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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: vicaea
cipher variations:
wjdbfb xkecgc ylfdhd zmgeie anhfjf
boigkg cpjhlh dqkimi erljnj fsmkok
gtnlpl huomqm ivpnrn jwqoso kxrptp
lysquq mztrvr nausws obvtxt pcwuyu
qdxvzv reywaw sfzxbx tgaycy uhbzdz

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: vicaea
Cipher: erxzvz

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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: vicaea

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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: vicaea
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: vicaea
Cipher: ivpnrn

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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: vicaea
Cipher: 154231115111

Extended Methods:
Method #1

Plaintext: vicaea
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
v i c a e a 
1 4 3 1 5 1 
5 2 1 1 1 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: vicaea
Cipher: qcekaa

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Method #3

Plaintext: vicaea
method variations:
umavaa mavaau avaaum
vaauma aaumav aumava

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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: vicaea

all 720 cipher variations:
vicaea vicaae viceaa viceaa vicaea vicaae viacea viacae viaeca viaeac viaaec
viaace vieaca vieaac viecaa viecaa vieaca vieaac viaaec viaace viaeac viaeca
viacea viacae vciaea vciaae vcieaa vcieaa vciaea vciaae vcaiea vcaiae vcaeia
vcaeai vcaaei vcaaie vceaia vceaai vceiaa vceiaa vceaia vceaai vcaaei vcaaie
vcaeai vcaeia vcaiea vcaiae vaciea vaciae vaceia vaceai vacaei vacaie vaicea
vaicae vaieca vaieac vaiaec vaiace vaeica vaeiac vaecia vaecai vaeaci vaeaic
vaaiec vaaice vaaeic vaaeci vaacei vaacie vecaia vecaai veciaa veciaa vecaia
vecaai veacia veacai veaica veaiac veaaic veaaci veiaca veiaac veicaa veicaa
veiaca veiaac veaaic veaaci veaiac veaica veacia veacai vacaei vacaie vaceai
vaceia vaciea vaciae vaacei vaacie vaaeci vaaeic vaaiec vaaice vaeaci vaeaic
vaecai vaecia vaeica vaeiac vaiaec vaiace vaieac vaieca vaicea vaicae ivcaea
ivcaae ivceaa ivceaa ivcaea ivcaae ivacea ivacae ivaeca ivaeac ivaaec ivaace
iveaca iveaac ivecaa ivecaa iveaca iveaac ivaaec ivaace ivaeac ivaeca ivacea
ivacae icvaea icvaae icveaa icveaa icvaea icvaae icavea icavae icaeva icaeav
icaaev icaave iceava iceaav icevaa icevaa iceava iceaav icaaev icaave icaeav
icaeva icavea icavae iacvea iacvae iaceva iaceav iacaev iacave iavcea iavcae
iaveca iaveac iavaec iavace iaevca iaevac iaecva iaecav iaeacv iaeavc iaavec
iaavce iaaevc iaaecv iaacev iaacve iecava iecaav iecvaa iecvaa iecava iecaav
ieacva ieacav ieavca ieavac ieaavc ieaacv ievaca ievaac ievcaa ievcaa ievaca
ievaac ieaavc ieaacv ieavac ieavca ieacva ieacav iacaev iacave iaceav iaceva
iacvea iacvae iaacev iaacve iaaecv iaaevc iaavec iaavce iaeacv iaeavc iaecav
iaecva iaevca iaevac iavaec iavace iaveac iaveca iavcea iavcae civaea civaae
civeaa civeaa civaea civaae ciavea ciavae ciaeva ciaeav ciaaev ciaave cieava
cieaav cievaa cievaa cieava cieaav ciaaev ciaave ciaeav ciaeva ciavea ciavae
cviaea cviaae cvieaa cvieaa cviaea cviaae cvaiea cvaiae cvaeia cvaeai cvaaei
