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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: jaunty
cipher variations:
kbvouz lcwpva mdxqwb neyrxc ofzsyd
pgatze qhbuaf ricvbg sjdwch tkexdi
ulfyej vmgzfk wnhagl xoibhm ypjcin
zqkdjo arlekp bsmflq ctngmr duohns
evpiot fwqjpu gxrkqv hyslrw iztmsx

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: jaunty
Cipher: qzfmgb

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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: jaunty

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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: jaunty
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: jaunty
Cipher: wnhagl

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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: jaunty
Cipher: 421154334445

Extended Methods:
Method #1

Plaintext: jaunty
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
j a u n t y 
4 1 5 3 4 4 
2 1 4 3 4 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: jaunty
Cipher: dptboy

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Method #3

Plaintext: jaunty
method variations:
bvostu vostub ostubv
stubvo tubvos ubvost

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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: jaunty

all 720 cipher variations:
jaunty jaunyt jautny jautyn jauytn jauynt januty januyt jantuy jantyu janytu
janyut jatnuy jatnyu jatuny jatuyn jatyun jatynu jayntu jaynut jaytnu jaytun
jayutn jayunt juanty juanyt juatny juatyn juaytn juaynt junaty junayt juntay
juntya junyta junyat jutnay jutnya jutany jutayn jutyan jutyna juynta juynat
juytna juytan juyatn juyant jnuaty jnuayt jnutay jnutya jnuyta jnuyat jnauty
jnauyt jnatuy jnatyu jnaytu jnayut jntauy jntayu jntuay jntuya jntyua jntyau
jnyatu jnyaut jnytau jnytua jnyuta jnyuat jtunay jtunya jtuany jtuayn jtuyan
jtuyna jtnuay jtnuya jtnauy jtnayu jtnyau jtnyua jtanuy jtanyu jtauny jtauyn
jtayun jtaynu jtynau jtynua jtyanu jtyaun jtyuan jtyuna jyunta jyunat jyutna
jyutan jyuatn jyuant jynuta jynuat jyntua jyntau jynatu jynaut jytnua jytnau
jytuna jytuan jytaun jytanu jyantu jyanut jyatnu jyatun jyautn jyaunt ajunty
ajunyt ajutny ajutyn ajuytn ajuynt ajnuty ajnuyt ajntuy ajntyu ajnytu ajnyut
ajtnuy ajtnyu ajtuny ajtuyn ajtyun ajtynu ajyntu ajynut ajytnu ajytun ajyutn
ajyunt aujnty aujnyt aujtny aujtyn aujytn aujynt aunjty aunjyt auntjy auntyj
aunytj aunyjt autnjy autnyj autjny autjyn autyjn autynj auyntj auynjt auytnj
auytjn auyjtn auyjnt anujty anujyt anutjy anutyj anuytj anuyjt anjuty anjuyt
anjtuy anjtyu anjytu anjyut antjuy antjyu antujy antuyj antyuj antyju anyjtu
anyjut anytju anytuj anyutj anyujt atunjy atunyj atujny atujyn atuyjn atuynj
atnujy atnuyj atnjuy atnjyu atnyju atnyuj atjnuy atjnyu atjuny atjuyn atjyun
atjynu atynju atynuj atyjnu atyjun atyujn atyunj ayuntj ayunjt ayutnj ayutjn
ayujtn ayujnt aynutj aynujt ayntuj ayntju aynjtu aynjut aytnuj aytnju aytunj
aytujn aytjun aytjnu ayjntu ayjnut ayjtnu ayjtun ayjutn ayjunt uajnty uajnyt
uajtny uajtyn uajytn uajynt uanjty uanjyt uantjy uantyj uanytj uanyjt uatnjy
uatnyj uatjny uatjyn uatyjn uatynj uayntj uaynjt uaytnj uaytjn uayjtn uayjnt
ujanty ujanyt ujatny ujatyn ujaytn ujaynt ujnaty ujnayt ujntay ujntya ujnyta
