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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: ovated
cipher variations:
pwbufe qxcvgf rydwhg szexih tafyji
ubgzkj vchalk wdibml xejcnm yfkdon
zglepo ahmfqp bingrq cjohsr dkpits
elqjut fmrkvu gnslwv hotmxw ipunyx
jqvozy krwpaz lsxqba mtyrcb nuzsdc

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: ovated
Cipher: lezgvw

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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: ovated

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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: ovated
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: ovated
Cipher: bingrq

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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: ovated
Cipher: 431511445141

Extended Methods:
Method #1

Plaintext: ovated
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
o v a t e d 
4 1 1 4 5 4 
3 5 1 4 1 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: ovated
Cipher: dquxqa

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Method #3

Plaintext: ovated
method variations:
ceqyqq eqyqqc qyqqce
yqqceq qqceqy qceqyq

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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: ovated

all 720 cipher variations:
ovated ovatde ovaetd ovaedt ovadet ovadte ovtaed ovtade ovtead ovteda ovtdea
ovtdae ovetad ovetda oveatd oveadt ovedat ovedta ovdtea ovdtae ovdeta ovdeat
ovdaet ovdate oavted oavtde oavetd oavedt oavdet oavdte oatved oatvde oatevd
oatedv oatdev oatdve oaetvd oaetdv oaevtd oaevdt oaedvt oaedtv oadtev oadtve
oadetv oadevt oadvet oadvte otaved otavde otaevd otaedv otadev otadve otvaed
otvade otvead otveda otvdea otvdae otevad otevda oteavd oteadv otedav otedva
otdvea otdvae otdeva otdeav otdaev otdave oeatvd oeatdv oeavtd oeavdt oeadvt
oeadtv oetavd oetadv oetvad oetvda oetdva oetdav oevtad oevtda oevatd oevadt
oevdat oevdta oedtva oedtav oedvta oedvat oedavt oedatv odatev odatve odaetv
odaevt odavet odavte odtaev odtave odteav odteva odtvea odtvae odetav odetva
odeatv odeavt odevat odevta odvtea odvtae odveta odveat odvaet odvate voated
voatde voaetd voaedt voadet voadte votaed votade votead voteda votdea votdae
voetad voetda voeatd voeadt voedat voedta vodtea vodtae vodeta vodeat vodaet
vodate vaoted vaotde vaoetd vaoedt vaodet vaodte vatoed vatode vateod vatedo
vatdeo vatdoe vaetod vaetdo vaeotd vaeodt vaedot vaedto vadteo vadtoe vadeto
vadeot vadoet vadote vtaoed vtaode vtaeod vtaedo vtadeo vtadoe vtoaed vtoade
vtoead vtoeda vtodea vtodae vteoad vteoda vteaod vteado vtedao vtedoa vtdoea
vtdoae vtdeoa vtdeao vtdaeo vtdaoe veatod veatdo veaotd veaodt veadot veadto
vetaod vetado vetoad vetoda vetdoa vetdao veotad veotda veoatd veoadt veodat
veodta vedtoa vedtao vedota vedoat vedaot vedato vdateo vdatoe vdaeto vdaeot
vdaoet vdaote vdtaeo vdtaoe vdteao vdteoa vdtoea vdtoae vdetao vdetoa vdeato
vdeaot vdeoat vdeota vdotea vdotae vdoeta vdoeat vdoaet vdoate avoted avotde
avoetd avoedt avodet avodte avtoed avtode avteod avtedo avtdeo avtdoe avetod
avetdo aveotd aveodt avedot avedto avdteo avdtoe avdeto avdeot avdoet avdote
aovted aovtde aovetd aovedt aovdet aovdte aotved aotvde aotevd aotedv aotdev
