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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: teafix
cipher variations:
ufbgjy vgchkz whdila xiejmb yjfknc
zkglod alhmpe bminqf cnjorg dokpsh
eplqti fqmruj grnsvk hsotwl itpuxm
juqvyn kvrwzo lwsxap mxtybq nyuzcr
ozvads pawbet qbxcfu rcydgv sdzehw

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: teafix
Cipher: gvzurc

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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: teafix

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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: teafix
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: teafix
Cipher: grnsvk

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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: teafix
Cipher: 445111124235

Extended Methods:
Method #1

Plaintext: teafix
method variations:

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

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Method #3

Plaintext: teafix
method variations:
yaarmu aarmuy armuya
rmuyaa muyaar uyaarm

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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: teafix

all 720 cipher variations:
teafix teafxi teaifx teaixf teaxif teaxfi tefaix tefaxi tefiax tefixa tefxia
tefxai teifax teifxa teiafx teiaxf teixaf teixfa texfia texfai texifa texiaf
texaif texafi taefix taefxi taeifx taeixf taexif taexfi tafeix tafexi tafiex
tafixe tafxie tafxei taifex taifxe taiefx taiexf taixef taixfe taxfie taxfei
taxife taxief taxeif taxefi tfaeix tfaexi tfaiex tfaixe tfaxie tfaxei tfeaix
tfeaxi tfeiax tfeixa tfexia tfexai tfieax tfiexa tfiaex tfiaxe tfixae tfixea
tfxeia tfxeai tfxiea tfxiae tfxaie tfxaei tiafex tiafxe tiaefx tiaexf tiaxef
tiaxfe tifaex tifaxe tifeax tifexa tifxea tifxae tiefax tiefxa tieafx tieaxf
tiexaf tiexfa tixfea tixfae tixefa tixeaf tixaef tixafe txafie txafei txaife
txaief txaeif txaefi txfaie txfaei txfiae txfiea txfeia txfeai txifae txifea
txiafe txiaef txieaf txiefa txefia txefai txeifa txeiaf txeaif txeafi etafix
etafxi etaifx etaixf etaxif etaxfi etfaix etfaxi etfiax etfixa etfxia etfxai
etifax etifxa etiafx etiaxf etixaf etixfa etxfia etxfai etxifa etxiaf etxaif
etxafi eatfix eatfxi eatifx eatixf eatxif eatxfi eaftix eaftxi eafitx eafixt
eafxit eafxti eaiftx eaifxt eaitfx eaitxf eaixtf eaixft eaxfit eaxfti eaxift
eaxitf eaxtif eaxtfi efatix efatxi efaitx efaixt efaxit efaxti eftaix eftaxi
eftiax eftixa eftxia eftxai efitax efitxa efiatx efiaxt efixat efixta efxtia
efxtai efxita efxiat efxait efxati eiaftx eiafxt eiatfx eiatxf eiaxtf eiaxft
eifatx eifaxt eiftax eiftxa eifxta eifxat eitfax eitfxa eitafx eitaxf eitxaf
eitxfa eixfta eixfat eixtfa eixtaf eixatf eixaft exafit exafti exaift exaitf
exatif exatfi exfait exfati exfiat exfita exftia exftai exifat exifta exiaft
exiatf exitaf exitfa extfia extfai extifa extiaf extaif extafi aetfix aetfxi
aetifx aetixf aetxif aetxfi aeftix aeftxi aefitx aefixt aefxit aefxti aeiftx
aeifxt aeitfx aeitxf aeixtf aeixft aexfit aexfti aexift aexitf aextif aextfi
atefix atefxi ateifx ateixf atexif atexfi atfeix atfexi atfiex atfixe atfxie
atfxei atifex atifxe atiefx atiexf atixef atixfe atxfie atxfei atxife atxief
