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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: shoppy
cipher variations:
tipqqz ujqrra vkrssb wlsttc xmtuud
ynuvve zovwwf apwxxg bqxyyh cryzzi
dszaaj etabbk fubccl gvcddm hwdeen
ixeffo jyfggp kzghhq lahiir mbijjs
ncjkkt odkllu pelmmv qfmnnw rgnoox

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: shoppy
Cipher: hslkkb

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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: shoppy

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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: shoppy
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: shoppy
Cipher: fubccl

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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: shoppy
Cipher: 343243535345

Extended Methods:
Method #1

Plaintext: shoppy
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
s h o p p y 
3 3 4 5 5 4 
4 2 3 3 3 5 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: shoppy
Cipher: nyuinx

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Method #3

Plaintext: shoppy
method variations:
orxxsp rxxspo xxspor
xsporx sporxx porxxs

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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: shoppy

all 720 cipher variations:
shoppy shopyp shoppy shopyp shoypp shoypp shpopy shpoyp shppoy shppyo shpypo
shpyop shppoy shppyo shpopy shpoyp shpyop shpypo shyppo shypop shyppo shypop
shyopp shyopp sohppy sohpyp sohppy sohpyp sohypp sohypp sophpy sophyp sopphy
soppyh sopyph sopyhp sopphy soppyh sophpy sophyp sopyhp sopyph soypph soyphp
soypph soyphp soyhpp soyhpp spohpy spohyp spophy spopyh spoyph spoyhp sphopy
sphoyp sphpoy sphpyo sphypo sphyop spphoy spphyo sppohy sppoyh sppyoh sppyho
spyhpo spyhop spypho spypoh spyoph spyohp spophy spopyh spohpy spohyp spoyhp
spoyph sppohy sppoyh spphoy spphyo sppyho sppyoh sphpoy sphpyo sphopy sphoyp
sphyop sphypo spypho spypoh spyhpo spyhop spyohp spyoph syopph syophp syopph
syophp syohpp syohpp sypoph sypohp syppoh syppho syphpo syphop syppoh syppho
sypoph sypohp syphop syphpo syhppo syhpop syhppo syhpop syhopp syhopp hsoppy
hsopyp hsoppy hsopyp hsoypp hsoypp hspopy hspoyp hsppoy hsppyo hspypo hspyop
hsppoy hsppyo hspopy hspoyp hspyop hspypo hsyppo hsypop hsyppo hsypop hsyopp
hsyopp hosppy hospyp hosppy hospyp hosypp hosypp hopspy hopsyp hoppsy hoppys
hopyps hopysp hoppsy hoppys hopspy hopsyp hopysp hopyps hoypps hoypsp hoypps
hoypsp hoyspp hoyspp hpospy hposyp hpopsy hpopys hpoyps hpoysp hpsopy hpsoyp
hpspoy hpspyo hpsypo hpsyop hppsoy hppsyo hpposy hppoys hppyos hppyso hpyspo
hpysop hpypso hpypos hpyops hpyosp hpopsy hpopys hpospy hposyp hpoysp hpoyps
hpposy hppoys hppsoy hppsyo hppyso hppyos hpspoy hpspyo hpsopy hpsoyp hpsyop
hpsypo hpypso hpypos hpyspo hpysop hpyosp hpyops hyopps hyopsp hyopps hyopsp
hyospp hyospp hypops hyposp hyppos hyppso hypspo hypsop hyppos hyppso hypops
hyposp hypsop hypspo hysppo hyspop hysppo hyspop hysopp hysopp ohsppy ohspyp
ohsppy ohspyp ohsypp ohsypp ohpspy ohpsyp ohppsy ohppys ohpyps ohpysp ohppsy
ohppys ohpspy ohpsyp ohpysp ohpyps ohypps ohypsp ohypps ohypsp ohyspp ohyspp
oshppy oshpyp oshppy oshpyp oshypp oshypp osphpy osphyp ospphy osppyh ospyph
