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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: stupex
cipher variations:
tuvqfy uvwrgz vwxsha wxytib xyzujc
yzavkd zabwle abcxmf bcdyng cdezoh
defapi efgbqj fghcrk ghidsl hijetm
ijkfun jklgvo klmhwp lmnixq mnojyr
nopkzs opqlat pqrmbu qrsncv rstodw

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: stupex
Cipher: hgfkvc

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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: stupex

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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: stupex
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: stupex
Cipher: fghcrk

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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: stupex
Cipher: 344454535135

Extended Methods:
Method #1

Plaintext: stupex
method variations:

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

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Method #3

Plaintext: stupex
method variations:
tyyxlp yyxlpt yxlpty
xlptyy lptyyx ptyyxl

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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: stupex

all 720 cipher variations:
stupex stupxe stuepx stuexp stuxep stuxpe stpuex stpuxe stpeux stpexu stpxeu
stpxue stepux stepxu steupx steuxp stexup stexpu stxpeu stxpue stxepu stxeup
stxuep stxupe sutpex sutpxe sutepx sutexp sutxep sutxpe suptex suptxe supetx
supext supxet supxte sueptx suepxt suetpx suetxp suextp suexpt suxpet suxpte
suxept suxetp suxtep suxtpe sputex sputxe spuetx spuext spuxet spuxte sptuex
sptuxe spteux sptexu sptxeu sptxue spetux spetxu speutx speuxt spexut spextu
spxteu spxtue spxetu spxeut spxuet spxute seuptx seupxt seutpx seutxp seuxtp
seuxpt seputx sepuxt septux septxu sepxtu sepxut setpux setpxu setupx setuxp
setxup setxpu sexptu sexput sextpu sextup sexutp sexupt sxupet sxupte sxuept
sxuetp sxutep sxutpe sxpuet sxpute sxpeut sxpetu sxpteu sxptue sxeput sxeptu
sxeupt sxeutp sxetup sxetpu sxtpeu sxtpue sxtepu sxteup sxtuep sxtupe tsupex
tsupxe tsuepx tsuexp tsuxep tsuxpe tspuex tspuxe tspeux tspexu tspxeu tspxue
tsepux tsepxu tseupx tseuxp tsexup tsexpu tsxpeu tsxpue tsxepu tsxeup tsxuep
tsxupe tuspex tuspxe tusepx tusexp tusxep tusxpe tupsex tupsxe tupesx tupexs
tupxes tupxse tuepsx tuepxs tuespx tuesxp tuexsp tuexps tuxpes tuxpse tuxeps
tuxesp tuxsep tuxspe tpusex tpusxe tpuesx tpuexs tpuxes tpuxse tpsuex tpsuxe
tpseux tpsexu tpsxeu tpsxue tpesux tpesxu tpeusx tpeuxs tpexus tpexsu tpxseu
tpxsue tpxesu tpxeus tpxues tpxuse teupsx teupxs teuspx teusxp teuxsp teuxps
tepusx tepuxs tepsux tepsxu tepxsu tepxus tespux tespxu tesupx tesuxp tesxup
tesxpu texpsu texpus texspu texsup texusp texups txupes txupse txueps txuesp
txusep txuspe txpues txpuse txpeus txpesu txpseu txpsue txepus txepsu txeups
txeusp txesup txespu txspeu txspue txsepu txseup txsuep txsupe utspex utspxe
utsepx utsexp utsxep utsxpe utpsex utpsxe utpesx utpexs utpxes utpxse utepsx
utepxs utespx utesxp utexsp utexps utxpes utxpse utxeps utxesp utxsep utxspe
ustpex ustpxe ustepx ustexp ustxep ustxpe usptex usptxe uspetx uspext uspxet
uspxte useptx usepxt usetpx usetxp usextp usexpt usxpet usxpte usxept usxetp
