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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: exults
cipher variations:
fyvmut gzwnvu haxowv ibypxw jczqyx
kdarzy lebsaz mfctba ngducb ohevdc
pifwed qjgxfe rkhygf slizhg tmjaih
unkbji volckj wpmdlk xqneml yrofnm
zspgon atqhpo buriqp cvsjrq dwtksr

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: exults
Cipher: vcfogh

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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: exults

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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: exults
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: exults
Cipher: rkhygf

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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: exults
Cipher: 513554134434

Extended Methods:
Method #1

Plaintext: exults
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
e x u l t s 
5 3 5 1 4 3 
1 5 4 3 4 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: exults
Cipher: peovot

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Method #3

Plaintext: exults
method variations:
lzdsoy zdsoyl dsoylz
soylzd oylzds ylzdso

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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: exults

all 720 cipher variations:
exults exulst exutls exutsl exustl exuslt exluts exlust exltus exltsu exlstu
exlsut extlus extlsu extuls extusl extsul extslu exsltu exslut exstlu exstul
exsutl exsult euxlts euxlst euxtls euxtsl euxstl euxslt eulxts eulxst eultxs
eultsx eulstx eulsxt eutlxs eutlsx eutxls eutxsl eutsxl eutslx eusltx euslxt
eustlx eustxl eusxtl eusxlt eluxts eluxst elutxs elutsx elustx elusxt elxuts
elxust elxtus elxtsu elxstu elxsut eltxus eltxsu eltuxs eltusx eltsux eltsxu
elsxtu elsxut elstxu elstux elsutx elsuxt etulxs etulsx etuxls etuxsl etusxl
etuslx etluxs etlusx etlxus etlxsu etlsxu etlsux etxlus etxlsu etxuls etxusl
etxsul etxslu etslxu etslux etsxlu etsxul etsuxl etsulx esultx esulxt esutlx
esutxl esuxtl esuxlt eslutx esluxt esltux esltxu eslxtu eslxut estlux estlxu
estulx estuxl estxul estxlu esxltu esxlut esxtlu esxtul esxutl esxult xeults
xeulst xeutls xeutsl xeustl xeuslt xeluts xelust xeltus xeltsu xelstu xelsut
xetlus xetlsu xetuls xetusl xetsul xetslu xesltu xeslut xestlu xestul xesutl
xesult xuelts xuelst xuetls xuetsl xuestl xueslt xulets xulest xultes xultse
xulste xulset xutles xutlse xutels xutesl xutsel xutsle xuslte xuslet xustle
xustel xusetl xuselt xluets xluest xlutes xlutse xluste xluset xleuts xleust
xletus xletsu xlestu xlesut xlteus xltesu xltues xltuse xltsue xltseu xlsetu
xlseut xlsteu xlstue xlsute xlsuet xtules xtulse xtuels xtuesl xtusel xtusle
xtlues xtluse xtleus xtlesu xtlseu xtlsue xtelus xtelsu xteuls xteusl xtesul
xteslu xtsleu xtslue xtselu xtseul xtsuel xtsule xsulte xsulet xsutle xsutel
xsuetl xsuelt xslute xsluet xsltue xslteu xsletu xsleut xstlue xstleu xstule
xstuel xsteul xstelu xseltu xselut xsetlu xsetul xseutl xseult uxelts uxelst
uxetls uxetsl uxestl uxeslt uxlets uxlest uxltes uxltse uxlste uxlset uxtles
uxtlse uxtels uxtesl uxtsel uxtsle uxslte uxslet uxstle uxstel uxsetl uxselt
uexlts uexlst uextls uextsl uexstl uexslt uelxts uelxst ueltxs ueltsx uelstx
