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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: tailge
cipher variations:
ubjmhf vcknig wdlojh xempki yfnqlj
zgormk ahpsnl biqtom cjrupn dksvqo
eltwrp fmuxsq gnvytr howzus ipxavt
jqybwu krzcxv lsadyw mtbezx nucfay
ovdgbz pwehca qxfidb rygjec szhkfd

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: tailge
Cipher: gzrotv

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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: tailge

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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: tailge
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: tailge
Cipher: gnvytr

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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: tailge
Cipher: 441142132251

Extended Methods:
Method #1

Plaintext: tailge
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
t a i l g e 
4 1 4 1 2 5 
4 1 2 3 2 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: tailge
Cipher: ddwdmb

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Method #3

Plaintext: tailge
method variations:
dqbhwq qbhwqd bhwqdq
hwqdqb wqdqbh qdqbhw

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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: tailge

all 720 cipher variations:
tailge taileg taigle taigel taiegl taielg talige talieg talgie talgei talegi
taleig taglie taglei tagile tagiel tageil tageli taelgi taelig taegli taegil
taeigl taeilg tialge tialeg tiagle tiagel tiaegl tiaelg tilage tilaeg tilgae
tilgea tilega tileag tiglae tiglea tigale tigael tigeal tigela tielga tielag
tiegla tiegal tieagl tiealg tliage tliaeg tligae tligea tliega tlieag tlaige
tlaieg tlagie tlagei tlaegi tlaeig tlgaie tlgaei tlgiae tlgiea tlgeia tlgeai
tleagi tleaig tlegai tlegia tleiga tleiag tgilae tgilea tgiale tgiael tgieal
tgiela tgliae tgliea tglaie tglaei tgleai tgleia tgalie tgalei tgaile tgaiel
tgaeil tgaeli tgelai tgelia tgeali tgeail tgeial tgeila teilga teilag teigla
teigal teiagl teialg teliga teliag telgia telgai telagi telaig teglia teglai
tegila tegial tegail tegali tealgi tealig teagli teagil teaigl teailg atilge
atileg atigle atigel atiegl atielg atlige atlieg atlgie atlgei atlegi atleig
atglie atglei atgile atgiel atgeil atgeli atelgi atelig ategli ategil ateigl
ateilg aitlge aitleg aitgle aitgel aitegl aitelg ailtge ailteg ailgte ailget
ailegt ailetg aiglte aiglet aigtle aigtel aigetl aigelt aielgt aieltg aieglt
aiegtl aietgl aietlg alitge aliteg aligte aliget aliegt alietg altige altieg
altgie altgei altegi alteig algtie algtei algite algiet algeit algeti aletgi
aletig alegti alegit aleigt aleitg agilte agilet agitle agitel agietl agielt
aglite agliet agltie agltei agleti agleit agtlie agtlei agtile agtiel agteil
agteli agelti agelit agetli agetil ageitl ageilt aeilgt aeiltg aeiglt aeigtl
aeitgl aeitlg aeligt aelitg aelgit aelgti aeltgi aeltig aeglit aeglti aegilt
aegitl aegtil aegtli aetlgi aetlig aetgli aetgil aetigl aetilg iatlge iatleg
iatgle iatgel iategl iatelg ialtge ialteg ialgte ialget ialegt ialetg iaglte
iaglet iagtle iagtel iagetl iagelt iaelgt iaeltg iaeglt iaegtl iaetgl iaetlg
italge italeg itagle itagel itaegl itaelg itlage itlaeg itlgae itlgea itlega
itleag itglae itglea itgale itgael itgeal itgela itelga itelag itegla itegal
iteagl itealg iltage iltaeg iltgae iltgea iltega ilteag ilatge ilateg ilagte
ilaget ilaegt ilaetg ilgate ilgaet ilgtae ilgtea ilgeta ilgeat ileagt ileatg
ilegat ilegta iletga iletag igtlae igtlea igtale igtael igteal igtela igltae
igltea iglate iglaet igleat igleta igalte igalet igatle igatel igaetl igaelt
igelat igelta igealt igeatl igetal igetla ietlga ietlag ietgla ietgal ietagl
ietalg ieltga ieltag ielgta ielgat ielagt ielatg ieglta ieglat iegtla iegtal
iegatl iegalt iealgt iealtg ieaglt ieagtl ieatgl ieatlg laitge laiteg laigte
laiget laiegt laietg latige latieg latgie latgei lategi lateig lagtie lagtei
lagite lagiet lageit lageti laetgi laetig laegti laegit laeigt laeitg liatge
liateg liagte liaget liaegt liaetg litage litaeg litgae litgea litega liteag
ligtae ligtea ligate ligaet ligeat ligeta lietga lietag liegta liegat lieagt
lieatg ltiage ltiaeg ltigae ltigea ltiega ltieag ltaige ltaieg ltagie ltagei
ltaegi ltaeig ltgaie ltgaei ltgiae ltgiea ltgeia ltgeai lteagi lteaig ltegai
ltegia lteiga lteiag lgitae lgitea lgiate lgiaet lgieat lgieta lgtiae lgtiea
lgtaie lgtaei lgteai lgteia lgatie lgatei lgaite lgaiet lgaeit lgaeti lgetai
lgetia lgeati lgeait lgeiat lgeita leitga leitag leigta leigat leiagt leiatg
letiga letiag letgia letgai letagi letaig legtia legtai legita legiat legait
legati leatgi leatig leagti leagit leaigt leaitg gailte gailet gaitle gaitel
gaietl gaielt galite galiet galtie galtei galeti galeit gatlie gatlei gatile
gatiel gateil gateli gaelti gaelit gaetli gaetil gaeitl gaeilt gialte gialet
giatle giatel giaetl giaelt gilate gilaet giltae giltea gileta gileat gitlae
gitlea gitale gitael giteal gitela gielta gielat gietla gietal gieatl giealt
gliate gliaet glitae glitea glieta glieat glaite glaiet glatie glatei glaeti
glaeit gltaie gltaei gltiae gltiea glteia glteai gleati gleait gletai gletia
gleita gleiat gtilae gtilea gtiale gtiael gtieal gtiela gtliae gtliea gtlaie
gtlaei gtleai gtleia gtalie gtalei gtaile gtaiel gtaeil gtaeli gtelai gtelia
gteali gteail gteial gteila geilta geilat geitla geital geiatl geialt gelita
geliat geltia geltai gelati gelait getlia getlai getila getial getail getali
gealti gealit geatli geatil geaitl geailt eailgt eailtg eaiglt eaigtl eaitgl
eaitlg ealigt ealitg ealgit ealgti ealtgi ealtig eaglit eaglti eagilt eagitl
eagtil eagtli eatlgi eatlig eatgli eatgil eatigl eatilg eialgt eialtg eiaglt
eiagtl eiatgl eiatlg eilagt eilatg eilgat eilgta eiltga eiltag eiglat eiglta
eigalt eigatl eigtal eigtla eitlga eitlag eitgla eitgal eitagl eitalg eliagt
eliatg eligat eligta elitga elitag elaigt elaitg elagit elagti elatgi elatig
elgait elgati elgiat elgita elgtia elgtai eltagi eltaig eltgai eltgia eltiga
eltiag egilat egilta egialt egiatl egital egitla egliat eglita eglait eglati
egltai egltia egalit egalti egailt egaitl egatil egatli egtlai egtlia egtali
egtail egtial egtila etilga etilag etigla etigal etiagl etialg etliga etliag
etlgia etlgai etlagi etlaig etglia etglai etgila etgial etgail etgali etalgi
etalig etagli etagil etaigl etailg

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History of cryptography
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