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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: hating
cipher variations:
ibujoh jcvkpi kdwlqj lexmrk mfynsl
ngzotm ohapun pibqvo qjcrwp rkdsxq
sletyr tmfuzs ungvat vohwbu wpixcv
xqjydw yrkzex zslafy atmbgz buncha
cvodib dwpejc exqfkd fyrgle gzshmf

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: hating
Cipher: szgrmt

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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: hating

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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: hating
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: hating
Cipher: ungvat

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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: hating
Cipher: 321144423322

Extended Methods:
Method #1

Plaintext: hating
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
h a t i n g 
3 1 4 4 3 2 
2 1 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: hating
Cipher: cthbih

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Method #3

Plaintext: hating
method variations:
bqtmhm qtmhmb tmhmbq
mhmbqt hmbqtm mbqtmh

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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: hating

all 720 cipher variations:
hating hatign hatnig hatngi hatgni hatgin haitng haitgn haintg haingt haignt
haigtn hanitg hanigt hantig hantgi hangti hangit hagint hagitn hagnit hagnti
hagtni hagtin htaing htaign htanig htangi htagni htagin htiang htiagn htinag
htinga htigna htigan htniag htniga htnaig htnagi htngai htngia htgina htgian
htgnia htgnai htgani htgain hitang hitagn hitnag hitnga hitgna hitgan hiatng
hiatgn hiantg hiangt hiagnt hiagtn hinatg hinagt hintag hintga hingta hingat
higant higatn hignat hignta higtna higtan hntiag hntiga hntaig hntagi hntgai
hntgia hnitag hnitga hniatg hniagt hnigat hnigta hnaitg hnaigt hnatig hnatgi
hnagti hnagit hngiat hngita hngait hngati hngtai hngtia hgtina hgtian hgtnia
hgtnai hgtani hgtain hgitna hgitan hginta hginat hgiant hgiatn hgnita hgniat
hgntia hgntai hgnati hgnait hgaint hgaitn hganit hganti hgatni hgatin ahting
ahtign ahtnig ahtngi ahtgni ahtgin ahitng ahitgn ahintg ahingt ahignt ahigtn
ahnitg ahnigt ahntig ahntgi ahngti ahngit ahgint ahgitn ahgnit ahgnti ahgtni
ahgtin athing athign athnig athngi athgni athgin atihng atihgn atinhg atingh
atignh atighn atnihg atnigh atnhig atnhgi atnghi atngih atginh atgihn atgnih
atgnhi atghni atghin aithng aithgn aitnhg aitngh aitgnh aitghn aihtng aihtgn
aihntg aihngt aihgnt aihgtn ainhtg ainhgt ainthg aintgh aingth ainght aighnt
aightn aignht aignth aigtnh aigthn antihg antigh anthig anthgi antghi antgih
anithg anitgh anihtg anihgt anight anigth anhitg anhigt anhtig anhtgi anhgti
anhgit angiht angith anghit anghti angthi angtih agtinh agtihn agtnih agtnhi
agthni agthin agitnh agithn aginth aginht agihnt agihtn agnith agniht agntih
agnthi agnhti agnhit aghint aghitn aghnit aghnti aghtni aghtin tahing tahign
tahnig tahngi tahgni tahgin taihng taihgn tainhg taingh taignh taighn tanihg
tanigh tanhig tanhgi tanghi tangih taginh tagihn tagnih tagnhi taghni taghin
thaing thaign thanig thangi thagni thagin thiang thiagn thinag thinga thigna
