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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: grupos
cipher variations:
hsvqpt itwrqu juxsrv kvytsw lwzutx
mxavuy nybwvz ozcxwa padyxb qbezyc
rcfazd sdgbae tehcbf ufidcg vgjedh
whkfei xilgfj yjmhgk zknihl alojim
bmpkjn cnqlko dormlp epsnmq fqtonr

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: grupos
Cipher: tifklh

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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: grupos

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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: grupos
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: grupos
Cipher: tehcbf

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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: grupos
Cipher: 222454534334

Extended Methods:
Method #1

Plaintext: grupos
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
g r u p o s 
2 2 5 5 4 3 
2 4 4 3 3 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: grupos
Cipher: gzoros

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Method #3

Plaintext: grupos
method variations:
gyysni yysnig ysnigy
snigyy nigyys igyysn

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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: grupos

all 720 cipher variations:
grupos grupso gruops gruosp grusop gruspo grpuos grpuso grpous grposu grpsou
grpsuo gropus gropsu groups grousp grosup grospu grspou grspuo grsopu grsoup
grsuop grsupo gurpos gurpso gurops gurosp gursop gurspo gupros guprso gupors
guposr gupsor gupsro guoprs guopsr guorps guorsp guosrp guospr guspor guspro
gusopr gusorp gusrop gusrpo gpuros gpurso gpuors gpuosr gpusor gpusro gpruos
gpruso gprous gprosu gprsou gprsuo gporus gporsu gpours gpousr gposur gposru
gpsrou gpsruo gpsoru gpsour gpsuor gpsuro gouprs goupsr gourps goursp gousrp
gouspr gopurs gopusr goprus goprsu gopsru gopsur gorpus gorpsu gorups gorusp
gorsup gorspu gospru gospur gosrpu gosrup gosurp gosupr gsupor gsupro gsuopr
gsuorp gsurop gsurpo gspuor gspuro gspour gsporu gsprou gspruo gsopur gsopru
gsoupr gsourp gsorup gsorpu gsrpou gsrpuo gsropu gsroup gsruop gsrupo rgupos
rgupso rguops rguosp rgusop rguspo rgpuos rgpuso rgpous rgposu rgpsou rgpsuo
rgopus rgopsu rgoups rgousp rgosup rgospu rgspou rgspuo rgsopu rgsoup rgsuop
rgsupo rugpos rugpso rugops rugosp rugsop rugspo rupgos rupgso rupogs ruposg
rupsog rupsgo ruopgs ruopsg ruogps ruogsp ruosgp ruospg ruspog ruspgo rusopg
rusogp rusgop rusgpo rpugos rpugso rpuogs rpuosg rpusog rpusgo rpguos rpguso
rpgous rpgosu rpgsou rpgsuo rpogus rpogsu rpougs rpousg rposug rposgu rpsgou
rpsguo rpsogu rpsoug rpsuog rpsugo roupgs roupsg rougps rougsp rousgp rouspg
ropugs ropusg ropgus ropgsu ropsgu ropsug rogpus rogpsu rogups rogusp rogsup
rogspu rospgu rospug rosgpu rosgup rosugp rosupg rsupog rsupgo rsuopg rsuogp
rsugop rsugpo rspuog rspugo rspoug rspogu rspgou rspguo rsopug rsopgu rsoupg
rsougp rsogup rsogpu rsgpou rsgpuo rsgopu rsgoup rsguop rsgupo urgpos urgpso
urgops urgosp urgsop urgspo urpgos urpgso urpogs urposg urpsog urpsgo uropgs
uropsg urogps urogsp urosgp urospg urspog urspgo ursopg ursogp ursgop ursgpo
ugrpos ugrpso ugrops ugrosp ugrsop ugrspo ugpros ugprso ugpors ugposr ugpsor
