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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: gremio
cipher variations:
hsfnjp itgokq juhplr kviqms lwjrnt
mxksou nyltpv ozmuqw panvrx qbowsy
rcpxtz sdqyua terzvb ufsawc vgtbxd
whucye xivdzf yjweag zkxfbh alygci
bmzhdj cnaiek dobjfl epckgm fqdlhn

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: gremio
Cipher: tivnrl

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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: gremio

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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: gremio
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: gremio
Cipher: terzvb

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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: gremio
Cipher: 222451234243

Extended Methods:
Method #1

Plaintext: gremio
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 e m i o 
2 2 5 2 4 4 
2 4 1 3 2 3 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: gremio
Cipher: gktrlm

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Method #3

Plaintext: gremio
method variations:
gyfsrh yfsrhg fsrhgy
srhgyf rhgyfs hgyfsr

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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: gremio

all 720 cipher variations:
gremio gremoi greimo greiom greoim greomi grmeio grmeoi grmieo grmioe grmoie
grmoei grimeo grimoe griemo grieom grioem griome gromie gromei groime groiem
groeim groemi germio germoi gerimo geriom geroim geromi gemrio gemroi gemiro
gemior gemoir gemori geimro geimor geirmo geirom geiorm geiomr geomir geomri
geoimr geoirm georim geormi gmerio gmeroi gmeiro gmeior gmeoir gmeori gmreio
gmreoi gmrieo gmrioe gmroie gmroei gmireo gmiroe gmiero gmieor gmioer gmiore
gmorie gmorei gmoire gmoier gmoeir gmoeri giemro giemor giermo gierom gieorm
gieomr gimero gimeor gimreo gimroe gimore gimoer girmeo girmoe giremo gireom
giroem girome giomre giomer giorme giorem gioerm gioemr goemir goemri goeimr
goeirm goerim goermi gomeir gomeri gomier gomire gomrie gomrei goimer goimre
goiemr goierm goirem goirme gormie gormei gorime goriem goreim goremi rgemio
rgemoi rgeimo rgeiom rgeoim rgeomi rgmeio rgmeoi rgmieo rgmioe rgmoie rgmoei
rgimeo rgimoe rgiemo rgieom rgioem rgiome rgomie rgomei rgoime rgoiem rgoeim
rgoemi regmio regmoi regimo regiom regoim regomi remgio remgoi remigo remiog
remoig remogi reimgo reimog reigmo reigom reiogm reiomg reomig reomgi reoimg
reoigm reogim reogmi rmegio rmegoi rmeigo rmeiog rmeoig rmeogi rmgeio rmgeoi
rmgieo rmgioe rmgoie rmgoei rmigeo rmigoe rmiego rmieog rmioeg rmioge rmogie
rmogei rmoige rmoieg rmoeig rmoegi riemgo riemog riegmo riegom rieogm rieomg
rimego rimeog rimgeo rimgoe rimoge rimoeg rigmeo rigmoe rigemo rigeom rigoem
rigome riomge riomeg riogme riogem rioegm rioemg roemig roemgi roeimg roeigm
roegim roegmi romeig romegi romieg romige romgie romgei roimeg roimge roiemg
roiegm roigem roigme rogmie rogmei rogime rogiem rogeim rogemi ergmio ergmoi
ergimo ergiom ergoim ergomi ermgio ermgoi ermigo ermiog ermoig ermogi erimgo
erimog erigmo erigom eriogm eriomg eromig eromgi eroimg eroigm erogim erogmi
egrmio egrmoi egrimo egriom egroim egromi egmrio egmroi egmiro egmior egmoir