thigan thniag thniga thnaig thnagi thngai thngia thgina thgian thgnia thgnai
thgani thgain tihang tihagn tihnag tihnga tihgna tihgan tiahng tiahgn tianhg
tiangh tiagnh tiaghn tinahg tinagh tinhag tinhga tingha tingah tiganh tigahn
tignah tignha tighna tighan tnhiag tnhiga tnhaig tnhagi tnhgai tnhgia tnihag
tnihga tniahg tniagh tnigah tnigha tnaihg tnaigh tnahig tnahgi tnaghi tnagih
tngiah tngiha tngaih tngahi tnghai tnghia tghina tghian tghnia tghnai tghani
tghain tgihna tgihan tginha tginah tgianh tgiahn tgniha tgniah tgnhia tgnhai
tgnahi tgnaih tgainh tgaihn tganih tganhi tgahni tgahin iathng iathgn iatnhg
iatngh iatgnh iatghn iahtng iahtgn iahntg iahngt iahgnt iahgtn ianhtg ianhgt
ianthg iantgh iangth ianght iaghnt iaghtn iagnht iagnth iagtnh iagthn itahng
itahgn itanhg itangh itagnh itaghn ithang ithagn ithnag ithnga ithgna ithgan
itnhag itnhga itnahg itnagh itngah itngha itghna itghan itgnha itgnah itganh
itgahn ihtang ihtagn ihtnag ihtnga ihtgna ihtgan ihatng ihatgn ihantg ihangt
ihagnt ihagtn ihnatg ihnagt ihntag ihntga ihngta ihngat ihgant ihgatn ihgnat
ihgnta ihgtna ihgtan inthag inthga intahg intagh intgah intgha inhtag inhtga
inhatg inhagt inhgat inhgta inahtg inahgt inathg inatgh inagth inaght inghat
inghta ingaht ingath ingtah ingtha igthna igthan igtnha igtnah igtanh igtahn
ightna ightan ighnta ighnat ighant ighatn ignhta ignhat igntha igntah ignath
ignaht igahnt igahtn iganht iganth igatnh igathn natihg natigh nathig nathgi
natghi natgih naithg naitgh naihtg naihgt naight naigth nahitg nahigt nahtig
nahtgi nahgti nahgit nagiht nagith naghit naghti nagthi nagtih ntaihg ntaigh
ntahig ntahgi ntaghi ntagih ntiahg ntiagh ntihag ntihga ntigha ntigah nthiag
nthiga nthaig nthagi nthgai nthgia ntgiha ntgiah ntghia ntghai ntgahi ntgaih
nitahg nitagh nithag nithga nitgha nitgah niathg niatgh niahtg niahgt niaght
niagth nihatg nihagt nihtag nihtga nihgta nihgat nigaht nigath nighat nighta
nigtha nigtah nhtiag nhtiga nhtaig nhtagi nhtgai nhtgia nhitag nhitga nhiatg
nhiagt nhigat nhigta nhaitg nhaigt nhatig nhatgi nhagti nhagit nhgiat nhgita
nhgait nhgati nhgtai nhgtia ngtiha ngtiah ngthia ngthai ngtahi ngtaih ngitha
ngitah ngihta ngihat ngiaht ngiath nghita nghiat nghtia nghtai nghati nghait
ngaiht ngaith ngahit ngahti ngathi ngatih gatinh gatihn gatnih gatnhi gathni
gathin gaitnh gaithn gainth gainht gaihnt gaihtn ganith ganiht gantih ganthi
ganhti ganhit gahint gahitn gahnit gahnti gahtni gahtin gtainh gtaihn gtanih
gtanhi gtahni gtahin gtianh gtiahn gtinah gtinha gtihna gtihan gtniah gtniha
gtnaih gtnahi gtnhai gtnhia gthina gthian gthnia gthnai gthani gthain gitanh
gitahn gitnah gitnha githna githan giatnh giathn gianth gianht giahnt giahtn
ginath ginaht gintah gintha ginhta ginhat gihant gihatn gihnat gihnta gihtna
gihtan gntiah gntiha gntaih gntahi gnthai gnthia gnitah gnitha gniath gniaht
gnihat gnihta gnaith gnaiht gnatih gnathi gnahti gnahit gnhiat gnhita gnhait
gnhati gnhtai gnhtia ghtina ghtian ghtnia ghtnai ghtani ghtain ghitna ghitan
ghinta ghinat ghiant ghiatn ghnita ghniat ghntia ghntai ghnati ghnait ghaint
ghaitn ghanit ghanti ghatni ghatin

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History of cryptography
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