ugpsro ugoprs ugopsr ugorps ugorsp ugosrp ugospr ugspor ugspro ugsopr ugsorp
ugsrop ugsrpo upgros upgrso upgors upgosr upgsor upgsro uprgos uprgso uprogs
uprosg uprsog uprsgo uporgs uporsg upogrs upogsr uposgr uposrg upsrog upsrgo
upsorg upsogr upsgor upsgro uogprs uogpsr uogrps uogrsp uogsrp uogspr uopgrs
uopgsr uoprgs uoprsg uopsrg uopsgr uorpgs uorpsg uorgps uorgsp uorsgp uorspg
uosprg uospgr uosrpg uosrgp uosgrp uosgpr usgpor usgpro usgopr usgorp usgrop
usgrpo uspgor uspgro uspogr usporg usprog usprgo usopgr usoprg usogpr usogrp
usorgp usorpg usrpog usrpgo usropg usrogp usrgop usrgpo prugos prugso pruogs
pruosg prusog prusgo prguos prguso prgous prgosu prgsou prgsuo progus progsu
prougs prousg prosug prosgu prsgou prsguo prsogu prsoug prsuog prsugo purgos
purgso purogs purosg pursog pursgo pugros pugrso pugors pugosr pugsor pugsro
puogrs puogsr puorgs puorsg puosrg puosgr pusgor pusgro pusogr pusorg pusrog
pusrgo pguros pgurso pguors pguosr pgusor pgusro pgruos pgruso pgrous pgrosu
pgrsou pgrsuo pgorus pgorsu pgours pgousr pgosur pgosru pgsrou pgsruo pgsoru
pgsour pgsuor pgsuro pougrs pougsr pourgs poursg pousrg pousgr pogurs pogusr
pogrus pogrsu pogsru pogsur porgus porgsu porugs porusg porsug porsgu posgru
posgur posrgu posrug posurg posugr psugor psugro psuogr psuorg psurog psurgo
psguor psguro psgour psgoru psgrou psgruo psogur psogru psougr psourg psorug
psorgu psrgou psrguo psrogu psroug psruog psrugo orupgs orupsg orugps orugsp
orusgp oruspg orpugs orpusg orpgus orpgsu orpsgu orpsug orgpus orgpsu orgups
orgusp orgsup orgspu orspgu orspug orsgpu orsgup orsugp orsupg ourpgs ourpsg
ourgps ourgsp oursgp ourspg ouprgs ouprsg oupgrs oupgsr oupsgr oupsrg ougprs
ougpsr ougrps ougrsp ougsrp ougspr ouspgr ousprg ousgpr ousgrp ousrgp ousrpg
opurgs opursg opugrs opugsr opusgr opusrg oprugs oprusg oprgus oprgsu oprsgu
oprsug opgrus opgrsu opgurs opgusr opgsur opgsru opsrgu opsrug opsgru opsgur
opsugr opsurg oguprs ogupsr ogurps ogursp ogusrp oguspr ogpurs ogpusr ogprus
ogprsu ogpsru ogpsur ogrpus ogrpsu ogrups ogrusp ogrsup ogrspu ogspru ogspur
ogsrpu ogsrup ogsurp ogsupr osupgr osuprg osugpr osugrp osurgp osurpg ospugr
ospurg ospgur ospgru osprgu osprug osgpur osgpru osgupr osgurp osgrup osgrpu
osrpgu osrpug osrgpu osrgup osrugp osrupg srupog srupgo sruopg sruogp srugop
srugpo srpuog srpugo srpoug srpogu srpgou srpguo sropug sropgu sroupg srougp
srogup srogpu srgpou srgpuo srgopu srgoup srguop srgupo surpog surpgo suropg
surogp surgop surgpo suprog suprgo suporg supogr supgor supgro suoprg suopgr
suorpg suorgp suogrp suogpr sugpor sugpro sugopr sugorp sugrop sugrpo spurog
spurgo spuorg spuogr spugor spugro spruog sprugo sproug sprogu sprgou sprguo
sporug sporgu spourg spougr spogur spogru spgrou spgruo spgoru spgour spguor
spguro souprg soupgr sourpg sourgp sougrp sougpr sopurg sopugr soprug soprgu
sopgru sopgur sorpug sorpgu sorupg sorugp sorgup sorgpu sogpru sogpur sogrpu
sogrup sogurp sogupr sgupor sgupro sguopr sguorp sgurop sgurpo sgpuor sgpuro
sgpour sgporu sgprou sgpruo sgopur sgopru sgoupr sgourp sgorup sgorpu sgrpou
sgrpuo sgropu sgroup sgruop sgrupo

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History of cryptography
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