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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: dosing
cipher variations:
eptjoh fqukpi grvlqj hswmrk itxnsl
juyotm kvzpun lwaqvo mxbrwp nycsxq
ozdtyr paeuzs qbfvat rcgwbu sdhxcv
teiydw ufjzex vgkafy whlbgz ximcha
yjndib zkoejc alpfkd bmqgle cnrhmf

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: dosing
Cipher: wlhrmt

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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: dosing

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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: dosing
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: dosing
Cipher: qbfvat

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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: dosing
Cipher: 414334423322

Extended Methods:
Method #1

Plaintext: dosing
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
d o s i n g 
4 4 3 4 3 2 
1 3 4 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: dosing
Cipher: tshlih

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Method #3

Plaintext: dosing
method variations:
qntmhr ntmhrq tmhrqn
mhrqnt hrqntm rqntmh

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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: dosing

all 720 cipher variations:
dosing dosign dosnig dosngi dosgni dosgin doisng doisgn doinsg doings doigns
doigsn donisg donigs donsig donsgi dongsi dongis dogins dogisn dognis dognsi
dogsni dogsin dsoing dsoign dsonig dsongi dsogni dsogin dsiong dsiogn dsinog
dsingo dsigno dsigon dsniog dsnigo dsnoig dsnogi dsngoi dsngio dsgino dsgion
dsgnio dsgnoi dsgoni dsgoin disong disogn disnog disngo disgno disgon diosng
diosgn dionsg diongs diogns diogsn dinosg dinogs dinsog dinsgo dingso dingos
digons digosn dignos dignso digsno digson dnsiog dnsigo dnsoig dnsogi dnsgoi
dnsgio dnisog dnisgo dniosg dniogs dnigos dnigso dnoisg dnoigs dnosig dnosgi
dnogsi dnogis dngios dngiso dngois dngosi dngsoi dngsio dgsino dgsion dgsnio
dgsnoi dgsoni dgsoin dgisno dgison dginso dginos dgions dgiosn dgniso dgnios
dgnsio dgnsoi dgnosi dgnois dgoins dgoisn dgonis dgonsi dgosni dgosin odsing
odsign odsnig odsngi odsgni odsgin odisng odisgn odinsg odings odigns odigsn
odnisg odnigs odnsig odnsgi odngsi odngis odgins odgisn odgnis odgnsi odgsni
odgsin osding osdign osdnig osdngi osdgni osdgin osidng osidgn osindg osingd
osignd osigdn osnidg osnigd osndig osndgi osngdi osngid osgind osgidn osgnid
osgndi osgdni osgdin oisdng oisdgn oisndg oisngd oisgnd oisgdn oidsng oidsgn
oidnsg oidngs oidgns oidgsn oindsg oindgs oinsdg oinsgd oingsd oingds oigdns
oigdsn oignds oignsd oigsnd oigsdn onsidg onsigd onsdig onsdgi onsgdi onsgid
onisdg onisgd onidsg onidgs onigds onigsd ondisg ondigs ondsig ondsgi ondgsi
ondgis ongids ongisd ongdis ongdsi ongsdi ongsid ogsind ogsidn ogsnid ogsndi
ogsdni ogsdin ogisnd ogisdn oginsd oginds ogidns ogidsn ognisd ognids ognsid
ognsdi ogndsi ogndis ogdins ogdisn ogdnis ogdnsi ogdsni ogdsin soding sodign
sodnig sodngi sodgni sodgin soidng soidgn soindg soingd soignd soigdn sonidg
sonigd sondig sondgi songdi songid sogind sogidn sognid sogndi sogdni sogdin
sdoing sdoign sdonig sdongi sdogni sdogin sdiong sdiogn sdinog sdingo sdigno
