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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: audile
cipher variations:
bvejmf cwfkng dxgloh eyhmpi fzinqj
gajork hbkpsl iclqtm jdmrun kensvo
lfotwp mgpuxq nhqvyr oirwzs pjsxat
qktybu rluzcv smvadw tnwbex uoxcfy
vpydgz wqzeha xrafib ysbgjc ztchkd

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: audile
Cipher: zfwrov

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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: audile

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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: audile
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: audile
Cipher: nhqvyr

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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: audile
Cipher: 115441421351

Extended Methods:
Method #1

Plaintext: audile
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
a u d i l e 
1 5 4 4 1 5 
1 4 1 2 3 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: audile
Cipher: vtvqfc

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Method #3

Plaintext: audile
method variations:
vtqbxa tqbxav qbxavt
bxavtq xavtqb avtqbx

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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: audile

all 720 cipher variations:
audile audiel audlie audlei audeli audeil auidle auidel auilde auiled auield
auiedl aulide aulied auldie auldei auledi auleid aueild aueidl auelid aueldi
auedli auedil aduile aduiel adulie adulei adueli adueil adiule adiuel adilue
adileu adielu adieul adliue adlieu adluie adluei adleui adleiu adeilu adeiul
adeliu adelui adeuli adeuil aidule aiduel aidlue aidleu aidelu aideul aiudle
aiudel aiulde aiuled aiueld aiuedl ailude ailued aildue aildeu ailedu aileud
aieuld aieudl aielud aieldu aiedlu aiedul aldiue aldieu alduie alduei aldeui
aldeiu alidue alideu aliude aliued alieud aliedu aluide aluied aludie aludei
aluedi alueid aleiud aleidu aleuid aleudi aledui alediu aedilu aediul aedliu
aedlui aeduli aeduil aeidlu aeidul aeildu aeilud aeiuld aeiudl aelidu aeliud
aeldiu aeldui aeludi aeluid aeuild aeuidl aeulid aeuldi aeudli aeudil uadile
uadiel uadlie uadlei uadeli uadeil uaidle uaidel uailde uailed uaield uaiedl
ualide ualied ualdie ualdei ualedi ualeid uaeild uaeidl uaelid uaeldi uaedli
uaedil udaile udaiel udalie udalei udaeli udaeil udiale udiael udilae udilea
udiela udieal udliae udliea udlaie udlaei udleai udleia udeila udeial udelia
udelai udeali udeail uidale uidael uidlae uidlea uidela uideal uiadle uiadel
uialde uialed uiaeld uiaedl uilade uilaed uildae uildea uileda uilead uieald
uieadl uielad uielda uiedla uiedal uldiae uldiea uldaie uldaei uldeai uldeia
ulidae ulidea uliade uliaed uliead ulieda ulaide ulaied uladie uladei ulaedi
ulaeid uleiad uleida uleaid uleadi uledai uledia uedila uedial uedlia uedlai
uedali uedail ueidla ueidal ueilda ueilad ueiald ueiadl uelida ueliad ueldia
ueldai ueladi uelaid ueaild ueaidl uealid uealdi ueadli ueadil duaile duaiel
dualie dualei duaeli duaeil duiale duiael duilae duilea duiela duieal duliae
duliea dulaie dulaei duleai duleia dueila dueial duelia duelai dueali dueail
dauile dauiel daulie daulei daueli daueil daiule daiuel dailue daileu daielu
daieul daliue dalieu daluie daluei daleui daleiu daeilu daeiul daeliu daelui
daeuli daeuil diaule diauel dialue dialeu diaelu diaeul diuale diuael diulae
diulea diuela diueal diluae diluea dilaue dilaeu dileau dileua dieula dieual
dielua dielau diealu dieaul dlaiue dlaieu dlauie dlauei dlaeui dlaeiu dliaue
dliaeu dliuae dliuea dlieua dlieau dluiae dluiea dluaie dluaei dlueai dlueia
dleiua dleiau dleuia dleuai dleaui dleaiu deailu deaiul dealiu dealui deauli
deauil deialu deiaul deilau deilua deiula deiual deliau deliua delaiu delaui
deluai deluia deuila deuial deulia deulai deuali deuail iudale iudael iudlae
iudlea iudela iudeal iuadle iuadel iualde iualed iuaeld iuaedl iulade iulaed
iuldae iuldea iuleda iulead iueald iueadl iuelad iuelda iuedla iuedal iduale
iduael idulae idulea iduela idueal idaule idauel idalue idaleu idaelu idaeul
idlaue idlaeu idluae idluea idleua idleau idealu ideaul idelau idelua ideula
ideual iadule iaduel iadlue iadleu iadelu iadeul iaudle iaudel iaulde iauled
iaueld iauedl ialude ialued ialdue ialdeu ialedu ialeud iaeuld iaeudl iaelud
iaeldu iaedlu iaedul ildaue ildaeu ilduae ilduea ildeua ildeau iladue iladeu
ilaude ilaued ilaeud ilaedu iluade iluaed iludae iludea ilueda iluead ileaud
ileadu ileuad ileuda iledua iledau iedalu iedaul iedlau iedlua iedula iedual
ieadlu ieadul iealdu iealud ieauld ieaudl ieladu ielaud ieldau ieldua ieluda
ieluad ieuald ieuadl ieulad ieulda ieudla ieudal ludiae ludiea ludaie ludaei
ludeai ludeia luidae luidea luiade luiaed luiead luieda luaide luaied luadie
luadei luaedi luaeid lueiad lueida lueaid lueadi luedai luedia lduiae lduiea
lduaie lduaei ldueai ldueia ldiuae ldiuea ldiaue ldiaeu ldieau ldieua ldaiue
ldaieu ldauie ldauei ldaeui ldaeiu ldeiau ldeiua ldeaiu ldeaui ldeuai ldeuia
liduae liduea lidaue lidaeu lideau lideua liudae liudea liuade liuaed liuead
liueda liaude liaued liadue liadeu liaedu liaeud lieuad lieuda lieaud lieadu
liedau liedua ladiue ladieu laduie laduei ladeui ladeiu laidue laideu laiude
laiued laieud laiedu lauide lauied laudie laudei lauedi laueid laeiud laeidu
laeuid laeudi laedui laediu lediau lediua ledaiu ledaui leduai leduia leidau
leidua leiadu leiaud leiuad leiuda leaidu leaiud leadiu leadui leaudi leauid
leuiad leuida leuaid leuadi leudai leudia eudila eudial eudlia eudlai eudali
eudail euidla euidal euilda euilad euiald euiadl eulida euliad euldia euldai
euladi eulaid euaild euaidl eualid eualdi euadli euadil eduila eduial edulia
edulai eduali eduail ediula ediual edilua edilau edialu ediaul edliua edliau
edluia edluai edlaui edlaiu edailu edaiul edaliu edalui edauli edauil eidula
eidual eidlua eidlau eidalu eidaul eiudla eiudal eiulda eiulad eiuald eiuadl
eiluda eiluad eildua eildau eiladu eilaud eiauld eiaudl eialud eialdu eiadlu
eiadul eldiua eldiau elduia elduai eldaui eldaiu elidua elidau eliuda eliuad
eliaud eliadu eluida eluiad eludia eludai eluadi eluaid elaiud elaidu elauid
elaudi eladui eladiu eadilu eadiul eadliu eadlui eaduli eaduil eaidlu eaidul
eaildu eailud eaiuld eaiudl ealidu ealiud ealdiu ealdui ealudi ealuid eauild
eauidl eaulid eauldi eaudli eaudil

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History of cryptography
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