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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: boemia
cipher variations:
cpfnjb dqgokc erhpld fsiqme gtjrnf
huksog ivltph jwmuqi kxnvrj lyowsk
mzpxtl naqyum obrzvn pcsawo qdtbxp
reucyq sfvdzr tgweas uhxfbt viygcu
wjzhdv xkaiew ylbjfx zmckgy andlhz

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: boemia
Cipher: ylvnrz

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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: boemia

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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: boemia
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: boemia
Cipher: obrzvn

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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: boemia
Cipher: 214351234211

Extended Methods:
Method #1

Plaintext: boemia
method variations:

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

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Method #3

Plaintext: boemia
method variations:
qxfsbf xfsbfq fsbfqx
sbfqxf bfqxfs fqxfsb

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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: boemia

all 720 cipher variations:
boemia boemai boeima boeiam boeaim boeami bomeia bomeai bomiea bomiae bomaie
bomaei boimea boimae boiema boieam boiaem boiame boamie boamei boaime boaiem
boaeim boaemi beomia beomai beoima beoiam beoaim beoami bemoia bemoai bemioa
bemiao bemaio bemaoi beimoa beimao beioma beioam beiaom beiamo beamio beamoi
beaimo beaiom beaoim beaomi bmeoia bmeoai bmeioa bmeiao bmeaio bmeaoi bmoeia
bmoeai bmoiea bmoiae bmoaie bmoaei bmioea bmioae bmieoa bmieao bmiaeo bmiaoe
bmaoie bmaoei bmaioe bmaieo bmaeio bmaeoi biemoa biemao bieoma bieoam bieaom
bieamo bimeoa bimeao bimoea bimoae bimaoe bimaeo biomea biomae bioema bioeam
bioaem bioame biamoe biameo biaome biaoem biaeom biaemo baemio baemoi baeimo
baeiom baeoim baeomi bameio bameoi bamieo bamioe bamoie bamoei baimeo baimoe
baiemo baieom baioem baiome baomie baomei baoime baoiem baoeim baoemi obemia
obemai obeima obeiam obeaim obeami obmeia obmeai obmiea obmiae obmaie obmaei
obimea obimae obiema obieam obiaem obiame obamie obamei obaime obaiem obaeim
obaemi oebmia oebmai oebima oebiam oebaim oebami oembia oembai oemiba oemiab
oemaib oemabi oeimba oeimab oeibma oeibam oeiabm oeiamb oeamib oeambi oeaimb
oeaibm oeabim oeabmi omebia omebai omeiba omeiab omeaib omeabi ombeia ombeai
ombiea ombiae ombaie ombaei omibea omibae omieba omieab omiaeb omiabe omabie
omabei omaibe omaieb omaeib omaebi oiemba oiemab oiebma oiebam oieabm oieamb
oimeba oimeab oimbea oimbae oimabe oimaeb oibmea oibmae oibema oibeam oibaem
oibame oiambe oiameb oiabme oiabem oiaebm oiaemb oaemib oaembi oaeimb oaeibm
oaebim oaebmi oameib oamebi oamieb oamibe oambie oambei oaimeb oaimbe oaiemb
oaiebm oaibem oaibme oabmie oabmei oabime oabiem oabeim oabemi eobmia eobmai
eobima eobiam eobaim eobami eombia eombai eomiba eomiab eomaib eomabi eoimba
eoimab eoibma eoibam eoiabm eoiamb eoamib eoambi eoaimb eoaibm eoabim eoabmi
ebomia ebomai eboima eboiam eboaim eboami ebmoia ebmoai ebmioa ebmiao ebmaio
ebmaoi ebimoa ebimao ebioma ebioam ebiaom ebiamo ebamio ebamoi ebaimo ebaiom
