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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: bathos
cipher variations:
cbuipt dcvjqu edwkrv fexlsw gfymtx
hgznuy ihaovz jibpwa kjcqxb lkdryc
mleszd nmftae ongubf pohvcg qpiwdh
rqjxei srkyfj tslzgk utmahl vunbim
wvocjn xwpdko yxqelp zyrfmq azsgnr

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: bathos
Cipher: yzgslh

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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: bathos

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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: bathos
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: bathos
Cipher: ongubf

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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: bathos
Cipher: 211144324334

Extended Methods:
Method #1

Plaintext: bathos
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
b a t h o s 
2 1 4 3 4 3 
1 1 4 2 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: bathos
Cipher: booais

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Method #3

Plaintext: bathos
method variations:
aqorni qornia orniaq
rniaqo niaqor iaqorn

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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: bathos

all 720 cipher variations:
bathos bathso batohs batosh batsoh batsho bahtos bahtso bahots bahost bahsot
bahsto baohts baohst baoths baotsh baosth baosht bashot bashto basoht basoth
bastoh bastho btahos btahso btaohs btaosh btasoh btasho bthaos bthaso bthoas
bthosa bthsoa bthsao btohas btohsa btoahs btoash btosah btosha btshoa btshao
btsoha btsoah btsaoh btsaho bhtaos bhtaso bhtoas bhtosa bhtsoa bhtsao bhatos
bhatso bhaots bhaost bhasot bhasto bhoats bhoast bhotas bhotsa bhosta bhosat
bhsaot bhsato bhsoat bhsota bhstoa bhstao bothas bothsa botahs botash botsah
botsha bohtas bohtsa bohats bohast bohsat bohsta boahts boahst boaths boatsh
boasth boasht boshat boshta bosaht bosath bostah bostha bsthoa bsthao bstoha
bstoah bstaoh bstaho bshtoa bshtao bshota bshoat bshaot bshato bsohta bsohat
bsotha bsotah bsoath bsoaht bsahot bsahto bsaoht bsaoth bsatoh bsatho abthos
abthso abtohs abtosh abtsoh abtsho abhtos abhtso abhots abhost abhsot abhsto
abohts abohst aboths abotsh abosth abosht abshot abshto absoht absoth abstoh
abstho atbhos atbhso atbohs atbosh atbsoh atbsho athbos athbso athobs athosb
athsob athsbo atohbs atohsb atobhs atobsh atosbh atoshb atshob atshbo atsohb
atsobh atsboh atsbho ahtbos ahtbso ahtobs ahtosb ahtsob ahtsbo ahbtos ahbtso
ahbots ahbost ahbsot ahbsto ahobts ahobst ahotbs ahotsb ahostb ahosbt ahsbot
ahsbto ahsobt ahsotb ahstob ahstbo aothbs aothsb aotbhs aotbsh aotsbh aotshb
aohtbs aohtsb aohbts aohbst aohsbt aohstb aobhts aobhst aobths aobtsh aobsth
aobsht aoshbt aoshtb aosbht aosbth aostbh aosthb asthob asthbo astohb astobh
astboh astbho ashtob ashtbo ashotb ashobt ashbot ashbto asohtb asohbt asothb
asotbh asobth asobht asbhot asbhto asboht asboth asbtoh asbtho tabhos tabhso
tabohs tabosh tabsoh tabsho tahbos tahbso tahobs tahosb tahsob tahsbo taohbs
taohsb taobhs taobsh taosbh taoshb tashob tashbo tasohb tasobh tasboh tasbho
tbahos tbahso tbaohs tbaosh tbasoh tbasho tbhaos tbhaso tbhoas tbhosa tbhsoa