usxtep usxtpe upstex upstxe upsetx upsext upsxet upsxte uptsex uptsxe uptesx
uptexs uptxes uptxse upetsx upetxs upestx upesxt upexst upexts upxtes upxtse
upxets upxest upxset upxste uesptx uespxt uestpx uestxp uesxtp uesxpt uepstx
uepsxt ueptsx ueptxs uepxts uepxst uetpsx uetpxs uetspx uetsxp uetxsp uetxps
uexpts uexpst uextps uextsp uexstp uexspt uxspet uxspte uxsept uxsetp uxstep
uxstpe uxpset uxpste uxpest uxpets uxptes uxptse uxepst uxepts uxespt uxestp
uxetsp uxetps uxtpes uxtpse uxteps uxtesp uxtsep uxtspe ptusex ptusxe ptuesx
ptuexs ptuxes ptuxse ptsuex ptsuxe ptseux ptsexu ptsxeu ptsxue ptesux ptesxu
pteusx pteuxs ptexus ptexsu ptxseu ptxsue ptxesu ptxeus ptxues ptxuse putsex
putsxe putesx putexs putxes putxse pustex pustxe pusetx pusext pusxet pusxte
puestx puesxt puetsx puetxs puexts puexst puxset puxste puxest puxets puxtes
puxtse psutex psutxe psuetx psuext psuxet psuxte pstuex pstuxe psteux pstexu
pstxeu pstxue psetux psetxu pseutx pseuxt psexut psextu psxteu psxtue psxetu
psxeut psxuet psxute peustx peusxt peutsx peutxs peuxts peuxst pesutx pesuxt
pestux pestxu pesxtu pesxut petsux petsxu petusx petuxs petxus petxsu pexstu
pexsut pextsu pextus pexuts pexust pxuset pxuste pxuest pxuets pxutes pxutse
pxsuet pxsute pxseut pxsetu pxsteu pxstue pxesut pxestu pxeust pxeuts pxetus
pxetsu pxtseu pxtsue pxtesu pxteus pxtues pxtuse etupsx etupxs etuspx etusxp
etuxsp etuxps etpusx etpuxs etpsux etpsxu etpxsu etpxus etspux etspxu etsupx
etsuxp etsxup etsxpu etxpsu etxpus etxspu etxsup etxusp etxups eutpsx eutpxs
eutspx eutsxp eutxsp eutxps euptsx euptxs eupstx eupsxt eupxst eupxts eusptx
euspxt eustpx eustxp eusxtp eusxpt euxpst euxpts euxspt euxstp euxtsp euxtps
eputsx eputxs epustx epusxt epuxst epuxts eptusx eptuxs eptsux eptsxu eptxsu
eptxus epstux epstxu epsutx epsuxt epsxut epsxtu epxtsu epxtus epxstu epxsut
epxust epxuts esuptx esupxt esutpx esutxp esuxtp esuxpt esputx espuxt esptux
esptxu espxtu espxut estpux estpxu estupx estuxp estxup estxpu esxptu esxput
esxtpu esxtup esxutp esxupt exupst exupts exuspt exustp exutsp exutps expust
exputs expsut expstu exptsu exptus exsput exsptu exsupt exsutp exstup exstpu
extpsu extpus extspu extsup extusp extups xtupes xtupse xtueps xtuesp xtusep
xtuspe xtpues xtpuse xtpeus xtpesu xtpseu xtpsue xtepus xtepsu xteups xteusp
xtesup xtespu xtspeu xtspue xtsepu xtseup xtsuep xtsupe xutpes xutpse xuteps
xutesp xutsep xutspe xuptes xuptse xupets xupest xupset xupste xuepts xuepst
xuetps xuetsp xuestp xuespt xuspet xuspte xusept xusetp xustep xustpe xputes
xputse xpuets xpuest xpuset xpuste xptues xptuse xpteus xptesu xptseu xptsue
xpetus xpetsu xpeuts xpeust xpesut xpestu xpsteu xpstue xpsetu xpseut xpsuet
xpsute xeupts xeupst xeutps xeutsp xeustp xeuspt xeputs xepust xeptus xeptsu
xepstu xepsut xetpus xetpsu xetups xetusp xetsup xetspu xesptu xesput xestpu
xestup xesutp xesupt xsupet xsupte xsuept xsuetp xsutep xsutpe xspuet xspute
xspeut xspetu xspteu xsptue xseput xseptu xseupt xseutp xsetup xsetpu xstpeu
xstpue xstepu xsteup xstuep xstupe

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History of cryptography
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