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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: otreus
cipher variations:
pusfvt qvtgwu rwuhxv sxviyw tywjzx
uzxkay vaylbz wbzmca xcandb ydboec
zecpfd afdqge bgerhf chfsig digtjh
ejhuki fkivlj gljwmk hmkxnl inlyom
jomzpn kpnaqo lqobrp mrpcsq nsqdtr

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: otreus
Cipher: lgivfh

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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: otreus

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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: otreus
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: otreus
Cipher: bgerhf

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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: otreus
Cipher: 434424515434

Extended Methods:
Method #1

Plaintext: otreus
method variations:

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

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Method #3

Plaintext: otreus
method variations:
siyvot iyvots yvotsi
votsiy otsiyv tsiyvo

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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: otreus

all 720 cipher variations:
otreus otresu otrues otruse otrsue otrseu oterus otersu oteurs oteusr otesur
otesru otuers otuesr otures oturse otusre otuser otseur otseru otsuer otsure
otsrue otsreu orteus ortesu ortues ortuse ortsue ortseu oretus oretsu oreuts
oreust oresut orestu oruets oruest orutes orutse oruste oruset orseut orsetu
orsuet orsute orstue orsteu oertus oertsu oeruts oerust oersut oerstu oetrus
oetrsu oeturs oetusr oetsur oetsru oeutrs oeutsr oeurts oeurst oeusrt oeustr
oestur oestru oesutr oesurt oesrut oesrtu ourets ourest ourtes ourtse ourste
ourset ouerts ouerst ouetrs ouetsr ouestr ouesrt outers outesr outres outrse
outsre outser ousetr ousert ouster oustre ousrte ousret osreut osretu osruet
osrute osrtue osrteu oserut osertu oseurt oseutr osetur osetru osuert osuetr
osuret osurte osutre osuter osteur osteru ostuer osture ostrue ostreu toreus
toresu torues toruse torsue torseu toerus toersu toeurs toeusr toesur toesru
touers touesr toures tourse tousre touser toseur toseru tosuer tosure tosrue
tosreu troeus troesu troues trouse trosue troseu treous treosu treuos treuso
tresuo tresou trueos trueso truoes truose trusoe truseo trseuo trseou trsueo
trsuoe trsoue trsoeu terous terosu teruos teruso tersuo tersou teorus teorsu
teours teousr teosur teosru teuors teuosr teuros teurso teusro teusor tesour
tesoru tesuor tesuro tesruo tesrou tureos tureso turoes turose tursoe turseo
tueros tuerso tueors tueosr tuesor tuesro tuoers tuoesr tuores tuorse tuosre
tuoser tuseor tusero tusoer tusore tusroe tusreo tsreuo tsreou tsrueo tsruoe
tsroue tsroeu tseruo tserou tseuro tseuor tseour tseoru tsuero tsueor tsureo
tsuroe tsuore tsuoer tsoeur tsoeru tsouer tsoure tsorue tsoreu rtoeus rtoesu
rtoues rtouse rtosue rtoseu rteous rteosu rteuos rteuso rtesuo rtesou rtueos
rtueso rtuoes rtuose rtusoe rtuseo rtseuo rtseou rtsueo rtsuoe rtsoue rtsoeu
roteus rotesu rotues rotuse rotsue rotseu roetus roetsu roeuts roeust roesut
roestu rouets rouest routes routse rouste rouset roseut rosetu rosuet rosute
rostue rosteu reotus reotsu reouts reoust reosut reostu retous retosu retuos
retuso retsuo retsou reutos reutso reuots reuost reusot reusto restuo restou
resuto resuot resout resotu ruoets ruoest ruotes ruotse ruoste ruoset rueots
rueost ruetos ruetso ruesto ruesot ruteos ruteso rutoes rutose rutsoe rutseo
ruseto ruseot rusteo rustoe rusote rusoet rsoeut rsoetu rsouet rsoute rsotue
rsoteu rseout rseotu rseuot rseuto rsetuo rsetou rsueot rsueto rsuoet rsuote
rsutoe rsuteo rsteuo rsteou rstueo rstuoe rstoue rstoeu etrous etrosu etruos
etruso etrsuo etrsou etorus etorsu etours etousr etosur etosru etuors etuosr
eturos eturso etusro etusor etsour etsoru etsuor etsuro etsruo etsrou ertous
ertosu ertuos ertuso ertsuo ertsou erotus erotsu erouts eroust erosut erostu
eruots eruost erutos erutso erusto erusot ersout ersotu ersuot ersuto erstuo
erstou eortus eortsu eoruts eorust eorsut eorstu eotrus eotrsu eoturs eotusr
eotsur eotsru eoutrs eoutsr eourts eourst eousrt eoustr eostur eostru eosutr
eosurt eosrut eosrtu eurots eurost eurtos eurtso eursto eursot euorts euorst
euotrs euotsr euostr euosrt eutors eutosr eutros eutrso eutsro eutsor eusotr
eusort eustor eustro eusrto eusrot esrout esrotu esruot esruto esrtuo esrtou
esorut esortu esourt esoutr esotur esotru esuort esuotr esurot esurto esutro
esutor estour estoru estuor esturo estruo estrou utreos utreso utroes utrose
utrsoe utrseo uteros uterso uteors uteosr utesor utesro utoers utoesr utores
utorse utosre utoser utseor utsero utsoer utsore utsroe utsreo urteos urteso
urtoes urtose urtsoe urtseo uretos uretso ureots ureost uresot uresto uroets
uroest urotes urotse uroste uroset urseot urseto ursoet ursote urstoe ursteo
uertos uertso uerots uerost uersot uersto uetros uetrso uetors uetosr uetsor
uetsro ueotrs ueotsr ueorts ueorst ueosrt ueostr uestor uestro uesotr uesort
uesrot uesrto uorets uorest uortes uortse uorste uorset uoerts uoerst uoetrs
uoetsr uoestr uoesrt uoters uotesr uotres uotrse uotsre uotser uosetr uosert
uoster uostre uosrte uosret usreot usreto usroet usrote usrtoe usrteo userot
userto useort useotr usetor usetro usoert usoetr usoret usorte usotre usoter
usteor ustero ustoer ustore ustroe ustreo streuo streou strueo struoe stroue
stroeu steruo sterou steuro steuor steour steoru stuero stueor stureo sturoe
stuore stuoer stoeur stoeru stouer stoure storue storeu srteuo srteou srtueo
srtuoe srtoue srtoeu sretuo sretou sreuto sreuot sreout sreotu srueto srueot
sruteo srutoe sruote sruoet sroeut sroetu srouet sroute srotue sroteu sertuo
sertou seruto seruot serout serotu setruo setrou seturo setuor setour setoru
seutro seutor seurto seurot seuort seuotr seotur seotru seoutr seourt seorut
seortu sureto sureot surteo surtoe surote suroet suerto suerot suetro suetor
sueotr sueort sutero suteor sutreo sutroe sutore sutoer suoetr suoert suoter
suotre suorte suoret soreut soretu soruet sorute sortue sorteu soerut soertu
soeurt soeutr soetur soetru souert souetr souret sourte soutre souter soteur
soteru sotuer soture sotrue sotreu

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History of cryptography
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