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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: travus
cipher variations:
usbwvt vtcxwu wudyxv xvezyw ywfazx
zxgbay ayhcbz bzidca cajedb dbkfec
eclgfd fdmhge genihf hfojig igpkjh
jhqlki kirmlj ljsnmk mktonl nlupom
omvqpn pnwrqo qoxsrp rpytsq sqzutr

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: travus
Cipher: gizefh

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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: travus

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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: travus
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: travus
Cipher: genihf

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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: travus
Cipher: 442411155434

Extended Methods:
Method #1

Plaintext: travus
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
t r a v u s 
4 2 1 1 5 3 
4 4 1 5 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: travus
Cipher: iaptvt

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Method #3

Plaintext: travus
method variations:
idazot dazoti azotid
zotida otidaz tidazo

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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: travus

all 720 cipher variations:
travus travsu trauvs trausv trasuv trasvu trvaus trvasu trvuas trvusa trvsua
trvsau truvas truvsa truavs truasv trusav trusva trsvua trsvau trsuva trsuav
trsauv trsavu tarvus tarvsu taruvs tarusv tarsuv tarsvu tavrus tavrsu tavurs
tavusr tavsur tavsru tauvrs tauvsr taurvs taursv tausrv tausvr tasvur tasvru
tasuvr tasurv tasruv tasrvu tvarus tvarsu tvaurs tvausr tvasur tvasru tvraus
tvrasu tvruas tvrusa tvrsua tvrsau tvuras tvursa tvuars tvuasr tvusar tvusra
tvsrua tvsrau tvsura tvsuar tvsaur tvsaru tuavrs tuavsr tuarvs tuarsv tuasrv
tuasvr tuvars tuvasr tuvras tuvrsa tuvsra tuvsar turvas turvsa turavs turasv
tursav tursva tusvra tusvar tusrva tusrav tusarv tusavr tsavur tsavru tsauvr
tsaurv tsaruv tsarvu tsvaur tsvaru tsvuar tsvura tsvrua tsvrau tsuvar tsuvra
tsuavr tsuarv tsurav tsurva tsrvua tsrvau tsruva tsruav tsrauv tsravu rtavus
rtavsu rtauvs rtausv rtasuv rtasvu rtvaus rtvasu rtvuas rtvusa rtvsua rtvsau
rtuvas rtuvsa rtuavs rtuasv rtusav rtusva rtsvua rtsvau rtsuva rtsuav rtsauv
rtsavu ratvus ratvsu ratuvs ratusv ratsuv ratsvu ravtus ravtsu ravuts ravust
ravsut ravstu rauvts rauvst rautvs rautsv raustv rausvt rasvut rasvtu rasuvt
rasutv rastuv rastvu rvatus rvatsu rvauts rvaust rvasut rvastu rvtaus rvtasu
rvtuas rvtusa rvtsua rvtsau rvutas rvutsa rvuats rvuast rvusat rvusta rvstua
rvstau rvsuta rvsuat rvsaut rvsatu ruavts ruavst ruatvs ruatsv ruastv ruasvt
ruvats ruvast ruvtas ruvtsa ruvsta ruvsat rutvas rutvsa rutavs rutasv rutsav
rutsva rusvta rusvat rustva rustav rusatv rusavt rsavut rsavtu rsauvt rsautv
rsatuv rsatvu rsvaut rsvatu rsvuat rsvuta rsvtua rsvtau rsuvat rsuvta rsuavt
rsuatv rsutav rsutva rstvua rstvau rstuva rstuav rstauv rstavu artvus artvsu
artuvs artusv artsuv artsvu arvtus arvtsu arvuts arvust arvsut arvstu aruvts
aruvst arutvs arutsv arustv arusvt arsvut arsvtu arsuvt arsutv arstuv arstvu
atrvus atrvsu atruvs atrusv atrsuv atrsvu atvrus atvrsu atvurs atvusr atvsur
