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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: obtain
cipher variations:
pcubjo qdvckp rewdlq sfxemr tgyfns
uhzgot viahpu wjbiqv xkcjrw yldksx
zmelty anfmuz bognva cphowb dqipxc
erjqyd fskrze gtlsaf humtbg ivnuch
jwovdi kxpwej lyqxfk mzrygl naszhm

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: obtain
Cipher: lygzrm

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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: obtain

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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: obtain
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: obtain
Cipher: bognva

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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: obtain
Cipher: 432144114233

Extended Methods:
Method #1

Plaintext: obtain
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
o b t a i n 
4 2 4 1 4 3 
3 1 4 1 2 3 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: obtain
Cipher: idocdm

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Method #3

Plaintext: obtain
method variations:
hqdqms qdqmsh dqmshq
qmshqd mshqdq shqdqm

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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: obtain

all 720 cipher variations:
obtain obtani obtian obtina obtnia obtnai obatin obatni obaitn obaint obanit
obanti obiatn obiant obitan obitna obinta obinat obnait obnati obniat obnita
obntia obntai otbain otbani otbian otbina otbnia otbnai otabin otabni otaibn
otainb otanib otanbi otiabn otianb otiban otibna otinba otinab otnaib otnabi
otniab otniba otnbia otnbai oatbin oatbni oatibn oatinb oatnib oatnbi oabtin
oabtni oabitn oabint oabnit oabnti oaibtn oaibnt oaitbn oaitnb oaintb oainbt
oanbit oanbti oanibt oanitb oantib oantbi oitabn oitanb oitban oitbna oitnba
oitnab oiatbn oiatnb oiabtn oiabnt oianbt oiantb oibatn oibant oibtan oibtna
oibnta oibnat oinabt oinatb oinbat oinbta ointba ointab ontaib ontabi ontiab
ontiba ontbia ontbai onatib onatbi onaitb onaibt onabit onabti oniatb oniabt
onitab onitba onibta onibat onbait onbati onbiat onbita onbtia onbtai botain
botani botian botina botnia botnai boatin boatni boaitn boaint boanit boanti
boiatn boiant boitan boitna bointa boinat bonait bonati boniat bonita bontia
bontai btoain btoani btoian btoina btonia btonai btaoin btaoni btaion btaino
btanio btanoi btiaon btiano btioan btiona btinoa btinao btnaio btnaoi btniao
btnioa btnoia btnoai batoin batoni bation batino batnio batnoi baotin baotni
baoitn baoint baonit baonti baiotn baiont baiton baitno bainto bainot banoit
banoti baniot banito bantio bantoi bitaon bitano bitoan bitona bitnoa bitnao
biaton biatno biaotn biaont bianot bianto bioatn bioant biotan biotna bionta
bionat binaot binato binoat binota bintoa bintao bntaio bntaoi bntiao bntioa
bntoia bntoai bnatio bnatoi bnaito bnaiot bnaoit bnaoti bniato bniaot bnitao
bnitoa bniota bnioat bnoait bnoati bnoiat bnoita bnotia bnotai tboain tboani
tboian tboina tbonia tbonai tbaoin tbaoni tbaion tbaino tbanio tbanoi tbiaon
tbiano tbioan tbiona tbinoa tbinao tbnaio tbnaoi tbniao tbnioa tbnoia tbnoai
tobain tobani tobian tobina tobnia tobnai toabin toabni toaibn toainb toanib