egmori egimro egimor egirmo egirom egiorm egiomr egomir egomri egoimr egoirm
egorim egormi emgrio emgroi emgiro emgior emgoir emgori emrgio emrgoi emrigo
emriog emroig emrogi emirgo emirog emigro emigor emiogr emiorg emorig emorgi
emoirg emoigr emogir emogri eigmro eigmor eigrmo eigrom eigorm eigomr eimgro
eimgor eimrgo eimrog eimorg eimogr eirmgo eirmog eirgmo eirgom eirogm eiromg
eiomrg eiomgr eiormg eiorgm eiogrm eiogmr eogmir eogmri eogimr eogirm eogrim
eogrmi eomgir eomgri eomigr eomirg eomrig eomrgi eoimgr eoimrg eoigmr eoigrm
eoirgm eoirmg eormig eormgi eorimg eorigm eorgim eorgmi mregio mregoi mreigo
mreiog mreoig mreogi mrgeio mrgeoi mrgieo mrgioe mrgoie mrgoei mrigeo mrigoe
mriego mrieog mrioeg mrioge mrogie mrogei mroige mroieg mroeig mroegi mergio
mergoi merigo meriog meroig merogi megrio megroi megiro megior megoir megori
meigro meigor meirgo meirog meiorg meiogr meogir meogri meoigr meoirg meorig
meorgi mgerio mgeroi mgeiro mgeior mgeoir mgeori mgreio mgreoi mgrieo mgrioe
mgroie mgroei mgireo mgiroe mgiero mgieor mgioer mgiore mgorie mgorei mgoire
mgoier mgoeir mgoeri miegro miegor miergo mierog mieorg mieogr migero migeor
migreo migroe migore migoer mirgeo mirgoe mirego mireog miroeg miroge miogre
mioger miorge mioreg mioerg mioegr moegir moegri moeigr moeirg moerig moergi
mogeir mogeri mogier mogire mogrie mogrei moiger moigre moiegr moierg moireg
moirge morgie morgei morige morieg moreig moregi iremgo iremog iregmo iregom
ireogm ireomg irmego irmeog irmgeo irmgoe irmoge irmoeg irgmeo irgmoe irgemo
irgeom irgoem irgome iromge iromeg irogme irogem iroegm iroemg iermgo iermog
iergmo iergom ierogm ieromg iemrgo iemrog iemgro iemgor iemogr iemorg iegmro
iegmor iegrmo iegrom iegorm iegomr ieomgr ieomrg ieogmr ieogrm ieorgm ieormg
imergo imerog imegro imegor imeogr imeorg imrego imreog imrgeo imrgoe imroge
imroeg imgreo imgroe imgero imgeor imgoer imgore imorge imoreg imogre imoger
imoegr imoerg igemro igemor igermo igerom igeorm igeomr igmero igmeor igmreo
igmroe igmore igmoer igrmeo igrmoe igremo igreom igroem igrome igomre igomer
igorme igorem igoerm igoemr ioemgr ioemrg ioegmr ioegrm ioergm ioermg iomegr
iomerg iomger iomgre iomrge iomreg iogmer iogmre iogemr iogerm iogrem iogrme
iormge iormeg iorgme iorgem ioregm ioremg oremig oremgi oreimg oreigm oregim
oregmi ormeig ormegi ormieg ormige ormgie ormgei orimeg orimge oriemg oriegm
origem origme orgmie orgmei orgime orgiem orgeim orgemi oermig oermgi oerimg
oerigm oergim oergmi oemrig oemrgi oemirg oemigr oemgir oemgri oeimrg oeimgr
oeirmg oeirgm oeigrm oeigmr oegmir oegmri oegimr oegirm oegrim oegrmi omerig
omergi omeirg omeigr omegir omegri omreig omregi omrieg omrige omrgie omrgei
omireg omirge omierg omiegr omiger omigre omgrie omgrei omgire omgier omgeir
omgeri oiemrg oiemgr oiermg oiergm oiegrm oiegmr oimerg oimegr oimreg oimrge
oimgre oimger oirmeg oirmge oiremg oiregm oirgem oirgme oigmre oigmer oigrme
oigrem oigerm oigemr ogemir ogemri ogeimr ogeirm ogerim ogermi ogmeir ogmeri
ogmier ogmire ogmrie ogmrei ogimer ogimre ogiemr ogierm ogirem ogirme ogrmie
ogrmei ogrime ogriem ogreim ogremi

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History of cryptography
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