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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: codify
cipher variations:
dpejgz eqfkha frglib gshmjc htinkd
iujole jvkpmf kwlqng lxmroh mynspi
nzotqj oapurk pbqvsl qcrwtm rdsxun
setyvo tfuzwp ugvaxq vhwbyr wixczs
xjydat ykzebu zlafcv ambgdw bnchex

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: codify
Cipher: xlwrub

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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: codify

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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: codify
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: codify
Cipher: pbqvsl

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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: codify
Cipher: 314341421245

Extended Methods:
Method #1

Plaintext: codify
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
c o d i f y 
3 4 4 4 1 4 
1 3 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: codify
Cipher: stqlfw

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Method #3

Plaintext: codify
method variations:
qsqbrp sqbrpq qbrpqs
brpqsq rpqsqb pqsqbr

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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: codify

all 720 cipher variations:
codify codiyf codfiy codfyi codyfi codyif coidfy coidyf coifdy coifyd coiyfd
coiydf cofidy cofiyd cofdiy cofdyi cofydi cofyid coyifd coyidf coyfid coyfdi
coydfi coydif cdoify cdoiyf cdofiy cdofyi cdoyfi cdoyif cdiofy cdioyf cdifoy
cdifyo cdiyfo cdiyof cdfioy cdfiyo cdfoiy cdfoyi cdfyoi cdfyio cdyifo cdyiof
cdyfio cdyfoi cdyofi cdyoif cidofy cidoyf cidfoy cidfyo cidyfo cidyof ciodfy
ciodyf ciofdy ciofyd cioyfd cioydf cifody cifoyd cifdoy cifdyo cifydo cifyod
ciyofd ciyodf ciyfod ciyfdo ciydfo ciydof cfdioy cfdiyo cfdoiy cfdoyi cfdyoi
cfdyio cfidoy cfidyo cfiody cfioyd cfiyod cfiydo cfoidy cfoiyd cfodiy cfodyi
cfoydi cfoyid cfyiod cfyido cfyoid cfyodi cfydoi cfydio cydifo cydiof cydfio
cydfoi cydofi cydoif cyidfo cyidof cyifdo cyifod cyiofd cyiodf cyfido cyfiod
cyfdio cyfdoi cyfodi cyfoid cyoifd cyoidf cyofid cyofdi cyodfi cyodif ocdify
ocdiyf ocdfiy ocdfyi ocdyfi ocdyif ocidfy ocidyf ocifdy ocifyd ociyfd ociydf
ocfidy ocfiyd ocfdiy ocfdyi ocfydi ocfyid ocyifd ocyidf ocyfid ocyfdi ocydfi
ocydif odcify odciyf odcfiy odcfyi odcyfi odcyif odicfy odicyf odifcy odifyc
odiyfc odiycf odficy odfiyc odfciy odfcyi odfyci odfyic odyifc odyicf odyfic
odyfci odycfi odycif oidcfy oidcyf oidfcy oidfyc oidyfc oidycf oicdfy oicdyf
oicfdy oicfyd oicyfd oicydf oifcdy oifcyd oifdcy oifdyc oifydc oifycd oiycfd
oiycdf oiyfcd oiyfdc oiydfc oiydcf ofdicy ofdiyc ofdciy ofdcyi ofdyci ofdyic
ofidcy ofidyc oficdy oficyd ofiycd ofiydc ofcidy ofciyd ofcdiy ofcdyi ofcydi
ofcyid ofyicd ofyidc ofycid ofycdi ofydci ofydic oydifc oydicf oydfic oydfci
oydcfi oydcif oyidfc oyidcf oyifdc oyifcd oyicfd oyicdf oyfidc oyficd oyfdic
oyfdci oyfcdi oyfcid oycifd oycidf oycfid oycfdi oycdfi oycdif docify dociyf
docfiy docfyi docyfi docyif doicfy doicyf doifcy doifyc doiyfc doiycf doficy
dofiyc dofciy dofcyi dofyci dofyic doyifc doyicf doyfic doyfci doycfi doycif
dcoify dcoiyf dcofiy dcofyi dcoyfi dcoyif dciofy dcioyf dcifoy dcifyo dciyfo
