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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: holing
cipher variations:
ipmjoh jqnkpi krolqj lspmrk mtqnsl
nurotm ovspun pwtqvo qxurwp ryvsxq
szwtyr taxuzs ubyvat vczwbu wdaxcv
xebydw yfczex zgdafy ahebgz bifcha
cjgdib dkhejc elifkd fmjgle gnkhmf

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: holing
Cipher: slormt

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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: holing

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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: holing
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: holing
Cipher: ubyvat

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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: holing
Cipher: 324313423322

Extended Methods:
Method #1

Plaintext: holing
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
h o l i n g 
3 4 1 4 3 2 
2 3 3 2 3 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: holing
Cipher: sqhmhh

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Method #3

Plaintext: holing
method variations:
rcsmhm csmhmr smhmrc
mhmrcs hmrcsm mrcsmh

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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: holing

all 720 cipher variations:
holing holign holnig holngi holgni holgin hoilng hoilgn hoinlg hoingl hoignl
hoigln honilg honigl honlig honlgi hongli hongil hoginl hogiln hognil hognli
hoglni hoglin hloing hloign hlonig hlongi hlogni hlogin hliong hliogn hlinog
hlingo hligno hligon hlniog hlnigo hlnoig hlnogi hlngoi hlngio hlgino hlgion
hlgnio hlgnoi hlgoni hlgoin hilong hilogn hilnog hilngo hilgno hilgon hiolng
hiolgn hionlg hiongl hiognl hiogln hinolg hinogl hinlog hinlgo hinglo hingol
higonl higoln hignol hignlo higlno higlon hnliog hnligo hnloig hnlogi hnlgoi
hnlgio hnilog hnilgo hniolg hniogl hnigol hniglo hnoilg hnoigl hnolig hnolgi
hnogli hnogil hngiol hngilo hngoil hngoli hngloi hnglio hglino hglion hglnio
hglnoi hgloni hgloin hgilno hgilon hginlo hginol hgionl hgioln hgnilo hgniol
hgnlio hgnloi hgnoli hgnoil hgoinl hgoiln hgonil hgonli hgolni hgolin ohling
ohlign ohlnig ohlngi ohlgni ohlgin ohilng ohilgn ohinlg ohingl ohignl ohigln
ohnilg ohnigl ohnlig ohnlgi ohngli ohngil ohginl ohgiln ohgnil ohgnli ohglni
ohglin olhing olhign olhnig olhngi olhgni olhgin olihng olihgn olinhg olingh
olignh olighn olnihg olnigh olnhig olnhgi olnghi olngih olginh olgihn olgnih
olgnhi olghni olghin oilhng oilhgn oilnhg oilngh oilgnh oilghn oihlng oihlgn
oihnlg oihngl oihgnl oihgln oinhlg oinhgl oinlhg oinlgh oinglh oinghl oighnl
oighln oignhl oignlh oiglnh oiglhn onlihg onligh onlhig onlhgi onlghi onlgih
onilhg onilgh onihlg onihgl onighl oniglh onhilg onhigl onhlig onhlgi onhgli
onhgil ongihl ongilh onghil onghli onglhi onglih oglinh oglihn oglnih oglnhi
oglhni oglhin ogilnh ogilhn oginlh oginhl ogihnl ogihln ognilh ognihl ognlih
ognlhi ognhli ognhil oghinl oghiln oghnil oghnli oghlni oghlin lohing lohign
lohnig lohngi lohgni lohgin loihng loihgn loinhg loingh loignh loighn lonihg
lonigh lonhig lonhgi longhi longih loginh logihn lognih lognhi loghni loghin
lhoing lhoign lhonig lhongi lhogni lhogin lhiong lhiogn lhinog lhingo lhigno
