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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: begray
cipher variations:
cfhsbz dgitca ehjudb fikvec gjlwfd
hkmxge ilnyhf jmozig knpajh loqbki
mprclj nqsdmk ortenl psufom qtvgpn
ruwhqo svxirp twyjsq uxzktr vyalus
wzbmvt xacnwu ybdoxv zcepyw adfqzx

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: begray
Cipher: yvtizb

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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: begray

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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: begray
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: begray
Cipher: ortenl

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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: begray
Cipher: 215122241145

Extended Methods:
Method #1

Plaintext: begray
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
b e g r a y 
2 5 2 2 1 4 
1 1 2 4 1 5 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: begray
Cipher: wgqarv

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Method #3

Plaintext: begray
method variations:
vfgdqk fgdqkv gdqkvf
dqkvfg qkvfgd kvfgdq

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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: begray

all 720 cipher variations:
begray begrya begary begayr begyar begyra bergay bergya beragy berayg beryag
beryga beargy bearyg beagry beagyr beaygr beayrg beyrag beyrga beyarg beyagr
beygar beygra bgeray bgerya bgeary bgeayr bgeyar bgeyra bgreay bgreya bgraey
bgraye bgryae bgryea bgarey bgarye bgaery bgaeyr bgayer bgayre bgyrae bgyrea
bgyare bgyaer bgyear bgyera brgeay brgeya brgaey brgaye brgyae brgyea bregay
bregya breagy breayg breyag breyga braegy braeyg bragey bragye brayge brayeg
bryeag bryega bryaeg bryage brygae brygea bagrey bagrye bagery bageyr bagyer
bagyre bargey bargye baregy bareyg baryeg baryge baergy baeryg baegry baegyr
baeygr baeyrg bayreg bayrge bayerg bayegr bayger baygre bygrae bygrea bygare
bygaer bygear bygera byrgae byrgea byrage byraeg byreag byrega byarge byareg
byagre byager byaegr byaerg byerag byerga byearg byeagr byegar byegra ebgray
ebgrya ebgary ebgayr ebgyar ebgyra ebrgay ebrgya ebragy ebrayg ebryag ebryga
ebargy ebaryg ebagry ebagyr ebaygr ebayrg ebyrag ebyrga ebyarg ebyagr ebygar
ebygra egbray egbrya egbary egbayr egbyar egbyra egrbay egrbya egraby egrayb
egryab egryba egarby egaryb egabry egabyr egaybr egayrb egyrab egyrba egyarb
egyabr egybar egybra ergbay ergbya ergaby ergayb ergyab ergyba erbgay erbgya
erbagy erbayg erbyag erbyga erabgy erabyg eragby eragyb eraygb eraybg erybag
erybga eryabg eryagb erygab erygba eagrby eagryb eagbry eagbyr eagybr eagyrb
eargby eargyb earbgy earbyg earybg earygb eabrgy eabryg eabgry eabgyr eabygr
eabyrg eayrbg eayrgb eaybrg eaybgr eaygbr eaygrb eygrab eygrba eygarb eygabr
eygbar eygbra eyrgab eyrgba eyragb eyrabg eyrbag eyrbga eyargb eyarbg eyagrb
eyagbr eyabgr eyabrg eybrag eybrga eybarg eybagr eybgar eybgra gebray gebrya
gebary gebayr gebyar gebyra gerbay gerbya geraby gerayb geryab geryba gearby
gearyb geabry geabyr geaybr geayrb geyrab geyrba geyarb geyabr geybar geybra
gberay gberya gbeary gbeayr gbeyar gbeyra gbreay gbreya gbraey gbraye gbryae
