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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: torine
cipher variations:
upsjof vqtkpg wrulqh xsvmri ytwnsj
zuxotk avypul bwzqvm cxarwn dybsxo
ezctyp faduzq gbevar hcfwbs idgxct
jehydu kfizev lgjafw mhkbgx nilchy
ojmdiz pkneja qlofkb rmpglc snqhmd

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: torine
Cipher: glirmv

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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: torine

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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: torine
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: torine
Cipher: gbevar

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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: torine
Cipher: 444324423351

Extended Methods:
Method #1

Plaintext: torine
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
t o r i n e 
4 4 2 4 3 5 
4 3 4 2 3 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: torine
Cipher: trxoic

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Method #3

Plaintext: torine
method variations:
thtmxq htmxqt tmxqth
mxqtht xqthtm qthtmx

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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: torine

all 720 cipher variations:
torine torien tornie tornei toreni torein toirne toiren toinre toiner toienr
toiern tonire tonier tonrie tonrei toneri toneir toeinr toeirn toenir toenri
toerni toerin troine troien tronie tronei troeni troein trione trioen trinoe
trineo trieno trieon trnioe trnieo trnoie trnoei trneoi trneio treino treion
trenio trenoi treoni treoin tirone tiroen tirnoe tirneo tireno tireon tiorne
tioren tionre tioner tioenr tioern tinore tinoer tinroe tinreo tinero tineor
tieonr tieorn tienor tienro tierno tieron tnrioe tnrieo tnroie tnroei tnreoi
tnreio tniroe tnireo tniore tnioer tnieor tniero tnoire tnoier tnorie tnorei
tnoeri tnoeir tneior tneiro tneoir tneori tneroi tnerio terino terion ternio
ternoi teroni teroin teirno teiron teinro teinor teionr teiorn teniro tenior
tenrio tenroi tenori tenoir teoinr teoirn teonir teonri teorni teorin otrine
otrien otrnie otrnei otreni otrein otirne otiren otinre otiner otienr otiern
otnire otnier otnrie otnrei otneri otneir oteinr oteirn otenir otenri oterni
oterin ortine ortien ortnie ortnei orteni ortein oritne oriten orinte orinet
orient orietn ornite orniet orntie orntei orneti orneit oreint oreitn orenit
orenti oretni oretin oirtne oirten oirnte oirnet oirent oiretn oitrne oitren
oitnre oitner oitenr oitern ointre ointer oinrte oinret oinert oinetr oietnr
oietrn oientr oienrt oiernt oiertn onrite onriet onrtie onrtei onreti onreit
onirte oniret onitre oniter onietr oniert ontire ontier ontrie ontrei onteri
onteir oneitr oneirt onetir onetri onerti onerit oerint oeritn oernit oernti
oertni oertin oeirnt oeirtn oeinrt oeintr oeitnr oeitrn oenirt oenitr oenrit
oenrti oentri oentir oetinr oetirn oetnir oetnri oetrni oetrin rotine rotien
rotnie rotnei roteni rotein roitne roiten rointe roinet roient roietn ronite
roniet rontie rontei roneti roneit roeint roeitn roenit roenti roetni roetin
rtoine rtoien rtonie rtonei rtoeni rtoein rtione rtioen rtinoe rtineo rtieno
rtieon rtnioe rtnieo rtnoie rtnoei rtneoi rtneio rteino rteion rtenio rtenoi
rteoni rteoin ritone ritoen ritnoe ritneo riteno riteon riotne rioten rionte
rionet rioent rioetn rinote rinoet rintoe rinteo rineto rineot rieont rieotn
rienot riento rietno rieton rntioe rntieo rntoie rntoei rnteoi rnteio rnitoe
rniteo rniote rnioet rnieot rnieto rnoite rnoiet rnotie rnotei rnoeti rnoeit
rneiot rneito rneoit rneoti rnetoi rnetio retino retion retnio retnoi retoni
retoin reitno reiton reinto reinot reiont reiotn renito reniot rentio rentoi
renoti renoit reoint reoitn reonit reonti reotni reotin iortne iorten iornte
iornet iorent ioretn iotrne iotren iotnre iotner iotenr iotern iontre ionter
ionrte ionret ionert ionetr ioetnr ioetrn ioentr ioenrt ioernt ioertn irotne
iroten ironte ironet iroent iroetn irtone irtoen irtnoe irtneo irteno irteon
irntoe irnteo irnote irnoet irneot irneto iretno ireton irento irenot ireont
ireotn itrone itroen itrnoe itrneo itreno itreon itorne itoren itonre itoner
itoenr itoern itnore itnoer itnroe itnreo itnero itneor iteonr iteorn itenor
itenro iterno iteron inrtoe inrteo inrote inroet inreot inreto introe intreo
intore intoer inteor intero inotre inoter inorte inoret inoert inoetr inetor
inetro ineotr ineort inerot inerto iertno ierton iernto iernot ieront ierotn
ietrno ietron ietnro ietnor ietonr ietorn ientro ientor ienrto ienrot ienort
ienotr ieotnr ieotrn ieontr ieonrt ieornt ieortn norite noriet nortie nortei
noreti noreit noirte noiret noitre noiter noietr noiert notire notier notrie
notrei noteri noteir noeitr noeirt noetir noetri noerti noerit nroite nroiet
nrotie nrotei nroeti nroeit nriote nrioet nritoe nriteo nrieto nrieot nrtioe
nrtieo nrtoie nrtoei nrteoi nrteio nreito nreiot nretio nretoi nreoti nreoit
nirote niroet nirtoe nirteo nireto nireot niorte nioret niotre nioter nioetr
nioert nitore nitoer nitroe nitreo nitero niteor nieotr nieort nietor nietro
nierto nierot ntrioe ntrieo ntroie ntroei ntreoi ntreio ntiroe ntireo ntiore
ntioer ntieor ntiero ntoire ntoier ntorie ntorei ntoeri ntoeir nteior nteiro
nteoir nteori nteroi nterio nerito neriot nertio nertoi neroti neroit neirto
neirot neitro neitor neiotr neiort netiro netior netrio netroi netori netoir
neoitr neoirt neotir neotri neorti neorit eorint eoritn eornit eornti eortni
eortin eoirnt eoirtn eoinrt eointr eoitnr eoitrn eonirt eonitr eonrit eonrti
eontri eontir eotinr eotirn eotnir eotnri eotrni eotrin eroint eroitn eronit
eronti erotni erotin eriont eriotn erinot erinto eritno eriton erniot ernito
ernoit ernoti erntoi erntio ertino ertion ertnio ertnoi ertoni ertoin eiront
eirotn eirnot eirnto eirtno eirton eiornt eiortn eionrt eiontr eiotnr eiotrn
einort einotr einrot einrto eintro eintor eitonr eitorn eitnor eitnro eitrno
eitron enriot enrito enroit enroti enrtoi enrtio enirot enirto eniort eniotr
enitor enitro enoirt enoitr enorit enorti enotri enotir entior entiro entoir
entori entroi entrio etrino etrion etrnio etrnoi etroni etroin etirno etiron
etinro etinor etionr etiorn etniro etnior etnrio etnroi etnori etnoir etoinr
etoirn etonir etonri etorni etorin

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History of cryptography
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