ujnyat ujtnay ujtnya ujtany ujtayn ujtyan ujtyna ujynta ujynat ujytna ujytan
ujyatn ujyant unjaty unjayt unjtay unjtya unjyta unjyat unajty unajyt unatjy
unatyj unaytj unayjt untajy untayj untjay untjya untyja untyaj unyatj unyajt
unytaj unytja unyjta unyjat utjnay utjnya utjany utjayn utjyan utjyna utnjay
utnjya utnajy utnayj utnyaj utnyja utanjy utanyj utajny utajyn utayjn utaynj
utynaj utynja utyanj utyajn utyjan utyjna uyjnta uyjnat uyjtna uyjtan uyjatn
uyjant uynjta uynjat uyntja uyntaj uynatj uynajt uytnja uytnaj uytjna uytjan
uytajn uytanj uyantj uyanjt uyatnj uyatjn uyajtn uyajnt naujty naujyt nautjy
nautyj nauytj nauyjt najuty najuyt najtuy najtyu najytu najyut natjuy natjyu
natujy natuyj natyuj natyju nayjtu nayjut naytju naytuj nayutj nayujt nuajty
nuajyt nuatjy nuatyj nuaytj nuayjt nujaty nujayt nujtay nujtya nujyta nujyat
nutjay nutjya nutajy nutayj nutyaj nutyja nuyjta nuyjat nuytja nuytaj nuyatj
nuyajt njuaty njuayt njutay njutya njuyta njuyat njauty njauyt njatuy njatyu
njaytu njayut njtauy njtayu njtuay njtuya njtyua njtyau njyatu njyaut njytau
njytua njyuta njyuat ntujay ntujya ntuajy ntuayj ntuyaj ntuyja ntjuay ntjuya
ntjauy ntjayu ntjyau ntjyua ntajuy ntajyu ntaujy ntauyj ntayuj ntayju ntyjau
ntyjua ntyaju ntyauj ntyuaj ntyuja nyujta nyujat nyutja nyutaj nyuatj nyuajt
nyjuta nyjuat nyjtua nyjtau nyjatu nyjaut nytjua nytjau nytuja nytuaj nytauj
nytaju nyajtu nyajut nyatju nyatuj nyautj nyaujt taunjy taunyj taujny taujyn
tauyjn tauynj tanujy tanuyj tanjuy tanjyu tanyju tanyuj tajnuy tajnyu tajuny
tajuyn tajyun tajynu taynju taynuj tayjnu tayjun tayujn tayunj tuanjy tuanyj
tuajny tuajyn tuayjn tuaynj tunajy tunayj tunjay tunjya tunyja tunyaj tujnay
tujnya tujany tujayn tujyan tujyna tuynja tuynaj tuyjna tuyjan tuyajn tuyanj
tnuajy tnuayj tnujay tnujya tnuyja tnuyaj tnaujy tnauyj tnajuy tnajyu tnayju
tnayuj tnjauy tnjayu tnjuay tnjuya tnjyua tnjyau tnyaju tnyauj tnyjau tnyjua
tnyuja tnyuaj tjunay tjunya tjuany tjuayn tjuyan tjuyna tjnuay tjnuya tjnauy
tjnayu tjnyau tjnyua tjanuy tjanyu tjauny tjauyn tjayun tjaynu tjynau tjynua
tjyanu tjyaun tjyuan tjyuna tyunja tyunaj tyujna tyujan tyuajn tyuanj tynuja
tynuaj tynjua tynjau tynaju tynauj tyjnua tyjnau tyjuna tyjuan tyjaun tyjanu
tyanju tyanuj tyajnu tyajun tyaujn tyaunj yauntj yaunjt yautnj yautjn yaujtn
yaujnt yanutj yanujt yantuj yantju yanjtu yanjut yatnuj yatnju yatunj yatujn
yatjun yatjnu yajntu yajnut yajtnu yajtun yajutn yajunt yuantj yuanjt yuatnj
yuatjn yuajtn yuajnt yunatj yunajt yuntaj yuntja yunjta yunjat yutnaj yutnja
yutanj yutajn yutjan yutjna yujnta yujnat yujtna yujtan yujatn yujant ynuatj
ynuajt ynutaj ynutja ynujta ynujat ynautj ynaujt ynatuj ynatju ynajtu ynajut
yntauj yntaju yntuaj yntuja yntjua yntjau ynjatu ynjaut ynjtau ynjtua ynjuta
ynjuat ytunaj ytunja ytuanj ytuajn ytujan ytujna ytnuaj ytnuja ytnauj ytnaju
ytnjau ytnjua ytanuj ytanju ytaunj ytaujn ytajun ytajnu ytjnau ytjnua ytjanu
ytjaun ytjuan ytjuna yjunta yjunat yjutna yjutan yjuatn yjuant yjnuta yjnuat
yjntua yjntau yjnatu yjnaut yjtnua yjtnau yjtuna yjtuan yjtaun yjtanu yjantu
yjanut yjatnu yjatun yjautn yjaunt

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History of cryptography
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