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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: educat
cipher variations:
fevdbu gfwecv hgxfdw ihygex jizhfy
kjaigz lkbjha mlckib nmdljc onemkd
pofnle qpgomf rqhpng sriqoh tsjrpi
utksqj vultrk wvmusl xwnvtm yxowun
zypxvo azqywp barzxq cbsayr dctbzs

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: educat
Cipher: vwfxzg

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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: educat

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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: educat
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: educat
Cipher: rqhpng

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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: educat
Cipher: 514154311144

Extended Methods:
Method #1

Plaintext: educat
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
e d u c a t 
5 4 5 3 1 4 
1 1 4 1 1 4 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: educat
Cipher: upqadq

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Method #3

Plaintext: educat
method variations:
qvoaqy voaqyq oaqyqv
aqyqvo qyqvoa yqvoaq

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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: educat

all 720 cipher variations:
educat educta eduact eduatc edutac edutca edcuat edcuta edcaut edcatu edctau
edctua edacut edactu edauct edautc edatuc edatcu edtcau edtcua edtacu edtauc
edtuac edtuca eudcat eudcta eudact eudatc eudtac eudtca eucdat eucdta eucadt
eucatd euctad euctda euacdt euactd euadct euadtc euatdc euatcd eutcad eutcda
eutacd eutadc eutdac eutdca ecudat ecudta ecuadt ecuatd ecutad ecutda ecduat
ecduta ecdaut ecdatu ecdtau ecdtua ecadut ecadtu ecaudt ecautd ecatud ecatdu
ectdau ectdua ectadu ectaud ectuad ectuda eaucdt eauctd eaudct eaudtc eautdc
eautcd eacudt eacutd eacdut eacdtu eactdu eactud eadcut eadctu eaduct eadutc
eadtuc eadtcu eatcdu eatcud eatdcu eatduc eatudc eatucd etucad etucda etuacd
etuadc etudac etudca etcuad etcuda etcaud etcadu etcdau etcdua etacud etacdu
etaucd etaudc etaduc etadcu etdcau etdcua etdacu etdauc etduac etduca deucat
deucta deuact deuatc deutac deutca decuat decuta decaut decatu dectau dectua
deacut deactu deauct deautc deatuc deatcu detcau detcua detacu detauc detuac
detuca duecat duecta dueact dueatc duetac duetca duceat duceta ducaet ducate
ductae ductea duacet duacte duaect duaetc duatec duatce dutcae dutcea dutace
dutaec duteac duteca dcueat dcueta dcuaet dcuate dcutae dcutea dceuat dceuta
dceaut dceatu dcetau dcetua dcaeut dcaetu dcauet dcaute dcatue dcateu dcteau
dcteua dctaeu dctaue dctuae dctuea daucet daucte dauect dauetc dautec dautce
dacuet dacute daceut dacetu dacteu dactue daecut daectu daeuct daeutc daetuc
daetcu datceu datcue datecu dateuc datuec datuce dtucae dtucea dtuace dtuaec
dtueac dtueca dtcuae dtcuea dtcaue dtcaeu dtceau dtceua dtacue dtaceu dtauce
dtauec dtaeuc dtaecu dtecau dtecua dteacu dteauc dteuac dteuca udecat udecta
udeact udeatc udetac udetca udceat udceta udcaet udcate udctae udctea udacet
udacte udaect udaetc udatec udatce udtcae udtcea udtace udtaec udteac udteca
uedcat uedcta uedact uedatc uedtac uedtca uecdat uecdta uecadt uecatd uectad
