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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: hoagie
cipher variations:
ipbhjf jqcikg krdjlh lsekmi mtflnj
nugmok ovhnpl pwioqm qxjprn rykqso
szlrtp tamsuq ubntvr vcouws wdpvxt
xeqwyu yfrxzv zgsyaw ahtzbx biuacy
cjvbdz dkwcea elxdfb fmyegc gnzfhd

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: hoagie
Cipher: slztrv

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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: hoagie

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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: hoagie
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: hoagie
Cipher: ubntvr

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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: hoagie
Cipher: 324311224251

Extended Methods:
Method #1

Plaintext: hoagie
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
h o a g i e 
3 4 1 2 4 5 
2 3 1 2 2 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: hoagie
Cipher: sfymfb

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Method #3

Plaintext: hoagie
method variations:
rcfrwl cfrwlr frwlrc
rwlrcf wlrcfr lrcfrw

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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: hoagie

all 720 cipher variations:
hoagie hoagei hoaige hoaieg hoaeig hoaegi hogaie hogaei hogiae hogiea hogeia
hogeai hoigae hoigea hoiage hoiaeg hoieag hoiega hoegia hoegai hoeiga hoeiag
hoeaig hoeagi haogie haogei haoige haoieg haoeig haoegi hagoie hagoei hagioe
hagieo hageio hageoi haigoe haigeo haioge haioeg haieog haiego haegio haegoi
haeigo haeiog haeoig haeogi hgaoie hgaoei hgaioe hgaieo hgaeio hgaeoi hgoaie
hgoaei hgoiae hgoiea hgoeia hgoeai hgioae hgioea hgiaoe hgiaeo hgieao hgieoa
hgeoia hgeoai hgeioa hgeiao hgeaio hgeaoi hiagoe hiageo hiaoge hiaoeg hiaeog
hiaego higaoe higaeo higoae higoea higeoa higeao hiogae hiogea hioage hioaeg
hioeag hioega hiegoa hiegao hieoga hieoag hieaog hieago heagio heagoi heaigo
heaiog heaoig heaogi hegaio hegaoi hegiao hegioa hegoia hegoai heigao heigoa
heiago heiaog heioag heioga heogia heogai heoiga heoiag heoaig heoagi ohagie
ohagei ohaige ohaieg ohaeig ohaegi ohgaie ohgaei ohgiae ohgiea ohgeia ohgeai
ohigae ohigea ohiage ohiaeg ohieag ohiega ohegia ohegai oheiga oheiag oheaig
oheagi oahgie oahgei oahige oahieg oaheig oahegi oaghie oaghei oagihe oagieh
oageih oagehi oaighe oaigeh oaihge oaiheg oaiehg oaiegh oaegih oaeghi oaeigh
oaeihg oaehig oaehgi ogahie ogahei ogaihe ogaieh ogaeih ogaehi oghaie oghaei
oghiae oghiea ogheia ogheai ogihae ogihea ogiahe ogiaeh ogieah ogieha ogehia
ogehai ogeiha ogeiah ogeaih ogeahi oiaghe oiageh oiahge oiaheg oiaehg oiaegh
oigahe oigaeh oighae oighea oigeha oigeah oihgae oihgea oihage oihaeg oiheag
oihega oiegha oiegah oiehga oiehag oieahg oieagh oeagih oeaghi oeaigh oeaihg
oeahig oeahgi oegaih oegahi oegiah oegiha oeghia oeghai oeigah oeigha oeiagh
oeiahg oeihag oeihga oehgia oehgai oehiga oehiag oehaig oehagi aohgie aohgei
aohige aohieg aoheig aohegi aoghie aoghei aogihe aogieh aogeih aogehi aoighe
aoigeh aoihge aoiheg aoiehg aoiegh aoegih aoeghi aoeigh aoeihg aoehig aoehgi
ahogie ahogei ahoige ahoieg ahoeig ahoegi ahgoie ahgoei ahgioe ahgieo ahgeio
