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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: gusher
cipher variations:
hvtifs iwujgt jxvkhu kywliv lzxmjw
maynkx nbzoly ocapmz pdbqna qecrob
rfdspc sgetqd thfure uigvsf vjhwtg
wkixuh xljyvi ymkzwj znlaxk aombyl
bpnczm cqodan drpebo esqfcp ftrgdq

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: gusher
Cipher: tfhsvi

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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: gusher

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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: gusher
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: gusher
Cipher: thfure

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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: gusher
Cipher: 225434325124

Extended Methods:
Method #1

Plaintext: gusher
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
g u s h e r 
2 5 3 3 5 2 
2 4 4 2 1 4 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: gusher
Cipher: wnkriq

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Method #3

Plaintext: gusher
method variations:
woowfi oowfiw owfiwo
wfiwoo fiwoow iwoowf

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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: gusher

all 720 cipher variations:
gusher gushre gusehr guserh gusreh gusrhe guhser guhsre guhesr guhers guhres
guhrse guehsr guehrs gueshr guesrh guersh guerhs gurhes gurhse gurehs guresh
gurseh gurshe gsuher gsuhre gsuehr gsuerh gsureh gsurhe gshuer gshure gsheur
gsheru gshreu gshrue gsehur gsehru gseuhr gseurh gseruh gserhu gsrheu gsrhue
gsrehu gsreuh gsrueh gsruhe ghsuer ghsure ghseur ghseru ghsreu ghsrue ghuser
ghusre ghuesr ghuers ghures ghurse gheusr gheurs ghesur ghesru ghersu gherus
ghrues ghruse ghreus ghresu ghrseu ghrsue geshur geshru gesuhr gesurh gesruh
gesrhu gehsur gehsru gehusr gehurs gehrus gehrsu geuhsr geuhrs geushr geusrh
geursh geurhs gerhus gerhsu geruhs gerush gersuh gershu grsheu grshue grsehu
grseuh grsueh grsuhe grhseu grhsue grhesu grheus grhues grhuse grehsu grehus
greshu gresuh greush greuhs gruhes gruhse gruehs gruesh gruseh grushe ugsher
ugshre ugsehr ugserh ugsreh ugsrhe ughser ughsre ughesr ughers ughres ughrse
ugehsr ugehrs ugeshr ugesrh ugersh ugerhs ugrhes ugrhse ugrehs ugresh ugrseh
ugrshe usgher usghre usgehr usgerh usgreh usgrhe ushger ushgre ushegr usherg
ushreg ushrge usehgr usehrg useghr usegrh usergh userhg usrheg usrhge usrehg
usregh usrgeh usrghe uhsger uhsgre uhsegr uhserg uhsreg uhsrge uhgser uhgsre
uhgesr uhgers uhgres uhgrse uhegsr uhegrs uhesgr uhesrg uhersg uhergs uhrges
uhrgse uhregs uhresg uhrseg uhrsge ueshgr ueshrg uesghr uesgrh uesrgh uesrhg
uehsgr uehsrg uehgsr uehgrs uehrgs uehrsg ueghsr ueghrs uegshr uegsrh uegrsh
uegrhs uerhgs uerhsg uerghs uergsh uersgh uershg ursheg urshge ursehg ursegh
ursgeh ursghe urhseg urhsge urhesg urhegs urhges urhgse urehsg urehgs ureshg
uresgh uregsh ureghs urghes urghse urgehs urgesh urgseh urgshe sugher sughre
sugehr sugerh sugreh sugrhe suhger suhgre suhegr suherg suhreg suhrge suehgr
suehrg sueghr suegrh suergh suerhg surheg surhge surehg suregh surgeh surghe
sguher sguhre sguehr sguerh sgureh sgurhe sghuer sghure sgheur sgheru sghreu