uectda ueacdt ueactd ueadct ueadtc ueatdc ueatcd uetcad uetcda uetacd uetadc
uetdac uetdca ucedat ucedta uceadt uceatd ucetad ucetda ucdeat ucdeta ucdaet
ucdate ucdtae ucdtea ucadet ucadte ucaedt ucaetd ucated ucatde uctdae uctdea
uctade uctaed uctead ucteda uaecdt uaectd uaedct uaedtc uaetdc uaetcd uacedt
uacetd uacdet uacdte uactde uacted uadcet uadcte uadect uadetc uadtec uadtce
uatcde uatced uatdce uatdec uatedc uatecd utecad utecda uteacd uteadc utedac
utedca utcead utceda utcaed utcade utcdae utcdea utaced utacde utaecd utaedc
utadec utadce utdcae utdcea utdace utdaec utdeac utdeca cdueat cdueta cduaet
cduate cdutae cdutea cdeuat cdeuta cdeaut cdeatu cdetau cdetua cdaeut cdaetu
cdauet cdaute cdatue cdateu cdteau cdteua cdtaeu cdtaue cdtuae cdtuea cudeat
cudeta cudaet cudate cudtae cudtea cuedat cuedta cueadt cueatd cuetad cuetda
cuaedt cuaetd cuadet cuadte cuatde cuated cutead cuteda cutaed cutade cutdae
cutdea ceudat ceudta ceuadt ceuatd ceutad ceutda ceduat ceduta cedaut cedatu
cedtau cedtua ceadut ceadtu ceaudt ceautd ceatud ceatdu cetdau cetdua cetadu
cetaud cetuad cetuda cauedt cauetd caudet caudte cautde cauted caeudt caeutd
caedut caedtu caetdu caetud cadeut cadetu caduet cadute cadtue cadteu catedu
cateud catdeu catdue catude catued ctuead ctueda ctuaed ctuade ctudae ctudea
cteuad cteuda cteaud cteadu ctedau ctedua ctaeud ctaedu ctaued ctaude ctadue
ctadeu ctdeau ctdeua ctdaeu ctdaue ctduae ctduea aducet aducte aduect aduetc
adutec adutce adcuet adcute adceut adcetu adcteu adctue adecut adectu adeuct
adeutc adetuc adetcu adtceu adtcue adtecu adteuc adtuec adtuce audcet audcte
audect audetc audtec audtce aucdet aucdte aucedt aucetd aucted auctde auecdt
auectd auedct auedtc auetdc auetcd autced autcde autecd autedc autdec autdce
acudet acudte acuedt acuetd acuted acutde acduet acdute acdeut acdetu acdteu
acdtue acedut acedtu aceudt aceutd acetud acetdu actdeu actdue actedu acteud
actued actude aeucdt aeuctd aeudct aeudtc aeutdc aeutcd aecudt aecutd aecdut
aecdtu aectdu aectud aedcut aedctu aeduct aedutc aedtuc aedtcu aetcdu aetcud
aetdcu aetduc aetudc aetucd atuced atucde atuecd atuedc atudec atudce atcued
atcude atceud atcedu atcdeu atcdue atecud atecdu ateucd ateudc ateduc atedcu
atdceu atdcue atdecu atdeuc atduec atduce tducae tducea tduace tduaec tdueac
tdueca tdcuae tdcuea tdcaue tdcaeu tdceau tdceua tdacue tdaceu tdauce tdauec
tdaeuc tdaecu tdecau tdecua tdeacu tdeauc tdeuac tdeuca tudcae tudcea tudace
tudaec tudeac tudeca tucdae tucdea tucade tucaed tucead tuceda tuacde tuaced
tuadce tuadec tuaedc tuaecd tuecad tuecda tueacd tueadc tuedac tuedca tcudae
tcudea tcuade tcuaed tcuead tcueda tcduae tcduea tcdaue tcdaeu tcdeau tcdeua
tcadue tcadeu tcaude tcaued tcaeud tcaedu tcedau tcedua tceadu tceaud tceuad
tceuda taucde tauced taudce taudec tauedc tauecd tacude tacued tacdue tacdeu
tacedu taceud tadcue tadceu taduce taduec tadeuc tadecu taecdu taecud taedcu
taeduc taeudc taeucd teucad teucda teuacd teuadc teudac teudca tecuad tecuda
tecaud tecadu tecdau tecdua teacud teacdu teaucd teaudc teaduc teadcu tedcau
tedcua tedacu tedauc teduac teduca

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History of cryptography
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