ahgeoi ahigoe ahigeo ahioge ahioeg ahieog ahiego ahegio ahegoi aheigo aheiog
aheoig aheogi aghoie aghoei aghioe aghieo agheio agheoi agohie agohei agoihe
agoieh agoeih agoehi agiohe agioeh agihoe agiheo agieho agieoh ageoih ageohi
ageioh ageiho agehio agehoi aihgoe aihgeo aihoge aihoeg aiheog aihego aighoe
aigheo aigohe aigoeh aigeoh aigeho aioghe aiogeh aiohge aioheg aioehg aioegh
aiegoh aiegho aieogh aieohg aiehog aiehgo aehgio aehgoi aehigo aehiog aehoig
aehogi aeghio aeghoi aegiho aegioh aegoih aegohi aeigho aeigoh aeihgo aeihog
aeiohg aeiogh aeogih aeoghi aeoigh aeoihg aeohig aeohgi goahie goahei goaihe
goaieh goaeih goaehi gohaie gohaei gohiae gohiea goheia goheai goihae goihea
goiahe goiaeh goieah goieha goehia goehai goeiha goeiah goeaih goeahi gaohie
gaohei gaoihe gaoieh gaoeih gaoehi gahoie gahoei gahioe gahieo gaheio gaheoi
gaihoe gaiheo gaiohe gaioeh gaieoh gaieho gaehio gaehoi gaeiho gaeioh gaeoih
gaeohi ghaoie ghaoei ghaioe ghaieo ghaeio ghaeoi ghoaie ghoaei ghoiae ghoiea
ghoeia ghoeai ghioae ghioea ghiaoe ghiaeo ghieao ghieoa gheoia gheoai gheioa
gheiao gheaio gheaoi giahoe giaheo giaohe giaoeh giaeoh giaeho gihaoe gihaeo
gihoae gihoea giheoa giheao giohae giohea gioahe gioaeh gioeah gioeha giehoa
giehao gieoha gieoah gieaoh gieaho geahio geahoi geaiho geaioh geaoih geaohi
gehaio gehaoi gehiao gehioa gehoia gehoai geihao geihoa geiaho geiaoh geioah
geioha geohia geohai geoiha geoiah geoaih geoahi ioaghe ioageh ioahge ioaheg
ioaehg ioaegh iogahe iogaeh ioghae ioghea iogeha iogeah iohgae iohgea iohage
iohaeg ioheag iohega ioegha ioegah ioehga ioehag ioeahg ioeagh iaoghe iaogeh
iaohge iaoheg iaoehg iaoegh iagohe iagoeh iaghoe iagheo iageho iageoh iahgoe
iahgeo iahoge iahoeg iaheog iahego iaegho iaegoh iaehgo iaehog iaeohg iaeogh
igaohe igaoeh igahoe igaheo igaeho igaeoh igoahe igoaeh igohae igohea igoeha
igoeah ighoae ighoea ighaoe ighaeo igheao igheoa igeoha igeoah igehoa igehao
igeaho igeaoh ihagoe ihageo ihaoge ihaoeg ihaeog ihaego ihgaoe ihgaeo ihgoae
ihgoea ihgeoa ihgeao ihogae ihogea ihoage ihoaeg ihoeag ihoega ihegoa ihegao
iheoga iheoag iheaog iheago ieagho ieagoh ieahgo ieahog ieaohg ieaogh iegaho
iegaoh ieghao ieghoa iegoha iegoah iehgao iehgoa iehago iehaog iehoag iehoga
ieogha ieogah ieohga ieohag ieoahg ieoagh eoagih eoaghi eoaigh eoaihg eoahig
eoahgi eogaih eogahi eogiah eogiha eoghia eoghai eoigah eoigha eoiagh eoiahg
eoihag eoihga eohgia eohgai eohiga eohiag eohaig eohagi eaogih eaoghi eaoigh
eaoihg eaohig eaohgi eagoih eagohi eagioh eagiho eaghio eaghoi eaigoh eaigho
eaiogh eaiohg eaihog eaihgo eahgio eahgoi eahigo eahiog eahoig eahogi egaoih
egaohi egaioh egaiho egahio egahoi egoaih egoahi egoiah egoiha egohia egohai
egioah egioha egiaoh egiaho egihao egihoa eghoia eghoai eghioa eghiao eghaio
eghaoi eiagoh eiagho eiaogh eiaohg eiahog eiahgo eigaoh eigaho eigoah eigoha
eighoa eighao eiogah eiogha eioagh eioahg eiohag eiohga eihgoa eihgao eihoga
eihoag eihaog eihago ehagio ehagoi ehaigo ehaiog ehaoig ehaogi ehgaio ehgaoi
ehgiao ehgioa ehgoia ehgoai ehigao ehigoa ehiago ehiaog ehioag ehioga ehogia
ehogai ehoiga ehoiag ehoaig ehoagi

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History of cryptography
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