sghrue sgehur sgehru sgeuhr sgeurh sgeruh sgerhu sgrheu sgrhue sgrehu sgreuh
sgrueh sgruhe shguer shgure shgeur shgeru shgreu shgrue shuger shugre shuegr
shuerg shureg shurge sheugr sheurg shegur shegru shergu sherug shrueg shruge
shreug shregu shrgeu shrgue seghur seghru seguhr segurh segruh segrhu sehgur
sehgru sehugr sehurg sehrug sehrgu seuhgr seuhrg seughr seugrh seurgh seurhg
serhug serhgu seruhg serugh serguh serghu srgheu srghue srgehu srgeuh srgueh
srguhe srhgeu srhgue srhegu srheug srhueg srhuge srehgu srehug sreghu sreguh
sreugh sreuhg sruheg sruhge sruehg sruegh srugeh srughe husger husgre husegr
huserg husreg husrge hugser hugsre hugesr hugers hugres hugrse huegsr huegrs
huesgr huesrg huersg huergs hurges hurgse huregs huresg hurseg hursge hsuger
hsugre hsuegr hsuerg hsureg hsurge hsguer hsgure hsgeur hsgeru hsgreu hsgrue
hsegur hsegru hseugr hseurg hserug hsergu hsrgeu hsrgue hsregu hsreug hsrueg
hsruge hgsuer hgsure hgseur hgseru hgsreu hgsrue hguser hgusre hguesr hguers
hgures hgurse hgeusr hgeurs hgesur hgesru hgersu hgerus hgrues hgruse hgreus
hgresu hgrseu hgrsue hesgur hesgru hesugr hesurg hesrug hesrgu hegsur hegsru
hegusr hegurs hegrus hegrsu heugsr heugrs heusgr heusrg heursg heurgs hergus
hergsu herugs herusg hersug hersgu hrsgeu hrsgue hrsegu hrseug hrsueg hrsuge
hrgseu hrgsue hrgesu hrgeus hrgues hrguse hregsu hregus hresgu hresug hreusg
hreugs hruges hrugse hruegs hruesg hruseg hrusge eushgr eushrg eusghr eusgrh
eusrgh eusrhg euhsgr euhsrg euhgsr euhgrs euhrgs euhrsg eughsr eughrs eugshr
eugsrh eugrsh eugrhs eurhgs eurhsg eurghs eurgsh eursgh eurshg esuhgr esuhrg
esughr esugrh esurgh esurhg eshugr eshurg eshgur eshgru eshrgu eshrug esghur
esghru esguhr esgurh esgruh esgrhu esrhgu esrhug esrghu esrguh esrugh esruhg
ehsugr ehsurg ehsgur ehsgru ehsrgu ehsrug ehusgr ehusrg ehugsr ehugrs ehurgs
ehursg ehgusr ehgurs ehgsur ehgsru ehgrsu ehgrus ehrugs ehrusg ehrgus ehrgsu
ehrsgu ehrsug egshur egshru egsuhr egsurh egsruh egsrhu eghsur eghsru eghusr
eghurs eghrus eghrsu eguhsr eguhrs egushr egusrh egursh egurhs egrhus egrhsu
egruhs egrush egrsuh egrshu ershgu ershug ersghu ersguh ersugh ersuhg erhsgu
erhsug erhgsu erhgus erhugs erhusg erghsu erghus ergshu ergsuh ergush erguhs
eruhgs eruhsg erughs erugsh erusgh erushg rusheg rushge rusehg rusegh rusgeh
rusghe ruhseg ruhsge ruhesg ruhegs ruhges ruhgse ruehsg ruehgs rueshg ruesgh
ruegsh rueghs rughes rughse rugehs rugesh rugseh rugshe rsuheg rsuhge rsuehg
rsuegh rsugeh rsughe rshueg rshuge rsheug rshegu rshgeu rshgue rsehug rsehgu
rseuhg rseugh rseguh rseghu rsgheu rsghue rsgehu rsgeuh rsgueh rsguhe rhsueg
rhsuge rhseug rhsegu rhsgeu rhsgue rhuseg rhusge rhuesg rhuegs rhuges rhugse
rheusg rheugs rhesug rhesgu rhegsu rhegus rhgues rhguse rhgeus rhgesu rhgseu
rhgsue reshug reshgu resuhg resugh resguh resghu rehsug rehsgu rehusg rehugs
rehgus rehgsu reuhsg reuhgs reushg reusgh reugsh reughs reghus reghsu reguhs
regush regsuh regshu rgsheu rgshue rgsehu rgseuh rgsueh rgsuhe rghseu rghsue
rghesu rgheus rghues rghuse rgehsu rgehus rgeshu rgesuh rgeush rgeuhs rguhes
rguhse rguehs rguesh rguseh rgushe

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History of cryptography
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