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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: loving
cipher variations:
mpwjoh nqxkpi orylqj pszmrk qtansl
rubotm svcpun twdqvo uxerwp vyfsxq
wzgtyr xahuzs ybivat zcjwbu adkxcv
belydw cfmzex dgnafy ehobgz fipcha
gjqdib hkrejc ilsfkd jmtgle knuhmf

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: loving
Cipher: olermt

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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: loving

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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: loving
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: loving
Cipher: ybivat

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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: loving
Cipher: 134315423322

Extended Methods:
Method #1

Plaintext: loving
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
l o v i n g 
1 4 1 4 3 2 
3 3 5 2 3 2 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: loving
Cipher: qqhnkh

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Method #3

Plaintext: loving
method variations:
scumhb cumhbs umhbsc
mhbscu hbscum bscumh

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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: loving

all 720 cipher variations:
loving lovign lovnig lovngi lovgni lovgin loivng loivgn loinvg loingv loignv
loigvn lonivg lonigv lonvig lonvgi longvi longiv loginv logivn logniv lognvi
logvni logvin lvoing lvoign lvonig lvongi lvogni lvogin lviong lviogn lvinog
lvingo lvigno lvigon lvniog lvnigo lvnoig lvnogi lvngoi lvngio lvgino lvgion
lvgnio lvgnoi lvgoni lvgoin livong livogn livnog livngo livgno livgon liovng
liovgn lionvg liongv liognv liogvn linovg linogv linvog linvgo lingvo lingov
ligonv ligovn lignov lignvo ligvno ligvon lnviog lnvigo lnvoig lnvogi lnvgoi
lnvgio lnivog lnivgo lniovg lniogv lnigov lnigvo lnoivg lnoigv lnovig lnovgi
lnogvi lnogiv lngiov lngivo lngoiv lngovi lngvoi lngvio lgvino lgvion lgvnio
lgvnoi lgvoni lgvoin lgivno lgivon lginvo lginov lgionv lgiovn lgnivo lgniov
lgnvio lgnvoi lgnovi lgnoiv lgoinv lgoivn lgoniv lgonvi lgovni lgovin olving
olvign olvnig olvngi olvgni olvgin olivng olivgn olinvg olingv olignv oligvn
olnivg olnigv olnvig olnvgi olngvi olngiv olginv olgivn olgniv olgnvi olgvni
olgvin ovling ovlign ovlnig ovlngi ovlgni ovlgin ovilng ovilgn ovinlg ovingl
ovignl ovigln ovnilg ovnigl ovnlig ovnlgi ovngli ovngil ovginl ovgiln ovgnil
ovgnli ovglni ovglin oivlng oivlgn oivnlg oivngl oivgnl oivgln oilvng oilvgn
oilnvg oilngv oilgnv oilgvn oinlvg oinlgv oinvlg oinvgl oingvl oinglv oiglnv
oiglvn oignlv oignvl oigvnl oigvln onvilg onvigl onvlig onvlgi onvgli onvgil
onivlg onivgl onilvg onilgv oniglv onigvl onlivg onligv onlvig onlvgi onlgvi
onlgiv ongilv ongivl ongliv onglvi ongvli ongvil ogvinl ogviln ogvnil ogvnli
ogvlni ogvlin ogivnl ogivln oginvl oginlv ogilnv ogilvn ognivl ognilv ognvil
ognvli ognlvi ognliv oglinv oglivn oglniv oglnvi oglvni oglvin voling volign
volnig volngi volgni volgin voilng voilgn voinlg voingl voignl voigln vonilg
vonigl vonlig vonlgi vongli vongil voginl vogiln vognil vognli voglni voglin
vloing vloign vlonig vlongi vlogni vlogin vliong vliogn vlinog vlingo vligno