ebaoim ebaomi emboia emboai embioa embiao embaio embaoi emobia emobai emoiba
emoiab emoaib emoabi emioba emioab emiboa emibao emiabo emiaob emaoib emaobi
emaiob emaibo emabio emaboi eibmoa eibmao eiboma eiboam eibaom eibamo eimboa
eimbao eimoba eimoab eimaob eimabo eiomba eiomab eiobma eiobam eioabm eioamb
eiamob eiambo eiaomb eiaobm eiabom eiabmo eabmio eabmoi eabimo eabiom eaboim
eabomi eambio eamboi eamibo eamiob eamoib eamobi eaimbo eaimob eaibmo eaibom
eaiobm eaiomb eaomib eaombi eaoimb eaoibm eaobim eaobmi moebia moebai moeiba
moeiab moeaib moeabi mobeia mobeai mobiea mobiae mobaie mobaei moibea moibae
moieba moieab moiaeb moiabe moabie moabei moaibe moaieb moaeib moaebi meobia
meobai meoiba meoiab meoaib meoabi meboia meboai mebioa mebiao mebaio mebaoi
meiboa meibao meioba meioab meiaob meiabo meabio meaboi meaibo meaiob meaoib
meaobi mbeoia mbeoai mbeioa mbeiao mbeaio mbeaoi mboeia mboeai mboiea mboiae
mboaie mboaei mbioea mbioae mbieoa mbieao mbiaeo mbiaoe mbaoie mbaoei mbaioe
mbaieo mbaeio mbaeoi mieboa miebao mieoba mieoab mieaob mieabo mibeoa mibeao
miboea miboae mibaoe mibaeo miobea miobae mioeba mioeab mioaeb mioabe miaboe
miabeo miaobe miaoeb miaeob miaebo maebio maeboi maeibo maeiob maeoib maeobi
mabeio mabeoi mabieo mabioe maboie maboei maibeo maiboe maiebo maieob maioeb
maiobe maobie maobei maoibe maoieb maoeib maoebi ioemba ioemab ioebma ioebam
ioeabm ioeamb iomeba iomeab iombea iombae iomabe iomaeb iobmea iobmae iobema
iobeam iobaem iobame ioambe ioameb ioabme ioabem ioaebm ioaemb ieomba ieomab
ieobma ieobam ieoabm ieoamb iemoba iemoab iemboa iembao iemabo iemaob iebmoa
iebmao ieboma ieboam iebaom iebamo ieambo ieamob ieabmo ieabom ieaobm ieaomb
imeoba imeoab imeboa imebao imeabo imeaob imoeba imoeab imobea imobae imoabe
imoaeb imboea imboae imbeoa imbeao imbaeo imbaoe imaobe imaoeb imaboe imabeo
imaebo imaeob ibemoa ibemao ibeoma ibeoam ibeaom ibeamo ibmeoa ibmeao ibmoea
ibmoae ibmaoe ibmaeo ibomea ibomae iboema iboeam iboaem iboame ibamoe ibameo
ibaome ibaoem ibaeom ibaemo iaembo iaemob iaebmo iaebom iaeobm iaeomb iamebo
iameob iambeo iamboe iamobe iamoeb iabmeo iabmoe iabemo iabeom iaboem iabome
iaombe iaomeb iaobme iaobem iaoebm iaoemb aoemib aoembi aoeimb aoeibm aoebim
aoebmi aomeib aomebi aomieb aomibe aombie aombei aoimeb aoimbe aoiemb aoiebm
aoibem aoibme aobmie aobmei aobime aobiem aobeim aobemi aeomib aeombi aeoimb
aeoibm aeobim aeobmi aemoib aemobi aemiob aemibo aembio aemboi aeimob aeimbo
aeiomb aeiobm aeibom aeibmo aebmio aebmoi aebimo aebiom aeboim aebomi ameoib
ameobi ameiob ameibo amebio ameboi amoeib amoebi amoieb amoibe amobie amobei
amioeb amiobe amieob amiebo amibeo amiboe amboie amboei ambioe ambieo ambeio
ambeoi aiemob aiembo aieomb aieobm aiebom aiebmo aimeob aimebo aimoeb aimobe
aimboe aimbeo aiomeb aiombe aioemb aioebm aiobem aiobme aibmoe aibmeo aibome
aiboem aibeom aibemo abemio abemoi abeimo abeiom abeoim abeomi abmeio abmeoi
abmieo abmioe abmoie abmoei abimeo abimoe abiemo abieom abioem abiome abomie
abomei aboime aboiem aboeim aboemi

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History of cryptography
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