cvaaie cveaia cveaai cveiaa cveiaa cveaia cveaai cvaaei cvaaie cvaeai cvaeia
cvaiea cvaiae caviea caviae caveia caveai cavaei cavaie caivea caivae caieva
caieav caiaev caiave caeiva caeiav caevia caevai caeavi caeaiv caaiev caaive
caaeiv caaevi caavei caavie cevaia cevaai ceviaa ceviaa cevaia cevaai ceavia
ceavai ceaiva ceaiav ceaaiv ceaavi ceiava ceiaav ceivaa ceivaa ceiava ceiaav
ceaaiv ceaavi ceaiav ceaiva ceavia ceavai cavaei cavaie caveai caveia caviea
caviae caavei caavie caaevi caaeiv caaiev caaive caeavi caeaiv caevai caevia
caeiva caeiav caiaev caiave caieav caieva caivea caivae aicvea aicvae aiceva
aiceav aicaev aicave aivcea aivcae aiveca aiveac aivaec aivace aievca aievac
aiecva aiecav aieacv aieavc aiavec aiavce aiaevc aiaecv aiacev aiacve acivea
acivae acieva acieav aciaev aciave acviea acviae acveia acveai acvaei acvaie
acevia acevai aceiva aceiav aceaiv aceavi acavei acavie acaevi acaeiv acaiev
acaive avciea avciae avceia avceai avcaei avcaie avicea avicae avieca avieac
aviaec aviace aveica aveiac avecia avecai aveaci aveaic avaiec avaice avaeic
avaeci avacei avacie aecvia aecvai aeciva aeciav aecaiv aecavi aevcia aevcai
aevica aeviac aevaic aevaci aeivca aeivac aeicva aeicav aeiacv aeiavc aeavic
aeavci aeaivc aeaicv aeaciv aeacvi aacvei aacvie aacevi aaceiv aaciev aacive
aavcei aavcie aaveci aaveic aaviec aavice aaevci aaevic aaecvi aaeciv aaeicv
aaeivc aaivec aaivce aaievc aaiecv aaicev aaicve eicava eicaav eicvaa eicvaa
eicava eicaav eiacva eiacav eiavca eiavac eiaavc eiaacv eivaca eivaac eivcaa
eivcaa eivaca eivaac eiaavc eiaacv eiavac eiavca eiacva eiacav eciava eciaav
ecivaa ecivaa eciava eciaav ecaiva ecaiav ecavia ecavai ecaavi ecaaiv ecvaia
ecvaai ecviaa ecviaa ecvaia ecvaai ecaavi ecaaiv ecavai ecavia ecaiva ecaiav
eaciva eaciav eacvia eacvai eacavi eacaiv eaicva eaicav eaivca eaivac eaiavc
eaiacv eavica eaviac eavcia eavcai eavaci eavaic eaaivc eaaicv eaavic eaavci
eaacvi eaaciv evcaia evcaai evciaa evciaa evcaia evcaai evacia evacai evaica
evaiac evaaic evaaci eviaca eviaac evicaa evicaa eviaca eviaac evaaic evaaci
evaiac evaica evacia evacai eacavi eacaiv eacvai eacvia eaciva eaciav eaacvi
eaaciv eaavci eaavic eaaivc eaaicv eavaci eavaic eavcai eavcia eavica eaviac
eaiavc eaiacv eaivac eaivca eaicva eaicav aicaev aicave aiceav aiceva aicvea
aicvae aiacev aiacve aiaecv aiaevc aiavec aiavce aieacv aieavc aiecav aiecva
aievca aievac aivaec aivace aiveac aiveca aivcea aivcae aciaev aciave acieav
acieva acivea acivae acaiev acaive acaeiv acaevi acavei acavie aceaiv aceavi
aceiav aceiva acevia acevai acvaei acvaie acveai acveia acviea acviae aaciev
aacive aaceiv aacevi aacvei aacvie aaicev aaicve aaiecv aaievc aaivec aaivce
aaeicv aaeivc aaeciv aaecvi aaevci aaevic aaviec aavice aaveic aaveci aavcei
aavcie aecaiv aecavi aeciav aeciva aecvia aecvai aeaciv aeacvi aeaicv aeaivc
aeavic aeavci aeiacv aeiavc aeicav aeicva aeivca aeivac aevaic aevaci aeviac
aevica aevcia aevcai avcaei avcaie avceai avceia avciea avciae avacei avacie
avaeci avaeic avaiec avaice aveaci aveaic avecai avecia aveica aveiac aviaec
aviace avieac avieca avicea avicae

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History of cryptography
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