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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: obicat
cipher variations:
pcjdbu qdkecv relfdw sfmgex tgnhfy
uhoigz vipjha wjqkib xkrljc ylsmkd
zmtnle anuomf bovpng cpwqoh dqxrpi
erysqj fsztrk gtausl hubvtm ivcwun
jwdxvo kxeywp lyfzxq mzgayr nahbzs

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: obicat
Cipher: lyrxzg

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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: obicat

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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: obicat
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: obicat
Cipher: bovpng

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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: obicat
Cipher: 432142311144

Extended Methods:
Method #1

Plaintext: obicat
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 i c a t 
4 2 4 3 1 4 
3 1 2 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: obicat
Cipher: ioqcbq

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Method #3

Plaintext: obicat
method variations:
hqmaqt qmaqth maqthq
aqthqm qthqma thqmaq

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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: obicat

all 720 cipher variations:
obicat obicta obiact obiatc obitac obitca obciat obcita obcait obcati obctai
obctia obacit obacti obaict obaitc obatic obatci obtcai obtcia obtaci obtaic
obtiac obtica oibcat oibcta oibact oibatc oibtac oibtca oicbat oicbta oicabt
oicatb oictab oictba oiacbt oiactb oiabct oiabtc oiatbc oiatcb oitcab oitcba
oitacb oitabc oitbac oitbca ocibat ocibta ociabt ociatb ocitab ocitba ocbiat
ocbita ocbait ocbati ocbtai ocbtia ocabit ocabti ocaibt ocaitb ocatib ocatbi
octbai octbia octabi octaib octiab octiba oaicbt oaictb oaibct oaibtc oaitbc
oaitcb oacibt oacitb oacbit oacbti oactbi oactib oabcit oabcti oabict oabitc
oabtic oabtci oatcbi oatcib oatbci oatbic oatibc oaticb oticab oticba otiacb
otiabc otibac otibca otciab otciba otcaib otcabi otcbai otcbia otacib otacbi
otaicb otaibc otabic otabci otbcai otbcia otbaci otbaic otbiac otbica boicat
boicta boiact boiatc boitac boitca bociat bocita bocait bocati boctai boctia
boacit boacti boaict boaitc boatic boatci botcai botcia botaci botaic botiac
botica biocat biocta bioact bioatc biotac biotca bicoat bicota bicaot bicato
bictao bictoa biacot biacto biaoct biaotc biatoc biatco bitcao bitcoa bitaco
bitaoc bitoac bitoca bcioat bciota bciaot bciato bcitao bcitoa bcoiat bcoita
bcoait bcoati bcotai bcotia bcaoit bcaoti bcaiot bcaito bcatio bcatoi bctoai
bctoia bctaoi bctaio bctiao bctioa baicot baicto baioct baiotc baitoc baitco
baciot bacito bacoit bacoti bactoi bactio baocit baocti baoict baoitc baotic
baotci batcoi batcio batoci batoic batioc batico bticao bticoa btiaco btiaoc
btioac btioca btciao btcioa btcaio btcaoi btcoai btcoia btacio btacoi btaico
btaioc btaoic btaoci btocai btocia btoaci btoaic btoiac btoica ibocat ibocta
iboact iboatc ibotac ibotca ibcoat ibcota ibcaot ibcato ibctao ibctoa ibacot
ibacto ibaoct ibaotc ibatoc ibatco ibtcao ibtcoa ibtaco ibtaoc ibtoac ibtoca
iobcat iobcta iobact iobatc iobtac iobtca iocbat iocbta iocabt iocatb ioctab