toanbi toiabn toianb toiban toibna toinba toinab tonaib tonabi toniab toniba
tonbia tonbai taobin taobni taoibn taoinb taonib taonbi taboin taboni tabion
tabino tabnio tabnoi taibon taibno taiobn taionb tainob tainbo tanbio tanboi
tanibo taniob tanoib tanobi tioabn tioanb tioban tiobna tionba tionab tiaobn
tiaonb tiabon tiabno tianbo tianob tibaon tibano tiboan tibona tibnoa tibnao
tinabo tinaob tinbao tinboa tinoba tinoab tnoaib tnoabi tnoiab tnoiba tnobia
tnobai tnaoib tnaobi tnaiob tnaibo tnabio tnaboi tniaob tniabo tnioab tnioba
tniboa tnibao tnbaio tnbaoi tnbiao tnbioa tnboia tnboai abtoin abtoni abtion
abtino abtnio abtnoi abotin abotni aboitn aboint abonit abonti abiotn abiont
abiton abitno abinto abinot abnoit abnoti abniot abnito abntio abntoi atboin
atboni atbion atbino atbnio atbnoi atobin atobni atoibn atoinb atonib atonbi
atiobn ationb atibon atibno atinbo atinob atnoib atnobi atniob atnibo atnbio
atnboi aotbin aotbni aotibn aotinb aotnib aotnbi aobtin aobtni aobitn aobint
aobnit aobnti aoibtn aoibnt aoitbn aoitnb aointb aoinbt aonbit aonbti aonibt
aonitb aontib aontbi aitobn aitonb aitbon aitbno aitnbo aitnob aiotbn aiotnb
aiobtn aiobnt aionbt aiontb aibotn aibont aibton aibtno aibnto aibnot ainobt
ainotb ainbot ainbto aintbo aintob antoib antobi antiob antibo antbio antboi
anotib anotbi anoitb anoibt anobit anobti aniotb aniobt anitob anitbo anibto
anibot anboit anboti anbiot anbito anbtio anbtoi ibtaon ibtano ibtoan ibtona
ibtnoa ibtnao ibaton ibatno ibaotn ibaont ibanot ibanto iboatn iboant ibotan
ibotna ibonta ibonat ibnaot ibnato ibnoat ibnota ibntoa ibntao itbaon itbano
itboan itbona itbnoa itbnao itabon itabno itaobn itaonb itanob itanbo itoabn
itoanb itoban itobna itonba itonab itnaob itnabo itnoab itnoba itnboa itnbao
iatbon iatbno iatobn iatonb iatnob iatnbo iabton iabtno iabotn iabont iabnot
iabnto iaobtn iaobnt iaotbn iaotnb iaontb iaonbt ianbot ianbto ianobt ianotb
iantob iantbo iotabn iotanb iotban iotbna iotnba iotnab ioatbn ioatnb ioabtn
ioabnt ioanbt ioantb iobatn iobant iobtan iobtna iobnta iobnat ionabt ionatb
ionbat ionbta iontba iontab intaob intabo intoab intoba intboa intbao inatob
inatbo inaotb inaobt inabot inabto inoatb inoabt inotab inotba inobta inobat
inbaot inbato inboat inbota inbtoa inbtao nbtaio nbtaoi nbtiao nbtioa nbtoia
nbtoai nbatio nbatoi nbaito nbaiot nbaoit nbaoti nbiato nbiaot nbitao nbitoa
nbiota nbioat nboait nboati nboiat nboita nbotia nbotai ntbaio ntbaoi ntbiao
ntbioa ntboia ntboai ntabio ntaboi ntaibo ntaiob ntaoib ntaobi ntiabo ntiaob
ntibao ntiboa ntioba ntioab ntoaib ntoabi ntoiab ntoiba ntobia ntobai natbio
natboi natibo natiob natoib natobi nabtio nabtoi nabito nabiot naboit naboti
naibto naibot naitbo naitob naiotb naiobt naobit naobti naoibt naoitb naotib
naotbi nitabo nitaob nitbao nitboa nitoba nitoab niatbo niatob niabto niabot
niaobt niaotb nibato nibaot nibtao nibtoa nibota niboat nioabt nioatb niobat
niobta niotba niotab notaib notabi notiab notiba notbia notbai noatib noatbi
noaitb noaibt noabit noabti noiatb noiabt noitab noitba noibta noibat nobait
nobati nobiat nobita nobtia nobtai

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History of cryptography
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