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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: orphei
cipher variations:
psqifj qtrjgk ruskhl svtlim twumjn
uxvnko vywolp wzxpmq xayqnr ybzros
zcaspt adbtqu becurv cfdvsw dgewtx
ehfxuy figyvz gjhzwa hkiaxb iljbyc
jmkczd knldae lomebf mpnfcg nqogdh

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: orphei
Cipher: liksvr

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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: orphei

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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: orphei
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: orphei
Cipher: becurv

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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: orphei
Cipher: 432453325142

Extended Methods:
Method #1

Plaintext: orphei
method variations:

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

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Method #3

Plaintext: orphei
method variations:
hynwqr ynwqrh nwqrhy
wqrhyn qrhynw rhynwq

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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: orphei

all 720 cipher variations:
orphei orphie orpehi orpeih orpieh orpihe orhpei orhpie orhepi orheip orhiep
orhipe orehpi orehip orephi orepih oreiph oreihp orihep orihpe oriehp orieph
oripeh oriphe oprhei oprhie oprehi opreih oprieh oprihe ophrei ophrie opheri
opheir ophier ophire opehri opehir operhi operih opeirh opeihr opiher opihre
opiehr opierh opireh opirhe ohprei ohprie ohperi ohpeir ohpier ohpire ohrpei
ohrpie ohrepi ohreip ohriep ohripe oherpi oherip ohepri ohepir oheipr oheirp
ohirep ohirpe ohierp ohiepr ohiper ohipre oephri oephir oeprhi oeprih oepirh
oepihr oehpri oehpir oehrpi oehrip oehirp oehipr oerhpi oerhip oerphi oerpih
oeriph oerihp oeihrp oeihpr oeirhp oeirph oeiprh oeiphr oipher oiphre oipehr
oiperh oipreh oiprhe oihper oihpre oihepr oiherp oihrep oihrpe oiehpr oiehrp
oiephr oieprh oierph oierhp oirhep oirhpe oirehp oireph oirpeh oirphe rophei
rophie ropehi ropeih ropieh ropihe rohpei rohpie rohepi roheip rohiep rohipe
roehpi roehip roephi roepih roeiph roeihp roihep roihpe roiehp roieph roipeh
roiphe rpohei rpohie rpoehi rpoeih rpoieh rpoihe rphoei rphoie rpheoi rpheio
rphieo rphioe rpehoi rpehio rpeohi rpeoih rpeioh rpeiho rpiheo rpihoe rpieho
rpieoh rpioeh rpiohe rhpoei rhpoie rhpeoi rhpeio rhpieo rhpioe rhopei rhopie
rhoepi rhoeip rhoiep rhoipe rheopi rheoip rhepoi rhepio rheipo rheiop rhioep
rhiope rhieop rhiepo rhipeo rhipoe rephoi rephio repohi repoih repioh repiho
rehpoi rehpio rehopi rehoip rehiop rehipo reohpi reohip reophi reopih reoiph
reoihp reihop reihpo reiohp reioph reipoh reipho ripheo riphoe ripeho ripeoh
ripoeh ripohe rihpeo rihpoe rihepo riheop rihoep rihope riehpo riehop riepho
riepoh rieoph rieohp riohep riohpe rioehp rioeph riopeh riophe prohei prohie
proehi proeih proieh proihe prhoei prhoie prheoi prheio prhieo prhioe prehoi
prehio preohi preoih preioh preiho priheo prihoe prieho prieoh prioeh priohe
porhei porhie porehi poreih porieh porihe pohrei pohrie poheri poheir pohier
pohire poehri poehir poerhi poerih poeirh poeihr poiher poihre poiehr poierh
