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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: graewe
cipher variations:
hsbfxf itcgyg judhzh kveiai lwfjbj
mxgkck nyhldl ozimem pajnfn qbkogo
rclphp sdmqiq tenrjr ufosks vgptlt
whqumu xirvnv yjswow zktxpx aluyqy
bmvzrz cnwasa doxbtb epycuc fqzdvd

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: graewe
Cipher: tizvdv

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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: graewe

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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: graewe
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: graewe
Cipher: tenrjr

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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: graewe
Cipher: 222411512551

Extended Methods:
Method #1

Plaintext: graewe
method variations:

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

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Method #3

Plaintext: graewe
method variations:
gdvfzf dvfzfg vfzfgd
fzfgdv zfgdvf fgdvfz

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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: graewe

all 720 cipher variations:
graewe graeew grawee grawee graewe graeew greawe greaew grewae grewea greewa
greeaw grweae grweea grwaee grwaee grweae grweea greewa greeaw grewea grewae
greawe greaew garewe gareew garwee garwee garewe gareew gaerwe gaerew gaewre
gaewer gaeewr gaeerw gawere gaweer gawree gawree gawere gaweer gaeewr gaeerw
gaewer gaewre gaerwe gaerew gearwe gearew geawre geawer geaewr geaerw gerawe
geraew gerwae gerwea gerewa gereaw gewrae gewrea geware gewaer gewear gewera
geerwa geeraw geewra geewar geeawr geearw gwaere gwaeer gwaree gwaree gwaere
gwaeer gweare gweaer gwerae gwerea gweera gweear gwreae gwreea gwraee gwraee
gwreae gwreea gweera gweear gwerea gwerae gweare gweaer geaewr geaerw geawer
geawre gearwe gearew geeawr geearw geewar geewra geerwa geeraw gewear gewera
gewaer geware gewrae gewrea gerewa gereaw gerwea gerwae gerawe geraew rgaewe
rgaeew rgawee rgawee rgaewe rgaeew rgeawe rgeaew rgewae rgewea rgeewa rgeeaw
rgweae rgweea rgwaee rgwaee rgweae rgweea rgeewa rgeeaw rgewea rgewae rgeawe
rgeaew ragewe rageew ragwee ragwee ragewe rageew raegwe raegew raewge raeweg
raeewg raeegw rawege raweeg rawgee rawgee rawege raweeg raeewg raeegw raeweg
raewge raegwe raegew reagwe reagew reawge reaweg reaewg reaegw regawe regaew
regwae regwea regewa regeaw rewgae rewgea rewage rewaeg reweag rewega reegwa
reegaw reewga reewag reeawg reeagw rwaege rwaeeg rwagee rwagee rwaege rwaeeg
rweage rweaeg rwegae rwegea rweega rweeag rwgeae rwgeea rwgaee rwgaee rwgeae
rwgeea rweega rweeag rwegea rwegae rweage rweaeg reaewg reaegw reaweg reawge
reagwe reagew reeawg reeagw reewag reewga reegwa reegaw reweag rewega rewaeg
rewage rewgae rewgea regewa regeaw regwea regwae regawe regaew argewe argeew
argwee argwee argewe argeew aregwe aregew arewge areweg areewg areegw arwege
arweeg arwgee arwgee arwege arweeg areewg areegw areweg arewge aregwe aregew
agrewe agreew agrwee agrwee agrewe agreew agerwe agerew agewre agewer ageewr
ageerw agwere agweer agwree agwree agwere agweer ageewr ageerw agewer agewre