atxeif atxefi afteix aftexi aftiex aftixe aftxie aftxei afetix afetxi afeitx
afeixt afexit afexti afietx afiext afitex afitxe afixte afixet afxeit afxeti
afxiet afxite afxtie afxtei aitfex aitfxe aitefx aitexf aitxef aitxfe aiftex
aiftxe aifetx aifext aifxet aifxte aieftx aiefxt aietfx aietxf aiextf aiexft
aixfet aixfte aixeft aixetf aixtef aixtfe axtfie axtfei axtife axtief axteif
axtefi axftie axftei axfite axfiet axfeit axfeti axifte axifet axitfe axitef
axietf axieft axefit axefti axeift axeitf axetif axetfi featix featxi feaitx
feaixt feaxit feaxti fetaix fetaxi fetiax fetixa fetxia fetxai feitax feitxa
feiatx feiaxt feixat feixta fextia fextai fexita fexiat fexait fexati faetix
faetxi faeitx faeixt faexit faexti fateix fatexi fatiex fatixe fatxie fatxei
faitex faitxe faietx faiext faixet faixte faxtie faxtei faxite faxiet faxeit
faxeti ftaeix ftaexi ftaiex ftaixe ftaxie ftaxei fteaix fteaxi fteiax fteixa
ftexia ftexai ftieax ftiexa ftiaex ftiaxe ftixae ftixea ftxeia ftxeai ftxiea
ftxiae ftxaie ftxaei fiatex fiatxe fiaetx fiaext fiaxet fiaxte fitaex fitaxe
fiteax fitexa fitxea fitxae fietax fietxa fieatx fieaxt fiexat fiexta fixtea
fixtae fixeta fixeat fixaet fixate fxatie fxatei fxaite fxaiet fxaeit fxaeti
fxtaie fxtaei fxtiae fxtiea fxteia fxteai fxitae fxitea fxiate fxiaet fxieat
fxieta fxetia fxetai fxeita fxeiat fxeait fxeati ieaftx ieafxt ieatfx ieatxf
ieaxtf ieaxft iefatx iefaxt ieftax ieftxa iefxta iefxat ietfax ietfxa ietafx
ietaxf ietxaf ietxfa iexfta iexfat iextfa iextaf iexatf iexaft iaeftx iaefxt
iaetfx iaetxf iaextf iaexft iafetx iafext iaftex iaftxe iafxte iafxet iatfex
iatfxe iatefx iatexf iatxef iatxfe iaxfte iaxfet iaxtfe iaxtef iaxetf iaxeft
ifaetx ifaext ifatex ifatxe ifaxte ifaxet ifeatx ifeaxt ifetax ifetxa ifexta
ifexat ifteax iftexa iftaex iftaxe iftxae iftxea ifxeta ifxeat ifxtea ifxtae
ifxate ifxaet itafex itafxe itaefx itaexf itaxef itaxfe itfaex itfaxe itfeax
itfexa itfxea itfxae itefax itefxa iteafx iteaxf itexaf itexfa itxfea itxfae
itxefa itxeaf itxaef itxafe ixafte ixafet ixatfe ixatef ixaetf ixaeft ixfate
ixfaet ixftae ixftea ixfeta ixfeat ixtfae ixtfea ixtafe ixtaef ixteaf ixtefa
ixefta ixefat ixetfa ixetaf ixeatf ixeaft xeafit xeafti xeaift xeaitf xeatif
xeatfi xefait xefati xefiat xefita xeftia xeftai xeifat xeifta xeiaft xeiatf
xeitaf xeitfa xetfia xetfai xetifa xetiaf xetaif xetafi xaefit xaefti xaeift
xaeitf xaetif xaetfi xafeit xafeti xafiet xafite xaftie xaftei xaifet xaifte
xaieft xaietf xaitef xaitfe xatfie xatfei xatife xatief xateif xatefi xfaeit
xfaeti xfaiet xfaite xfatie xfatei xfeait xfeati xfeiat xfeita xfetia xfetai
xfieat xfieta xfiaet xfiate xfitae xfitea xfteia xfteai xftiea xftiae xftaie
xftaei xiafet xiafte xiaeft xiaetf xiatef xiatfe xifaet xifate xifeat xifeta
xiftea xiftae xiefat xiefta xieaft xieatf xietaf xietfa xitfea xitfae xitefa
xiteaf xitaef xitafe xtafie xtafei xtaife xtaief xtaeif xtaefi xtfaie xtfaei
xtfiae xtfiea xtfeia xtfeai xtifae xtifea xtiafe xtiaef xtieaf xtiefa xtefia
xtefai xteifa xteiaf xteaif xteafi

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History of cryptography
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