poireh poirhe phorei phorie phoeri phoeir phoier phoire phroei phroie phreoi
phreio phrieo phrioe pheroi pherio pheori pheoir pheior pheiro phireo phiroe
phiero phieor phioer phiore peohri peohir peorhi peorih peoirh peoihr pehori
pehoir pehroi pehrio pehiro pehior perhoi perhio perohi peroih perioh periho
peihro peihor peirho peiroh peiorh peiohr pioher piohre pioehr pioerh pioreh
piorhe pihoer pihore piheor pihero pihreo pihroe piehor piehro pieohr pieorh
pieroh pierho pirheo pirhoe pireho pireoh piroeh pirohe hrpoei hrpoie hrpeoi
hrpeio hrpieo hrpioe hropei hropie hroepi hroeip hroiep hroipe hreopi hreoip
hrepoi hrepio hreipo hreiop hrioep hriope hrieop hriepo hripeo hripoe hproei
hproie hpreoi hpreio hprieo hprioe hporei hporie hpoeri hpoeir hpoier hpoire
hpeori hpeoir hperoi hperio hpeiro hpeior hpioer hpiore hpieor hpiero hpireo
hpiroe hoprei hoprie hoperi hopeir hopier hopire horpei horpie horepi horeip
horiep horipe hoerpi hoerip hoepri hoepir hoeipr hoeirp hoirep hoirpe hoierp
hoiepr hoiper hoipre hepori hepoir heproi heprio hepiro hepior heopri heopir
heorpi heorip heoirp heoipr heropi heroip herpoi herpio heripo heriop heiorp
heiopr heirop heirpo heipro heipor hipoer hipore hipeor hipero hipreo hiproe
hioper hiopre hioepr hioerp hiorep hiorpe hieopr hieorp hiepor hiepro hierpo
hierop hiroep hirope hireop hirepo hirpeo hirpoe erphoi erphio erpohi erpoih
erpioh erpiho erhpoi erhpio erhopi erhoip erhiop erhipo erohpi erohip erophi
eropih eroiph eroihp erihop erihpo eriohp erioph eripoh eripho eprhoi eprhio
eprohi eproih eprioh epriho ephroi ephrio ephori ephoir ephior ephiro epohri
epohir eporhi eporih epoirh epoihr epihor epihro epiohr epiorh epiroh epirho
ehproi ehprio ehpori ehpoir ehpior ehpiro ehrpoi ehrpio ehropi ehroip ehriop
ehripo ehorpi ehorip ehopri ehopir ehoipr ehoirp ehirop ehirpo ehiorp ehiopr
ehipor ehipro eophri eophir eoprhi eoprih eopirh eopihr eohpri eohpir eohrpi
eohrip eohirp eohipr eorhpi eorhip eorphi eorpih eoriph eorihp eoihrp eoihpr
eoirhp eoirph eoiprh eoiphr eiphor eiphro eipohr eiporh eiproh eiprho eihpor
eihpro eihopr eihorp eihrop eihrpo eiohpr eiohrp eiophr eioprh eiorph eiorhp
eirhop eirhpo eirohp eiroph eirpoh eirpho irpheo irphoe irpeho irpeoh irpoeh
irpohe irhpeo irhpoe irhepo irheop irhoep irhope irehpo irehop irepho irepoh
ireoph ireohp irohep irohpe iroehp iroeph iropeh irophe iprheo iprhoe ipreho
ipreoh iproeh iprohe iphreo iphroe iphero ipheor iphoer iphore ipehro ipehor
iperho iperoh ipeorh ipeohr ipoher ipohre ipoehr ipoerh iporeh iporhe ihpreo
ihproe ihpero ihpeor ihpoer ihpore ihrpeo ihrpoe ihrepo ihreop ihroep ihrope
iherpo iherop ihepro ihepor iheopr iheorp ihorep ihorpe ihoerp ihoepr ihoper
ihopre iephro iephor ieprho ieproh ieporh iepohr iehpro iehpor iehrpo iehrop
iehorp iehopr ierhpo ierhop ierpho ierpoh ieroph ierohp ieohrp ieohpr ieorhp
ieorph ieoprh ieophr iopher iophre iopehr ioperh iopreh ioprhe iohper iohpre
iohepr ioherp iohrep iohrpe ioehpr ioehrp ioephr ioeprh ioerph ioerhp iorhep
iorhpe iorehp ioreph iorpeh iorphe

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History of cryptography
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