ospyhp ospphy osppyh osphpy osphyp ospyhp ospyph osypph osyphp osypph osyphp
osyhpp osyhpp opshpy opshyp opsphy opspyh opsyph opsyhp ophspy ophsyp ophpsy
ophpys ophyps ophysp opphsy opphys oppshy oppsyh oppysh oppyhs opyhps opyhsp
opyphs opypsh opysph opyshp opsphy opspyh opshpy opshyp opsyhp opsyph oppshy
oppsyh opphsy opphys oppyhs oppysh ophpsy ophpys ophspy ophsyp ophysp ophyps
opyphs opypsh opyhps opyhsp opyshp opysph oyspph oysphp oyspph oysphp oyshpp
oyshpp oypsph oypshp oyppsh oypphs oyphps oyphsp oyppsh oypphs oypsph oypshp
oyphsp oyphps oyhpps oyhpsp oyhpps oyhpsp oyhspp oyhspp phospy phosyp phopsy
phopys phoyps phoysp phsopy phsoyp phspoy phspyo phsypo phsyop phpsoy phpsyo
phposy phpoys phpyos phpyso physpo physop phypso phypos phyops phyosp pohspy
pohsyp pohpsy pohpys pohyps pohysp poshpy poshyp posphy pospyh posyph posyhp
popshy popsyh pophsy pophys popyhs popysh poysph poyshp poypsh poyphs poyhps
poyhsp psohpy psohyp psophy psopyh psoyph psoyhp pshopy pshoyp pshpoy pshpyo
pshypo pshyop psphoy psphyo pspohy pspoyh pspyoh pspyho psyhpo psyhop psypho
psypoh psyoph psyohp pposhy pposyh ppohsy ppohys ppoyhs ppoysh ppsohy ppsoyh
ppshoy ppshyo ppsyho ppsyoh pphsoy pphsyo pphosy pphoys pphyos pphyso ppysho
ppysoh ppyhso ppyhos ppyohs ppyosh pyosph pyoshp pyopsh pyophs pyohps pyohsp
pysoph pysohp pyspoh pyspho pyshpo pyshop pypsoh pypsho pyposh pypohs pyphos
pyphso pyhspo pyhsop pyhpso pyhpos pyhops pyhosp phopsy phopys phospy phosyp
phoysp phoyps phposy phpoys phpsoy phpsyo phpyso phpyos phspoy phspyo phsopy
phsoyp phsyop phsypo phypso phypos physpo physop phyosp phyops pohpsy pohpys
pohspy pohsyp pohysp pohyps pophsy pophys popshy popsyh popysh popyhs posphy
pospyh poshpy poshyp posyhp posyph poypsh poyphs poysph poyshp poyhsp poyhps
ppohsy ppohys pposhy pposyh ppoysh ppoyhs pphosy pphoys pphsoy pphsyo pphyso
pphyos ppshoy ppshyo ppsohy ppsoyh ppsyoh ppsyho ppyhso ppyhos ppysho ppysoh
ppyosh ppyohs psophy psopyh psohpy psohyp psoyhp psoyph pspohy pspoyh psphoy
psphyo pspyho pspyoh pshpoy pshpyo pshopy pshoyp pshyop pshypo psypho psypoh
psyhpo psyhop psyohp psyoph pyopsh pyophs pyosph pyoshp pyohsp pyohps pyposh
pypohs pypsoh pypsho pyphso pyphos pyspoh pyspho pysoph pysohp pyshop pyshpo
pyhpso pyhpos pyhspo pyhsop pyhosp pyhops yhopps yhopsp yhopps yhopsp yhospp
yhospp yhpops yhposp yhppos yhppso yhpspo yhpsop yhppos yhppso yhpops yhposp
yhpsop yhpspo yhsppo yhspop yhsppo yhspop yhsopp yhsopp yohpps yohpsp yohpps
yohpsp yohspp yohspp yophps yophsp yopphs yoppsh yopsph yopshp yopphs yoppsh
yophps yophsp yopshp yopsph yospph yosphp yospph yosphp yoshpp yoshpp ypohps
ypohsp ypophs ypopsh yposph yposhp yphops yphosp yphpos yphpso yphspo yphsop
ypphos ypphso yppohs ypposh yppsoh yppsho ypshpo ypshop ypspho ypspoh ypsoph
ypsohp ypophs ypopsh ypohps ypohsp yposhp yposph yppohs ypposh ypphos ypphso
yppsho yppsoh yphpos yphpso yphops yphosp yphsop yphspo ypspho ypspoh ypshpo
ypshop ypsohp ypsoph ysopph ysophp ysopph ysophp ysohpp ysohpp yspoph yspohp
ysppoh ysppho ysphpo ysphop ysppoh ysppho yspoph yspohp ysphop ysphpo yshppo
yshpop yshppo yshpop yshopp yshopp

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History of cryptography
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