ioctba ioacbt ioactb ioabct ioabtc ioatbc ioatcb iotcab iotcba iotacb iotabc
iotbac iotbca icobat icobta icoabt icoatb icotab icotba icboat icbota icbaot
icbato icbtao icbtoa icabot icabto icaobt icaotb icatob icatbo ictbao ictboa
ictabo ictaob ictoab ictoba iaocbt iaoctb iaobct iaobtc iaotbc iaotcb iacobt
iacotb iacbot iacbto iactbo iactob iabcot iabcto iaboct iabotc iabtoc iabtco
iatcbo iatcob iatbco iatboc iatobc iatocb itocab itocba itoacb itoabc itobac
itobca itcoab itcoba itcaob itcabo itcbao itcboa itacob itacbo itaocb itaobc
itaboc itabco itbcao itbcoa itbaco itbaoc itboac itboca cbioat cbiota cbiaot
cbiato cbitao cbitoa cboiat cboita cboait cboati cbotai cbotia cbaoit cbaoti
cbaiot cbaito cbatio cbatoi cbtoai cbtoia cbtaoi cbtaio cbtiao cbtioa ciboat
cibota cibaot cibato cibtao cibtoa ciobat ciobta cioabt cioatb ciotab ciotba
ciaobt ciaotb ciabot ciabto ciatbo ciatob citoab citoba citaob citabo citbao
citboa coibat coibta coiabt coiatb coitab coitba cobiat cobita cobait cobati
cobtai cobtia coabit coabti coaibt coaitb coatib coatbi cotbai cotbia cotabi
cotaib cotiab cotiba caiobt caiotb caibot caibto caitbo caitob caoibt caoitb
caobit caobti caotbi caotib caboit caboti cabiot cabito cabtio cabtoi catobi
catoib catboi catbio catibo catiob ctioab ctioba ctiaob ctiabo ctibao ctiboa
ctoiab ctoiba ctoaib ctoabi ctobai ctobia ctaoib ctaobi ctaiob ctaibo ctabio
ctaboi ctboai ctboia ctbaoi ctbaio ctbiao ctbioa abicot abicto abioct abiotc
abitoc abitco abciot abcito abcoit abcoti abctoi abctio abocit abocti aboict
aboitc abotic abotci abtcoi abtcio abtoci abtoic abtioc abtico aibcot aibcto
aiboct aibotc aibtoc aibtco aicbot aicbto aicobt aicotb aictob aictbo aiocbt
aioctb aiobct aiobtc aiotbc aiotcb aitcob aitcbo aitocb aitobc aitboc aitbco
acibot acibto aciobt aciotb acitob acitbo acbiot acbito acboit acboti acbtoi
acbtio acobit acobti acoibt acoitb acotib acotbi actboi actbio actobi actoib
actiob actibo aoicbt aoictb aoibct aoibtc aoitbc aoitcb aocibt aocitb aocbit
aocbti aoctbi aoctib aobcit aobcti aobict aobitc aobtic aobtci aotcbi aotcib
aotbci aotbic aotibc aoticb aticob aticbo atiocb atiobc atiboc atibco atciob
atcibo atcoib atcobi atcboi atcbio atocib atocbi atoicb atoibc atobic atobci
atbcoi atbcio atboci atboic atbioc atbico tbicao tbicoa tbiaco tbiaoc tbioac
tbioca tbciao tbcioa tbcaio tbcaoi tbcoai tbcoia tbacio tbacoi tbaico tbaioc
tbaoic tbaoci tbocai tbocia tboaci tboaic tboiac tboica tibcao tibcoa tibaco
tibaoc tiboac tiboca ticbao ticboa ticabo ticaob ticoab ticoba tiacbo tiacob
tiabco tiaboc tiaobc tiaocb tiocab tiocba tioacb tioabc tiobac tiobca tcibao
tciboa tciabo tciaob tcioab tcioba tcbiao tcbioa tcbaio tcbaoi tcboai tcboia
tcabio tcaboi tcaibo tcaiob tcaoib tcaobi tcobai tcobia tcoabi tcoaib tcoiab
tcoiba taicbo taicob taibco taiboc taiobc taiocb tacibo taciob tacbio tacboi
tacobi tacoib tabcio tabcoi tabico tabioc taboic taboci taocbi taocib taobci
taobic taoibc taoicb toicab toicba toiacb toiabc toibac toibca tociab tociba
tocaib tocabi tocbai tocbia toacib toacbi toaicb toaibc toabic toabci tobcai
tobcia tobaci tobaic tobiac tobica

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History of cryptography
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