sdigon sdniog sdnigo sdnoig sdnogi sdngoi sdngio sdgino sdgion sdgnio sdgnoi
sdgoni sdgoin sidong sidogn sidnog sidngo sidgno sidgon siodng siodgn siondg
siongd siognd siogdn sinodg sinogd sindog sindgo singdo singod sigond sigodn
signod signdo sigdno sigdon sndiog sndigo sndoig sndogi sndgoi sndgio snidog
snidgo sniodg sniogd snigod snigdo snoidg snoigd snodig snodgi snogdi snogid
sngiod sngido sngoid sngodi sngdoi sngdio sgdino sgdion sgdnio sgdnoi sgdoni
sgdoin sgidno sgidon sgindo sginod sgiond sgiodn sgnido sgniod sgndio sgndoi
sgnodi sgnoid sgoind sgoidn sgonid sgondi sgodni sgodin iosdng iosdgn iosndg
iosngd iosgnd iosgdn iodsng iodsgn iodnsg iodngs iodgns iodgsn iondsg iondgs
ionsdg ionsgd iongsd iongds iogdns iogdsn iognds iognsd iogsnd iogsdn isodng
isodgn isondg isongd isognd isogdn isdong isdogn isdnog isdngo isdgno isdgon
isndog isndgo isnodg isnogd isngod isngdo isgdno isgdon isgndo isgnod isgond
isgodn idsong idsogn idsnog idsngo idsgno idsgon idosng idosgn idonsg idongs
idogns idogsn idnosg idnogs idnsog idnsgo idngso idngos idgons idgosn idgnos
idgnso idgsno idgson insdog insdgo insodg insogd insgod insgdo indsog indsgo
indosg indogs indgos indgso inodsg inodgs inosdg inosgd inogsd inogds ingdos
ingdso ingods ingosd ingsod ingsdo igsdno igsdon igsndo igsnod igsond igsodn
igdsno igdson igdnso igdnos igdons igdosn igndso igndos ignsdo ignsod ignosd
ignods igodns igodsn igonds igonsd igosnd igosdn nosidg nosigd nosdig nosdgi
nosgdi nosgid noisdg noisgd noidsg noidgs noigds noigsd nodisg nodigs nodsig
nodsgi nodgsi nodgis nogids nogisd nogdis nogdsi nogsdi nogsid nsoidg nsoigd
nsodig nsodgi nsogdi nsogid nsiodg nsiogd nsidog nsidgo nsigdo nsigod nsdiog
nsdigo nsdoig nsdogi nsdgoi nsdgio nsgido nsgiod nsgdio nsgdoi nsgodi nsgoid
nisodg nisogd nisdog nisdgo nisgdo nisgod niosdg niosgd niodsg niodgs niogds
niogsd nidosg nidogs nidsog nidsgo nidgso nidgos nigods nigosd nigdos nigdso
nigsdo nigsod ndsiog ndsigo ndsoig ndsogi ndsgoi ndsgio ndisog ndisgo ndiosg
ndiogs ndigos ndigso ndoisg ndoigs ndosig ndosgi ndogsi ndogis ndgios ndgiso
ndgois ndgosi ndgsoi ndgsio ngsido ngsiod ngsdio ngsdoi ngsodi ngsoid ngisdo
ngisod ngidso ngidos ngiods ngiosd ngdiso ngdios ngdsio ngdsoi ngdosi ngdois
ngoids ngoisd ngodis ngodsi ngosdi ngosid gosind gosidn gosnid gosndi gosdni
gosdin goisnd goisdn goinsd goinds goidns goidsn gonisd gonids gonsid gonsdi
gondsi gondis godins godisn godnis godnsi godsni godsin gsoind gsoidn gsonid
gsondi gsodni gsodin gsiond gsiodn gsinod gsindo gsidno gsidon gsniod gsnido
gsnoid gsnodi gsndoi gsndio gsdino gsdion gsdnio gsdnoi gsdoni gsdoin gisond
gisodn gisnod gisndo gisdno gisdon giosnd giosdn gionsd gionds giodns giodsn
ginosd ginods ginsod ginsdo gindso gindos gidons gidosn gidnos gidnso gidsno
gidson gnsiod gnsido gnsoid gnsodi gnsdoi gnsdio gnisod gnisdo gniosd gniods
gnidos gnidso gnoisd gnoids gnosid gnosdi gnodsi gnodis gndios gndiso gndois
gndosi gndsoi gndsio gdsino gdsion gdsnio gdsnoi gdsoni gdsoin gdisno gdison
gdinso gdinos gdions gdiosn gdniso gdnios gdnsio gdnsoi gdnosi gdnois gdoins
gdoisn gdonis gdonsi gdosni gdosin

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History of cryptography
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