gbryea gbarey gbarye gbaery gbaeyr gbayer gbayre gbyrae gbyrea gbyare gbyaer
gbyear gbyera grbeay grbeya grbaey grbaye grbyae grbyea grebay grebya greaby
greayb greyab greyba graeby graeyb grabey grabye graybe grayeb gryeab gryeba
gryaeb gryabe grybae grybea gabrey gabrye gabery gabeyr gabyer gabyre garbey
garbye gareby gareyb garyeb garybe gaerby gaeryb gaebry gaebyr gaeybr gaeyrb
gayreb gayrbe gayerb gayebr gayber gaybre gybrae gybrea gybare gybaer gybear
gybera gyrbae gyrbea gyrabe gyraeb gyreab gyreba gyarbe gyareb gyabre gyaber
gyaebr gyaerb gyerab gyerba gyearb gyeabr gyebar gyebra regbay regbya regaby
regayb regyab regyba rebgay rebgya rebagy rebayg rebyag rebyga reabgy reabyg
reagby reagyb reaygb reaybg reybag reybga reyabg reyagb reygab reygba rgebay
rgebya rgeaby rgeayb rgeyab rgeyba rgbeay rgbeya rgbaey rgbaye rgbyae rgbyea
rgabey rgabye rgaeby rgaeyb rgayeb rgaybe rgybae rgybea rgyabe rgyaeb rgyeab
rgyeba rbgeay rbgeya rbgaey rbgaye rbgyae rbgyea rbegay rbegya rbeagy rbeayg
rbeyag rbeyga rbaegy rbaeyg rbagey rbagye rbayge rbayeg rbyeag rbyega rbyaeg
rbyage rbygae rbygea ragbey ragbye rageby rageyb ragyeb ragybe rabgey rabgye
rabegy rabeyg rabyeg rabyge raebgy raebyg raegby raegyb raeygb raeybg raybeg
raybge rayebg rayegb raygeb raygbe rygbae rygbea rygabe rygaeb rygeab rygeba
rybgae rybgea rybage rybaeg rybeag rybega ryabge ryabeg ryagbe ryageb ryaegb
ryaebg ryebag ryebga ryeabg ryeagb ryegab ryegba aegrby aegryb aegbry aegbyr
aegybr aegyrb aergby aergyb aerbgy aerbyg aerybg aerygb aebrgy aebryg aebgry
aebgyr aebygr aebyrg aeyrbg aeyrgb aeybrg aeybgr aeygbr aeygrb agerby ageryb
agebry agebyr ageybr ageyrb agreby agreyb agrbey agrbye agrybe agryeb agbrey
agbrye agbery agbeyr agbyer agbyre agyrbe agyreb agybre agyber agyebr agyerb
argeby argeyb argbey argbye argybe argyeb aregby aregyb arebgy arebyg areybg
areygb arbegy arbeyg arbgey arbgye arbyge arbyeg aryebg aryegb arybeg arybge
arygbe arygeb abgrey abgrye abgery abgeyr abgyer abgyre abrgey abrgye abregy
abreyg abryeg abryge abergy aberyg abegry abegyr abeygr abeyrg abyreg abyrge
abyerg abyegr abyger abygre aygrbe aygreb aygbre aygber aygebr aygerb ayrgbe
ayrgeb ayrbge ayrbeg ayrebg ayregb aybrge aybreg aybgre aybger aybegr ayberg
ayerbg ayergb ayebrg ayebgr ayegbr ayegrb yegrab yegrba yegarb yegabr yegbar
yegbra yergab yergba yeragb yerabg yerbag yerbga yeargb yearbg yeagrb yeagbr
yeabgr yeabrg yebrag yebrga yebarg yebagr yebgar yebgra ygerab ygerba ygearb
ygeabr ygebar ygebra ygreab ygreba ygraeb ygrabe ygrbae ygrbea ygareb ygarbe
ygaerb ygaebr ygaber ygabre ygbrae ygbrea ygbare ygbaer ygbear ygbera yrgeab
yrgeba yrgaeb yrgabe yrgbae yrgbea yregab yregba yreagb yreabg yrebag yrebga
yraegb yraebg yrageb yragbe yrabge yrabeg yrbeag yrbega yrbaeg yrbage yrbgae
yrbgea yagreb yagrbe yagerb yagebr yagber yagbre yargeb yargbe yaregb yarebg
yarbeg yarbge yaergb yaerbg yaegrb yaegbr yaebgr yaebrg yabreg yabrge yaberg
yabegr yabger yabgre ybgrae ybgrea ybgare ybgaer ybgear ybgera ybrgae ybrgea
ybrage ybraeg ybreag ybrega ybarge ybareg ybagre ybager ybaegr ybaerg yberag
yberga ybearg ybeagr ybegar ybegra

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History of cryptography
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