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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: merxia
cipher variations:
nfsyjb ogtzkc phuald qivbme rjwcnf
skxdog tlyeph umzfqi vnagrj wobhsk
xpcitl yqdjum zrekvn asflwo btgmxp
cuhnyq dviozr ewjpas fxkqbt gylrcu
hzmsdv iantew jboufx kcpvgy ldqwhz

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: merxia
Cipher: nvicrz

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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: merxia

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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: merxia
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: merxia
Cipher: zrekvn

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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: merxia
Cipher: 235124354211

Extended Methods:
Method #1

Plaintext: merxia
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
m e r x i a 
2 5 2 3 4 1 
3 1 4 5 2 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: merxia
Cipher: wmdcyb

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Method #3

Plaintext: merxia
method variations:
xfoubf foubfx oubfxf
ubfxfo bfxfou fxfoub

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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: merxia

all 720 cipher variations:
merxia merxai merixa meriax meraix meraxi mexria mexrai mexira mexiar mexair
mexari meixra meixar meirxa meirax meiarx meiaxr meaxir meaxri meaixr meairx
mearix mearxi mrexia mrexai mreixa mreiax mreaix mreaxi mrxeia mrxeai mrxiea
mrxiae mrxaie mrxaei mrixea mrixae mriexa mrieax mriaex mriaxe mraxie mraxei
mraixe mraiex mraeix mraexi mxreia mxreai mxriea mxriae mxraie mxraei mxeria
mxerai mxeira mxeiar mxeair mxeari mxiera mxiear mxirea mxirae mxiare mxiaer
mxaeir mxaeri mxaier mxaire mxarie mxarei mirxea mirxae mirexa mireax miraex
miraxe mixrea mixrae mixera mixear mixaer mixare miexra miexar mierxa mierax
miearx mieaxr miaxer miaxre miaexr miaerx miarex miarxe marxie marxei marixe
mariex mareix marexi maxrie maxrei maxire maxier maxeir maxeri maixre maixer
mairxe mairex maierx maiexr maexir maexri maeixr maeirx maerix maerxi emrxia
emrxai emrixa emriax emraix emraxi emxria emxrai emxira emxiar emxair emxari
emixra emixar emirxa emirax emiarx emiaxr emaxir emaxri emaixr emairx emarix
emarxi ermxia ermxai ermixa ermiax ermaix ermaxi erxmia erxmai erxima erxiam
erxaim erxami erixma erixam erimxa erimax eriamx eriaxm eraxim eraxmi eraixm
eraimx eramix eramxi exrmia exrmai exrima exriam exraim exrami exmria exmrai
exmira exmiar exmair exmari eximra eximar exirma exiram exiarm exiamr examir
examri exaimr exairm exarim exarmi eirxma eirxam eirmxa eirmax eiramx eiraxm
eixrma eixram eixmra eixmar eixamr eixarm eimxra eimxar eimrxa eimrax eimarx
eimaxr eiaxmr eiaxrm eiamxr eiamrx eiarmx eiarxm earxim earxmi earixm earimx
earmix earmxi eaxrim eaxrmi eaxirm eaximr eaxmir eaxmri eaixrm eaixmr eairxm
eairmx eaimrx eaimxr eamxir eamxri eamixr eamirx eamrix eamrxi remxia remxai
remixa remiax remaix remaxi rexmia rexmai rexima rexiam rexaim rexami reixma
reixam reimxa reimax reiamx reiaxm reaxim reaxmi reaixm reaimx reamix reamxi
rmexia rmexai rmeixa rmeiax rmeaix rmeaxi rmxeia rmxeai rmxiea rmxiae rmxaie