lhigon lhniog lhnigo lhnoig lhnogi lhngoi lhngio lhgino lhgion lhgnio lhgnoi
lhgoni lhgoin lihong lihogn lihnog lihngo lihgno lihgon liohng liohgn lionhg
liongh liognh lioghn linohg linogh linhog linhgo lingho lingoh ligonh ligohn
lignoh lignho lighno lighon lnhiog lnhigo lnhoig lnhogi lnhgoi lnhgio lnihog
lnihgo lniohg lniogh lnigoh lnigho lnoihg lnoigh lnohig lnohgi lnoghi lnogih
lngioh lngiho lngoih lngohi lnghoi lnghio lghino lghion lghnio lghnoi lghoni
lghoin lgihno lgihon lginho lginoh lgionh lgiohn lgniho lgnioh lgnhio lgnhoi
lgnohi lgnoih lgoinh lgoihn lgonih lgonhi lgohni lgohin iolhng iolhgn iolnhg
iolngh iolgnh iolghn iohlng iohlgn iohnlg iohngl iohgnl iohgln ionhlg ionhgl
ionlhg ionlgh ionglh ionghl ioghnl ioghln iognhl iognlh ioglnh ioglhn ilohng
ilohgn ilonhg ilongh ilognh iloghn ilhong ilhogn ilhnog ilhngo ilhgno ilhgon
ilnhog ilnhgo ilnohg ilnogh ilngoh ilngho ilghno ilghon ilgnho ilgnoh ilgonh
ilgohn ihlong ihlogn ihlnog ihlngo ihlgno ihlgon iholng iholgn ihonlg ihongl
ihognl ihogln ihnolg ihnogl ihnlog ihnlgo ihnglo ihngol ihgonl ihgoln ihgnol
ihgnlo ihglno ihglon inlhog inlhgo inlohg inlogh inlgoh inlgho inhlog inhlgo
inholg inhogl inhgol inhglo inohlg inohgl inolhg inolgh inoglh inoghl inghol
inghlo ingohl ingolh ingloh inglho iglhno iglhon iglnho iglnoh iglonh iglohn
ighlno ighlon ighnlo ighnol ighonl igholn ignhlo ignhol ignlho ignloh ignolh
ignohl igohnl igohln igonhl igonlh igolnh igolhn nolihg noligh nolhig nolhgi
nolghi nolgih noilhg noilgh noihlg noihgl noighl noiglh nohilg nohigl nohlig
nohlgi nohgli nohgil nogihl nogilh noghil noghli noglhi noglih nloihg nloigh
nlohig nlohgi nloghi nlogih nliohg nliogh nlihog nlihgo nligho nligoh nlhiog
nlhigo nlhoig nlhogi nlhgoi nlhgio nlgiho nlgioh nlghio nlghoi nlgohi nlgoih
nilohg nilogh nilhog nilhgo nilgho nilgoh niolhg niolgh niohlg niohgl nioghl
nioglh niholg nihogl nihlog nihlgo nihglo nihgol nigohl nigolh nighol nighlo
niglho nigloh nhliog nhligo nhloig nhlogi nhlgoi nhlgio nhilog nhilgo nhiolg
nhiogl nhigol nhiglo nhoilg nhoigl nholig nholgi nhogli nhogil nhgiol nhgilo
nhgoil nhgoli nhgloi nhglio ngliho nglioh nglhio nglhoi nglohi ngloih ngilho
ngiloh ngihlo ngihol ngiohl ngiolh nghilo nghiol nghlio nghloi ngholi nghoil
ngoihl ngoilh ngohil ngohli ngolhi ngolih golinh golihn golnih golnhi golhni
golhin goilnh goilhn goinlh goinhl goihnl goihln gonilh gonihl gonlih gonlhi
gonhli gonhil gohinl gohiln gohnil gohnli gohlni gohlin gloinh gloihn glonih
glonhi glohni glohin glionh gliohn glinoh glinho glihno glihon glnioh glniho
glnoih glnohi glnhoi glnhio glhino glhion glhnio glhnoi glhoni glhoin gilonh
gilohn gilnoh gilnho gilhno gilhon giolnh giolhn gionlh gionhl giohnl giohln
ginolh ginohl ginloh ginlho ginhlo ginhol gihonl giholn gihnol gihnlo gihlno
gihlon gnlioh gnliho gnloih gnlohi gnlhoi gnlhio gniloh gnilho gniolh gniohl
gnihol gnihlo gnoilh gnoihl gnolih gnolhi gnohli gnohil gnhiol gnhilo gnhoil
gnholi gnhloi gnhlio ghlino ghlion ghlnio ghlnoi ghloni ghloin ghilno ghilon
ghinlo ghinol ghionl ghioln ghnilo ghniol ghnlio ghnloi ghnoli ghnoil ghoinl
ghoiln ghonil ghonli gholni gholin

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History of cryptography
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