atvsru atuvrs atuvsr aturvs atursv atusrv atusvr atsvur atsvru atsuvr atsurv
atsruv atsrvu avtrus avtrsu avturs avtusr avtsur avtsru avrtus avrtsu avruts
avrust avrsut avrstu avurts avurst avutrs avutsr avustr avusrt avsrut avsrtu
avsurt avsutr avstur avstru autvrs autvsr autrvs autrsv autsrv autsvr auvtrs
auvtsr auvrts auvrst auvsrt auvstr aurvts aurvst aurtvs aurtsv aurstv aursvt
ausvrt ausvtr ausrvt ausrtv austrv austvr astvur astvru astuvr asturv astruv
astrvu asvtur asvtru asvutr asvurt asvrut asvrtu asuvtr asuvrt asutvr asutrv
asurtv asurvt asrvut asrvtu asruvt asrutv asrtuv asrtvu vratus vratsu vrauts
vraust vrasut vrastu vrtaus vrtasu vrtuas vrtusa vrtsua vrtsau vrutas vrutsa
vruats vruast vrusat vrusta vrstua vrstau vrsuta vrsuat vrsaut vrsatu vartus
vartsu varuts varust varsut varstu vatrus vatrsu vaturs vatusr vatsur vatsru
vautrs vautsr vaurts vaurst vausrt vaustr vastur vastru vasutr vasurt vasrut
vasrtu vtarus vtarsu vtaurs vtausr vtasur vtasru vtraus vtrasu vtruas vtrusa
vtrsua vtrsau vturas vtursa vtuars vtuasr vtusar vtusra vtsrua vtsrau vtsura
vtsuar vtsaur vtsaru vuatrs vuatsr vuarts vuarst vuasrt vuastr vutars vutasr
vutras vutrsa vutsra vutsar vurtas vurtsa vurats vurast vursat vursta vustra
vustar vusrta vusrat vusart vusatr vsatur vsatru vsautr vsaurt vsarut vsartu
vstaur vstaru vstuar vstura vstrua vstrau vsutar vsutra vsuatr vsuart vsurat
vsurta vsrtua vsrtau vsruta vsruat vsraut vsratu uravts uravst uratvs uratsv
urastv urasvt urvats urvast urvtas urvtsa urvsta urvsat urtvas urtvsa urtavs
urtasv urtsav urtsva ursvta ursvat urstva urstav ursatv ursavt uarvts uarvst
uartvs uartsv uarstv uarsvt uavrts uavrst uavtrs uavtsr uavstr uavsrt uatvrs
uatvsr uatrvs uatrsv uatsrv uatsvr uasvtr uasvrt uastvr uastrv uasrtv uasrvt
uvarts uvarst uvatrs uvatsr uvastr uvasrt uvrats uvrast uvrtas uvrtsa uvrsta
uvrsat uvtras uvtrsa uvtars uvtasr uvtsar uvtsra uvsrta uvsrat uvstra uvstar
uvsatr uvsart utavrs utavsr utarvs utarsv utasrv utasvr utvars utvasr utvras
utvrsa utvsra utvsar utrvas utrvsa utravs utrasv utrsav utrsva utsvra utsvar
utsrva utsrav utsarv utsavr usavtr usavrt usatvr usatrv usartv usarvt usvatr
usvart usvtar usvtra usvrta usvrat ustvar ustvra ustavr ustarv ustrav ustrva
usrvta usrvat usrtva usrtav usratv usravt sravut sravtu srauvt srautv sratuv
sratvu srvaut srvatu srvuat srvuta srvtua srvtau sruvat sruvta sruavt sruatv
srutav srutva srtvua srtvau srtuva srtuav srtauv srtavu sarvut sarvtu saruvt
sarutv sartuv sartvu savrut savrtu savurt savutr savtur savtru sauvrt sauvtr
saurvt saurtv sautrv sautvr satvur satvru satuvr saturv satruv satrvu svarut
svartu svaurt svautr svatur svatru svraut svratu svruat svruta svrtua svrtau
svurat svurta svuart svuatr svutar svutra svtrua svtrau svtura svtuar svtaur
svtaru suavrt suavtr suarvt suartv suatrv suatvr suvart suvatr suvrat suvrta
suvtra suvtar survat survta suravt suratv surtav surtva sutvra sutvar sutrva
sutrav sutarv sutavr stavur stavru stauvr staurv staruv starvu stvaur stvaru
stvuar stvura stvrua stvrau stuvar stuvra stuavr stuarv sturav sturva strvua
strvau struva struav strauv stravu

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History of cryptography
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