aotdve aoetvd aoetdv aoevtd aoevdt aoedvt aoedtv aodtev aodtve aodetv aodevt
aodvet aodvte atoved atovde atoevd atoedv atodev atodve atvoed atvode atveod
atvedo atvdeo atvdoe atevod atevdo ateovd ateodv atedov atedvo atdveo atdvoe
atdevo atdeov atdoev atdove aeotvd aeotdv aeovtd aeovdt aeodvt aeodtv aetovd
aetodv aetvod aetvdo aetdvo aetdov aevtod aevtdo aevotd aevodt aevdot aevdto
aedtvo aedtov aedvto aedvot aedovt aedotv adotev adotve adoetv adoevt adovet
adovte adtoev adtove adteov adtevo adtveo adtvoe adetov adetvo adeotv adeovt
adevot adevto advteo advtoe adveto adveot advoet advote tvaoed tvaode tvaeod
tvaedo tvadeo tvadoe tvoaed tvoade tvoead tvoeda tvodea tvodae tveoad tveoda
tveaod tveado tvedao tvedoa tvdoea tvdoae tvdeoa tvdeao tvdaeo tvdaoe tavoed
tavode taveod tavedo tavdeo tavdoe taoved taovde taoevd taoedv taodev taodve
taeovd taeodv taevod taevdo taedvo taedov tadoev tadove tadeov tadevo tadveo
tadvoe toaved toavde toaevd toaedv toadev toadve tovaed tovade tovead toveda
tovdea tovdae toevad toevda toeavd toeadv toedav toedva todvea todvae todeva
todeav todaev todave teaovd teaodv teavod teavdo teadvo teadov teoavd teoadv
teovad teovda teodva teodav tevoad tevoda tevaod tevado tevdao tevdoa tedova
tedoav tedvoa tedvao tedavo tedaov tdaoev tdaove tdaeov tdaevo tdaveo tdavoe
tdoaev tdoave tdoeav tdoeva tdovea tdovae tdeoav tdeova tdeaov tdeavo tdevao
tdevoa tdvoea tdvoae tdveoa tdveao tdvaeo tdvaoe evatod evatdo evaotd evaodt
evadot evadto evtaod evtado evtoad evtoda evtdoa evtdao evotad evotda evoatd
evoadt evodat evodta evdtoa evdtao evdota evdoat evdaot evdato eavtod eavtdo
eavotd eavodt eavdot eavdto eatvod eatvdo eatovd eatodv eatdov eatdvo eaotvd
eaotdv eaovtd eaovdt eaodvt eaodtv eadtov eadtvo eadotv eadovt eadvot eadvto
etavod etavdo etaovd etaodv etadov etadvo etvaod etvado etvoad etvoda etvdoa
etvdao etovad etovda etoavd etoadv etodav etodva etdvoa etdvao etdova etdoav
etdaov etdavo eoatvd eoatdv eoavtd eoavdt eoadvt eoadtv eotavd eotadv eotvad
eotvda eotdva eotdav eovtad eovtda eovatd eovadt eovdat eovdta eodtva eodtav
eodvta eodvat eodavt eodatv edatov edatvo edaotv edaovt edavot edavto edtaov
edtavo edtoav edtova edtvoa edtvao edotav edotva edoatv edoavt edovat edovta
edvtoa edvtao edvota edvoat edvaot edvato dvateo dvatoe dvaeto dvaeot dvaoet
dvaote dvtaeo dvtaoe dvteao dvteoa dvtoea dvtoae dvetao dvetoa dveato dveaot
dveoat dveota dvotea dvotae dvoeta dvoeat dvoaet dvoate davteo davtoe daveto
daveot davoet davote datveo datvoe datevo dateov datoev datove daetvo daetov
daevto daevot daeovt daeotv daotev daotve daoetv daoevt daovet daovte dtaveo
dtavoe dtaevo dtaeov dtaoev dtaove dtvaeo dtvaoe dtveao dtveoa dtvoea dtvoae
dtevao dtevoa dteavo dteaov dteoav dteova dtovea dtovae dtoeva dtoeav dtoaev
dtoave deatvo deatov deavto deavot deaovt deaotv detavo detaov detvao detvoa
detova detoav devtao devtoa devato devaot devoat devota deotva deotav deovta
deovat deoavt deoatv doatev doatve doaetv doaevt doavet doavte dotaev dotave
doteav doteva dotvea dotvae doetav doetva doeatv doeavt doevat doevta dovtea
dovtae doveta doveat dovaet dovate

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History of cryptography
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