dciyof dcfioy dcfiyo dcfoiy dcfoyi dcfyoi dcfyio dcyifo dcyiof dcyfio dcyfoi
dcyofi dcyoif dicofy dicoyf dicfoy dicfyo dicyfo dicyof diocfy diocyf diofcy
diofyc dioyfc dioycf difocy difoyc difcoy difcyo difyco difyoc diyofc diyocf
diyfoc diyfco diycfo diycof dfcioy dfciyo dfcoiy dfcoyi dfcyoi dfcyio dficoy
dficyo dfiocy dfioyc dfiyoc dfiyco dfoicy dfoiyc dfociy dfocyi dfoyci dfoyic
dfyioc dfyico dfyoic dfyoci dfycoi dfycio dycifo dyciof dycfio dycfoi dycofi
dycoif dyicfo dyicof dyifco dyifoc dyiofc dyiocf dyfico dyfioc dyfcio dyfcoi
dyfoci dyfoic dyoifc dyoicf dyofic dyofci dyocfi dyocif iodcfy iodcyf iodfcy
iodfyc iodyfc iodycf iocdfy iocdyf iocfdy iocfyd iocyfd iocydf iofcdy iofcyd
iofdcy iofdyc iofydc iofycd ioycfd ioycdf ioyfcd ioyfdc ioydfc ioydcf idocfy
idocyf idofcy idofyc idoyfc idoycf idcofy idcoyf idcfoy idcfyo idcyfo idcyof
idfcoy idfcyo idfocy idfoyc idfyoc idfyco idycfo idycof idyfco idyfoc idyofc
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icoyfd icoydf icfody icfoyd icfdoy icfdyo icfydo icfyod icyofd icyodf icyfod
icyfdo icydfo icydof ifdcoy ifdcyo ifdocy ifdoyc ifdyoc ifdyco ifcdoy ifcdyo
ifcody ifcoyd ifcyod ifcydo ifocdy ifocyd ifodcy ifodyc ifoydc ifoycd ifycod
ifycdo ifyocd ifyodc ifydoc ifydco iydcfo iydcof iydfco iydfoc iydofc iydocf
iycdfo iycdof iycfdo iycfod iycofd iycodf iyfcdo iyfcod iyfdco iyfdoc iyfodc
iyfocd iyocfd iyocdf iyofcd iyofdc iyodfc iyodcf fodicy fodiyc fodciy fodcyi
fodyci fodyic foidcy foidyc foicdy foicyd foiycd foiydc focidy fociyd focdiy
focdyi focydi focyid foyicd foyidc foycid foycdi foydci foydic fdoicy fdoiyc
fdociy fdocyi fdoyci fdoyic fdiocy fdioyc fdicoy fdicyo fdiyco fdiyoc fdcioy
fdciyo fdcoiy fdcoyi fdcyoi fdcyio fdyico fdyioc fdycio fdycoi fdyoci fdyoic
fidocy fidoyc fidcoy fidcyo fidyco fidyoc fiodcy fiodyc fiocdy fiocyd fioycd
fioydc ficody ficoyd ficdoy ficdyo ficydo ficyod fiyocd fiyodc fiycod fiycdo
fiydco fiydoc fcdioy fcdiyo fcdoiy fcdoyi fcdyoi fcdyio fcidoy fcidyo fciody
fcioyd fciyod fciydo fcoidy fcoiyd fcodiy fcodyi fcoydi fcoyid fcyiod fcyido
fcyoid fcyodi fcydoi fcydio fydico fydioc fydcio fydcoi fydoci fydoic fyidco
fyidoc fyicdo fyicod fyiocd fyiodc fycido fyciod fycdio fycdoi fycodi fycoid
fyoicd fyoidc fyocid fyocdi fyodci fyodic yodifc yodicf yodfic yodfci yodcfi
yodcif yoidfc yoidcf yoifdc yoifcd yoicfd yoicdf yofidc yoficd yofdic yofdci
yofcdi yofcid yocifd yocidf yocfid yocfdi yocdfi yocdif ydoifc ydoicf ydofic
ydofci ydocfi ydocif ydiofc ydiocf ydifoc ydifco ydicfo ydicof ydfioc ydfico
ydfoic ydfoci ydfcoi ydfcio ydcifo ydciof ydcfio ydcfoi ydcofi ydcoif yidofc
yidocf yidfoc yidfco yidcfo yidcof yiodfc yiodcf yiofdc yiofcd yiocfd yiocdf
yifodc yifocd yifdoc yifdco yifcdo yifcod yicofd yicodf yicfod yicfdo yicdfo
yicdof yfdioc yfdico yfdoic yfdoci yfdcoi yfdcio yfidoc yfidco yfiodc yfiocd
yficod yficdo yfoidc yfoicd yfodic yfodci yfocdi yfocid yfciod yfcido yfcoid
yfcodi yfcdoi yfcdio ycdifo ycdiof ycdfio ycdfoi ycdofi ycdoif ycidfo ycidof
ycifdo ycifod yciofd yciodf ycfido ycfiod ycfdio ycfdoi ycfodi ycfoid ycoifd
ycoidf ycofid ycofdi ycodfi ycodif

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History of cryptography
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