vligon vlniog vlnigo vlnoig vlnogi vlngoi vlngio vlgino vlgion vlgnio vlgnoi
vlgoni vlgoin vilong vilogn vilnog vilngo vilgno vilgon violng violgn vionlg
viongl viognl viogln vinolg vinogl vinlog vinlgo vinglo vingol vigonl vigoln
vignol vignlo viglno viglon vnliog vnligo vnloig vnlogi vnlgoi vnlgio vnilog
vnilgo vniolg vniogl vnigol vniglo vnoilg vnoigl vnolig vnolgi vnogli vnogil
vngiol vngilo vngoil vngoli vngloi vnglio vglino vglion vglnio vglnoi vgloni
vgloin vgilno vgilon vginlo vginol vgionl vgioln vgnilo vgniol vgnlio vgnloi
vgnoli vgnoil vgoinl vgoiln vgonil vgonli vgolni vgolin iovlng iovlgn iovnlg
iovngl iovgnl iovgln iolvng iolvgn iolnvg iolngv iolgnv iolgvn ionlvg ionlgv
ionvlg ionvgl iongvl ionglv ioglnv ioglvn iognlv iognvl iogvnl iogvln ivolng
ivolgn ivonlg ivongl ivognl ivogln ivlong ivlogn ivlnog ivlngo ivlgno ivlgon
ivnlog ivnlgo ivnolg ivnogl ivngol ivnglo ivglno ivglon ivgnlo ivgnol ivgonl
ivgoln ilvong ilvogn ilvnog ilvngo ilvgno ilvgon ilovng ilovgn ilonvg ilongv
ilognv ilogvn ilnovg ilnogv ilnvog ilnvgo ilngvo ilngov ilgonv ilgovn ilgnov
ilgnvo ilgvno ilgvon invlog invlgo involg invogl invgol invglo inlvog inlvgo
inlovg inlogv inlgov inlgvo inolvg inolgv inovlg inovgl inogvl inoglv inglov
inglvo ingolv ingovl ingvol ingvlo igvlno igvlon igvnlo igvnol igvonl igvoln
iglvno iglvon iglnvo iglnov iglonv iglovn ignlvo ignlov ignvlo ignvol ignovl
ignolv igolnv igolvn igonlv igonvl igovnl igovln novilg novigl novlig novlgi
novgli novgil noivlg noivgl noilvg noilgv noiglv noigvl nolivg noligv nolvig
nolvgi nolgvi nolgiv nogilv nogivl nogliv noglvi nogvli nogvil nvoilg nvoigl
nvolig nvolgi nvogli nvogil nviolg nviogl nvilog nvilgo nviglo nvigol nvliog
nvligo nvloig nvlogi nvlgoi nvlgio nvgilo nvgiol nvglio nvgloi nvgoli nvgoil
nivolg nivogl nivlog nivlgo nivglo nivgol niovlg niovgl niolvg niolgv nioglv
niogvl nilovg nilogv nilvog nilvgo nilgvo nilgov nigolv nigovl niglov niglvo
nigvlo nigvol nlviog nlvigo nlvoig nlvogi nlvgoi nlvgio nlivog nlivgo nliovg
nliogv nligov nligvo nloivg nloigv nlovig nlovgi nlogvi nlogiv nlgiov nlgivo
nlgoiv nlgovi nlgvoi nlgvio ngvilo ngviol ngvlio ngvloi ngvoli ngvoil ngivlo
ngivol ngilvo ngilov ngiolv ngiovl nglivo ngliov nglvio nglvoi nglovi ngloiv
ngoilv ngoivl ngoliv ngolvi ngovli ngovil govinl goviln govnil govnli govlni
govlin goivnl goivln goinvl goinlv goilnv goilvn gonivl gonilv gonvil gonvli
gonlvi gonliv golinv golivn golniv golnvi golvni golvin gvoinl gvoiln gvonil
gvonli gvolni gvolin gvionl gvioln gvinol gvinlo gvilno gvilon gvniol gvnilo
gvnoil gvnoli gvnloi gvnlio gvlino gvlion gvlnio gvlnoi gvloni gvloin givonl
givoln givnol givnlo givlno givlon giovnl giovln gionvl gionlv giolnv giolvn
ginovl ginolv ginvol ginvlo ginlvo ginlov gilonv gilovn gilnov gilnvo gilvno
gilvon gnviol gnvilo gnvoil gnvoli gnvloi gnvlio gnivol gnivlo gniovl gniolv
gnilov gnilvo gnoivl gnoilv gnovil gnovli gnolvi gnoliv gnliov gnlivo gnloiv
gnlovi gnlvoi gnlvio glvino glvion glvnio glvnoi glvoni glvoin glivno glivon
glinvo glinov glionv gliovn glnivo glniov glnvio glnvoi glnovi glnoiv gloinv
gloivn gloniv glonvi glovni glovin

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History of cryptography
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