tbhsao tbohas tbohsa tboahs tboash tbosah tbosha tbshoa tbshao tbsoha tbsoah
tbsaoh tbsaho thbaos thbaso thboas thbosa thbsoa thbsao thabos thabso thaobs
thaosb thasob thasbo thoabs thoasb thobas thobsa thosba thosab thsaob thsabo
thsoab thsoba thsboa thsbao tobhas tobhsa tobahs tobash tobsah tobsha tohbas
tohbsa tohabs tohasb tohsab tohsba toahbs toahsb toabhs toabsh toasbh toashb
toshab toshba tosahb tosabh tosbah tosbha tsbhoa tsbhao tsboha tsboah tsbaoh
tsbaho tshboa tshbao tshoba tshoab tshaob tshabo tsohba tsohab tsobha tsobah
tsoabh tsoahb tsahob tsahbo tsaohb tsaobh tsaboh tsabho hatbos hatbso hatobs
hatosb hatsob hatsbo habtos habtso habots habost habsot habsto haobts haobst
haotbs haotsb haostb haosbt hasbot hasbto hasobt hasotb hastob hastbo htabos
htabso htaobs htaosb htasob htasbo htbaos htbaso htboas htbosa htbsoa htbsao
htobas htobsa htoabs htoasb htosab htosba htsboa htsbao htsoba htsoab htsaob
htsabo hbtaos hbtaso hbtoas hbtosa hbtsoa hbtsao hbatos hbatso hbaots hbaost
hbasot hbasto hboats hboast hbotas hbotsa hbosta hbosat hbsaot hbsato hbsoat
hbsota hbstoa hbstao hotbas hotbsa hotabs hotasb hotsab hotsba hobtas hobtsa
hobats hobast hobsat hobsta hoabts hoabst hoatbs hoatsb hoastb hoasbt hosbat
hosbta hosabt hosatb hostab hostba hstboa hstbao hstoba hstoab hstaob hstabo
hsbtoa hsbtao hsbota hsboat hsbaot hsbato hsobta hsobat hsotba hsotab hsoatb
hsoabt hsabot hsabto hsaobt hsaotb hsatob hsatbo oathbs oathsb oatbhs oatbsh
oatsbh oatshb oahtbs oahtsb oahbts oahbst oahsbt oahstb oabhts oabhst oabths
oabtsh oabsth oabsht oashbt oashtb oasbht oasbth oastbh oasthb otahbs otahsb
otabhs otabsh otasbh otashb othabs othasb othbas othbsa othsba othsab otbhas
otbhsa otbahs otbash otbsah otbsha otshba otshab otsbha otsbah otsabh otsahb
ohtabs ohtasb ohtbas ohtbsa ohtsba ohtsab ohatbs ohatsb ohabts ohabst ohasbt
ohastb ohbats ohbast ohbtas ohbtsa ohbsta ohbsat ohsabt ohsatb ohsbat ohsbta
ohstba ohstab obthas obthsa obtahs obtash obtsah obtsha obhtas obhtsa obhats
obhast obhsat obhsta obahts obahst obaths obatsh obasth obasht obshat obshta
obsaht obsath obstah obstha osthba osthab ostbha ostbah ostabh ostahb oshtba
oshtab oshbta oshbat oshabt oshatb osbhta osbhat osbtha osbtah osbath osbaht
osahbt osahtb osabht osabth osatbh osathb sathob sathbo satohb satobh satboh
satbho sahtob sahtbo sahotb sahobt sahbot sahbto saohtb saohbt saothb saotbh
saobth saobht sabhot sabhto saboht saboth sabtoh sabtho stahob stahbo staohb
staobh staboh stabho sthaob sthabo sthoab sthoba sthboa sthbao stohab stohba
stoahb stoabh stobah stobha stbhoa stbhao stboha stboah stbaoh stbaho shtaob
shtabo shtoab shtoba shtboa shtbao shatob shatbo shaotb shaobt shabot shabto
shoatb shoabt shotab shotba shobta shobat shbaot shbato shboat shbota shbtoa
shbtao sothab sothba sotahb sotabh sotbah sotbha sohtab sohtba sohatb sohabt
sohbat sohbta soahtb soahbt soathb soatbh soabth soabht sobhat sobhta sobaht
sobath sobtah sobtha sbthoa sbthao sbtoha sbtoah sbtaoh sbtaho sbhtoa sbhtao
sbhota sbhoat sbhaot sbhato sbohta sbohat sbotha sbotah sboath sboaht sbahot
sbahto sbaoht sbaoth sbatoh sbatho

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History of cryptography
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