rmxaei rmixea rmixae rmiexa rmieax rmiaex rmiaxe rmaxie rmaxei rmaixe rmaiex
rmaeix rmaexi rxmeia rxmeai rxmiea rxmiae rxmaie rxmaei rxemia rxemai rxeima
rxeiam rxeaim rxeami rxiema rxieam rximea rximae rxiame rxiaem rxaeim rxaemi
rxaiem rxaime rxamie rxamei rimxea rimxae rimexa rimeax rimaex rimaxe rixmea
rixmae rixema rixeam rixaem rixame riexma riexam riemxa riemax rieamx rieaxm
riaxem riaxme riaexm riaemx riamex riamxe ramxie ramxei ramixe ramiex rameix
ramexi raxmie raxmei raxime raxiem raxeim raxemi raixme raixem raimxe raimex
raiemx raiexm raexim raexmi raeixm raeimx raemix raemxi xermia xermai xerima
xeriam xeraim xerami xemria xemrai xemira xemiar xemair xemari xeimra xeimar
xeirma xeiram xeiarm xeiamr xeamir xeamri xeaimr xeairm xearim xearmi xremia
xremai xreima xreiam xreaim xreami xrmeia xrmeai xrmiea xrmiae xrmaie xrmaei
xrimea xrimae xriema xrieam xriaem xriame xramie xramei xraime xraiem xraeim
xraemi xmreia xmreai xmriea xmriae xmraie xmraei xmeria xmerai xmeira xmeiar
xmeair xmeari xmiera xmiear xmirea xmirae xmiare xmiaer xmaeir xmaeri xmaier
xmaire xmarie xmarei xirmea xirmae xirema xiream xiraem xirame ximrea ximrae
ximera ximear ximaer ximare xiemra xiemar xierma xieram xiearm xieamr xiamer
xiamre xiaemr xiaerm xiarem xiarme xarmie xarmei xarime xariem xareim xaremi
xamrie xamrei xamire xamier xameir xameri xaimre xaimer xairme xairem xaierm
xaiemr xaemir xaemri xaeimr xaeirm xaerim xaermi ierxma ierxam iermxa iermax
ieramx ieraxm iexrma iexram iexmra iexmar iexamr iexarm iemxra iemxar iemrxa
iemrax iemarx iemaxr ieaxmr ieaxrm ieamxr ieamrx iearmx iearxm irexma irexam
iremxa iremax ireamx ireaxm irxema irxeam irxmea irxmae irxame irxaem irmxea
irmxae irmexa irmeax irmaex irmaxe iraxme iraxem iramxe iramex iraemx iraexm
ixrema ixream ixrmea ixrmae ixrame ixraem ixerma ixeram ixemra ixemar ixeamr
ixearm ixmera ixmear ixmrea ixmrae ixmare ixmaer ixaemr ixaerm ixamer ixamre
ixarme ixarem imrxea imrxae imrexa imreax imraex imraxe imxrea imxrae imxera
imxear imxaer imxare imexra imexar imerxa imerax imearx imeaxr imaxer imaxre
imaexr imaerx imarex imarxe iarxme iarxem iarmxe iarmex iaremx iarexm iaxrme
iaxrem iaxmre iaxmer iaxemr iaxerm iamxre iamxer iamrxe iamrex iamerx iamexr
iaexmr iaexrm iaemxr iaemrx iaermx iaerxm aerxim aerxmi aerixm aerimx aermix
aermxi aexrim aexrmi aexirm aeximr aexmir aexmri aeixrm aeixmr aeirxm aeirmx
aeimrx aeimxr aemxir aemxri aemixr aemirx aemrix aemrxi arexim arexmi areixm
areimx aremix aremxi arxeim arxemi arxiem arxime arxmie arxmei arixem arixme
ariexm ariemx arimex arimxe armxie armxei armixe armiex armeix armexi axreim
axremi axriem axrime axrmie axrmei axerim axermi axeirm axeimr axemir axemri
axierm axiemr axirem axirme aximre aximer axmeir axmeri axmier axmire axmrie
axmrei airxem airxme airexm airemx airmex airmxe aixrem aixrme aixerm aixemr
aixmer aixmre aiexrm aiexmr aierxm aiermx aiemrx aiemxr aimxer aimxre aimexr
aimerx aimrex aimrxe amrxie amrxei amrixe amriex amreix amrexi amxrie amxrei
amxire amxier amxeir amxeri amixre amixer amirxe amirex amierx amiexr amexir
amexri ameixr ameirx amerix amerxi

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History of cryptography
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