agerwe agerew aegrwe aegrew aegwre aegwer aegewr aegerw aergwe aergew aerwge
aerweg aerewg aeregw aewrge aewreg aewgre aewger aewegr aewerg aeerwg aeergw
aeewrg aeewgr aeegwr aeegrw awgere awgeer awgree awgree awgere awgeer awegre
aweger awerge awereg aweerg aweegr awrege awreeg awrgee awrgee awrege awreeg
aweerg aweegr awereg awerge awegre aweger aegewr aegerw aegwer aegwre aegrwe
aegrew aeegwr aeegrw aeewgr aeewrg aeerwg aeergw aewegr aewerg aewger aewgre
aewrge aewreg aerewg aeregw aerweg aerwge aergwe aergew eragwe eragew erawge
eraweg eraewg eraegw ergawe ergaew ergwae ergwea ergewa ergeaw erwgae erwgea
erwage erwaeg erweag erwega eregwa eregaw erewga erewag ereawg ereagw eargwe
eargew earwge earweg earewg earegw eagrwe eagrew eagwre eagwer eagewr eagerw
eawgre eawger eawrge eawreg eawerg eawegr eaegwr eaegrw eaewgr eaewrg eaerwg
eaergw egarwe egarew egawre egawer egaewr egaerw egrawe egraew egrwae egrwea
egrewa egreaw egwrae egwrea egware egwaer egwear egwera egerwa egeraw egewra
egewar egeawr egearw ewagre ewager ewarge ewareg ewaerg ewaegr ewgare ewgaer
ewgrae ewgrea ewgera ewgear ewrgae ewrgea ewrage ewraeg ewreag ewrega ewegra
ewegar ewerga ewerag ewearg eweagr eeagwr eeagrw eeawgr eeawrg eearwg eeargw
eegawr eegarw eegwar eegwra eegrwa eegraw eewgar eewgra eewagr eewarg eewrag
eewrga eergwa eergaw eerwga eerwag eerawg eeragw wraege wraeeg wragee wragee
wraege wraeeg wreage wreaeg wregae wregea wreega wreeag wrgeae wrgeea wrgaee
wrgaee wrgeae wrgeea wreega wreeag wregea wregae wreage wreaeg warege wareeg
wargee wargee warege wareeg waerge waereg waegre waeger waeegr waeerg wagere
wageer wagree wagree wagere wageer waeegr waeerg waeger waegre waerge waereg
wearge weareg weagre weager weaegr weaerg werage weraeg wergae wergea werega
wereag wegrae wegrea wegare wegaer wegear wegera weerga weerag weegra weegar
weeagr weearg wgaere wgaeer wgaree wgaree wgaere wgaeer wgeare wgeaer wgerae
wgerea wgeera wgeear wgreae wgreea wgraee wgraee wgreae wgreea wgeera wgeear
wgerea wgerae wgeare wgeaer weaegr weaerg weager weagre wearge weareg weeagr
weearg weegar weegra weerga weerag wegear wegera wegaer wegare wegrae wegrea
werega wereag wergea wergae werage weraeg eraewg eraegw eraweg erawge eragwe
eragew ereawg ereagw erewag erewga eregwa eregaw erweag erwega erwaeg erwage
erwgae erwgea ergewa ergeaw ergwea ergwae ergawe ergaew earewg earegw earweg
earwge eargwe eargew eaerwg eaergw eaewrg eaewgr eaegwr eaegrw eawerg eawegr
eawreg eawrge eawgre eawger eagewr eagerw eagwer eagwre eagrwe eagrew eearwg
eeargw eeawrg eeawgr eeagwr eeagrw eerawg eeragw eerwag eerwga eergwa eergaw
eewrag eewrga eewarg eewagr eewgar eewgra eegrwa eegraw eegwra eegwar eegawr
eegarw ewaerg ewaegr ewareg ewarge ewagre ewager ewearg eweagr ewerag ewerga
ewegra ewegar ewreag ewrega ewraeg ewrage ewrgae ewrgea ewgera ewgear ewgrea
ewgrae ewgare ewgaer egaewr egaerw egawer egawre egarwe egarew egeawr egearw
egewar egewra egerwa egeraw egwear egwera egwaer egware egwrae egwrea egrewa
egreaw egrwea egrwae egrawe egraew

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History of cryptography
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