uelsxt uetlxs uetlsx uetxls uetxsl uetsxl uetslx uesltx ueslxt uestlx uestxl
uesxtl uesxlt ulexts ulexst uletxs uletsx ulestx ulesxt ulxets ulxest ulxtes
ulxtse ulxste ulxset ultxes ultxse ultexs ultesx ultsex ultsxe ulsxte ulsxet
ulstxe ulstex ulsetx ulsext utelxs utelsx utexls utexsl utesxl uteslx utlexs
utlesx utlxes utlxse utlsxe utlsex utxles utxlse utxels utxesl utxsel utxsle
utslxe utslex utsxle utsxel utsexl utselx useltx uselxt usetlx usetxl usextl
usexlt usletx uslext usltex usltxe uslxte uslxet ustlex ustlxe ustelx ustexl
ustxel ustxle usxlte usxlet usxtle usxtel usxetl usxelt lxuets lxuest lxutes
lxutse lxuste lxuset lxeuts lxeust lxetus lxetsu lxestu lxesut lxteus lxtesu
lxtues lxtuse lxtsue lxtseu lxsetu lxseut lxsteu lxstue lxsute lxsuet luxets
luxest luxtes luxtse luxste luxset luexts luexst luetxs luetsx luestx luesxt
lutexs lutesx lutxes lutxse lutsxe lutsex lusetx lusext lustex lustxe lusxte
lusxet leuxts leuxst leutxs leutsx leustx leusxt lexuts lexust lextus lextsu
lexstu lexsut letxus letxsu letuxs letusx letsux letsxu lesxtu lesxut lestxu
lestux lesutx lesuxt ltuexs ltuesx ltuxes ltuxse ltusxe ltusex lteuxs lteusx
ltexus ltexsu ltesxu ltesux ltxeus ltxesu ltxues ltxuse ltxsue ltxseu ltsexu
ltseux ltsxeu ltsxue ltsuxe ltsuex lsuetx lsuext lsutex lsutxe lsuxte lsuxet
lseutx lseuxt lsetux lsetxu lsextu lsexut lsteux lstexu lstuex lstuxe lstxue
lstxeu lsxetu lsxeut lsxteu lsxtue lsxute lsxuet txules txulse txuels txuesl
txusel txusle txlues txluse txleus txlesu txlseu txlsue txelus txelsu txeuls
txeusl txesul txeslu txsleu txslue txselu txseul txsuel txsule tuxles tuxlse
tuxels tuxesl tuxsel tuxsle tulxes tulxse tulexs tulesx tulsex tulsxe tuelxs
tuelsx tuexls tuexsl tuesxl tueslx tuslex tuslxe tuselx tusexl tusxel tusxle
tluxes tluxse tluexs tluesx tlusex tlusxe tlxues tlxuse tlxeus tlxesu tlxseu
tlxsue tlexus tlexsu tleuxs tleusx tlesux tlesxu tlsxeu tlsxue tlsexu tlseux
tlsuex tlsuxe teulxs teulsx teuxls teuxsl teusxl teuslx teluxs telusx telxus
telxsu telsxu telsux texlus texlsu texuls texusl texsul texslu teslxu teslux
tesxlu tesxul tesuxl tesulx tsulex tsulxe tsuelx tsuexl tsuxel tsuxle tsluex
tsluxe tsleux tslexu tslxeu tslxue tselux tselxu tseulx tseuxl tsexul tsexlu
tsxleu tsxlue tsxelu tsxeul tsxuel tsxule sxulte sxulet sxutle sxutel sxuetl
sxuelt sxlute sxluet sxltue sxlteu sxletu sxleut sxtlue sxtleu sxtule sxtuel
sxteul sxtelu sxeltu sxelut sxetlu sxetul sxeutl sxeult suxlte suxlet suxtle
suxtel suxetl suxelt sulxte sulxet sultxe sultex suletx sulext sutlxe sutlex
sutxle sutxel sutexl sutelx sueltx suelxt suetlx suetxl suextl suexlt sluxte
sluxet slutxe slutex sluetx sluext slxute slxuet slxtue slxteu slxetu slxeut
sltxue sltxeu sltuxe sltuex slteux sltexu slextu slexut sletxu sletux sleutx
sleuxt stulxe stulex stuxle stuxel stuexl stuelx stluxe stluex stlxue stlxeu
stlexu stleux stxlue stxleu stxule stxuel stxeul stxelu stelxu stelux stexlu
stexul steuxl steulx seultx seulxt seutlx seutxl seuxtl seuxlt selutx seluxt
seltux seltxu selxtu selxut setlux setlxu setulx setuxl setxul setxlu sexltu
sexlut sextlu sextul sexutl sexult

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History of cryptography
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