistel oistle olites olitse oliets oliest oliset oliste olties oltise
olteis oltesi oltsei oltsie oletis oletsi oleits oleist olesit olesti olstei
olstie olseti olseit olsiet olsite oeilts oeilst oeitls oeitsl oeistl oeislt
oelits oelist oeltis oeltsi oelsti oelsit oetlis oetlsi oetils oetisl oetsil
oetsli oeslti oeslit oestli oestil oesitl oesilt osilet osilte osielt osietl
ositel ositle osliet oslite osleit osleti osltei osltie oselit oselti oseilt
oseitl osetil osetli ostlei ostlie osteli osteil ostiel ostile iotles iotlse
iotels iotesl iotsel iotsle ioltes ioltse iolets iolest iolset iolste ioelts
ioelst ioetls ioetsl ioestl ioeslt ioslet ioslte ioselt iosetl iostel iostle
itoles itolse itoels itoesl itosel itosle itloes itlose itleos itleso itlseo
itlsoe itelos itelso iteols iteosl itesol iteslo itsleo itsloe itselo itseol
itsoel itsole iltoes iltose ilteos ilteso iltseo iltsoe ilotes ilotse iloets
iloest iloset iloste ileots ileost iletos iletso ilesto ilesot ilsoet ilsote
ilseot ilseto ilsteo ilstoe ietlos ietlso ietols ietosl ietsol ietslo ieltos
ieltso ielots ielost ielsot ielsto ieolts ieolst ieotls ieotsl ieostl ieoslt
ieslot ieslto iesolt iesotl iestol iestlo istleo istloe istelo isteol istoel
istole islteo isltoe isleto isleot isloet islote iselto iselot isetlo isetol
iseotl iseolt isolet isolte isoelt isoetl isotel isotle loites loitse loiets
loiest loiset loiste loties lotise loteis lotesi lotsei lotsie loetis loetsi
loeits loeist loesit loesti lostei lostie loseti loseit losiet losite liotes
liotse lioets lioest lioset lioste litoes litose liteos liteso litseo litsoe
lietos lietso lieots lieost liesot liesto listeo listoe liseto liseot lisoet
lisote ltioes ltiose ltieos ltieso ltiseo ltisoe ltoies ltoise ltoeis ltoesi
ltosei ltosie lteois lteosi lteios lteiso ltesio ltesoi ltsoei ltsoie ltseoi
ltseio ltsieo ltsioe leitos leitso leiots leiost leisot leisto letios letiso
letois letosi letsoi letsio leotis leotsi leoits leoist leosit leosti lestoi
lestio lesoti lesoit lesiot lesito lsiteo lsitoe lsieto lsieot lsioet lsiote
lstieo lstioe lsteio lsteoi lstoei lstoie lsetio lsetoi lseito lseiot lseoit
lseoti lsotei lsotie lsoeti lsoeit lsoiet lsoite eoilts eoilst eoitls eoitsl
eoistl eoislt eolits eolist eoltis eoltsi eolsti eolsit eotlis eotlsi eotils
eotisl eotsil eotsli eoslti eoslit eostli eostil eositl eosilt eiolts eiolst
eiotls eiotsl eiostl eioslt eilots eilost eiltos eiltso eilsto eilsot eitlos
eitlso eitols eitosl eitsol eitslo eislto eislot eistlo eistol eisotl eisolt
eliots eliost elitos elitso elisto elisot eloits eloist elotis elotsi elosti
elosit eltois eltosi eltios eltiso eltsio eltsoi elsoti elsoit elstoi elstio
elsito elsiot etilos etilso etiols etiosl etisol etislo etlios etliso etlois
etlosi etlsoi etlsio etolis etolsi etoils etoisl etosil etosli etsloi etslio
etsoli etsoil etsiol etsilo esilto esilot esitlo esitol esiotl esiolt eslito
esliot esltio esltoi esloti esloit estlio estloi estilo estiol estoil estoli
esolti esolit esotli esotil esoitl esoilt soilet soilte soielt soietl soitel
soitle soliet solite soleit soleti soltei soltie soelit soelti soeilt soeitl
soetil soetli sotlei sotlie soteli soteil sotiel sotile siolet siolte sioelt
sioetl siotel siotle siloet silote sileot sileto silteo siltoe sielot sielto
sieolt sieotl sietol sietlo sitleo sitloe sitelo siteol sitoel sitole slioet
sliote slieot slieto sliteo slitoe sloiet sloite sloeit sloeti slotei slotie
sleoit sleoti sleiot sleito sletio sletoi sltoei sltoie slteoi slteio sltieo
sltioe seilot seilto seiolt seiotl seitol seitlo seliot selito seloit seloti
seltoi seltio seolit seolti seoilt seoitl seotil seotli setloi setlio setoli
setoil setiol setilo stileo stiloe stielo stieol stioel stiole stlieo stlioe
stleio stleoi stloei stloie stelio steloi steilo steiol steoil steoli stolei
stolie stoeli stoeil stoiel stoile

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History of cryptography
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