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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: kyodai
cipher variations:
lzpebj maqfck nbrgdl ocshem pdtifn
qeujgo rfvkhp sgwliq thxmjr uiynks
vjzolt wkapmu xlbqnv ymcrow zndspx
aoetqy bpfurz cqgvsa drhwtb esixuc
ftjyvd gukzwe hvlaxf iwmbyg jxnczh

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: kyodai
Cipher: pblwzr

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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: kyodai

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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: kyodai
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: kyodai
Cipher: xlbqnv

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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: kyodai
Cipher: 524543411142

Extended Methods:
Method #1

Plaintext: kyodai
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
k y o d a i 
5 4 4 4 1 4 
2 5 3 1 1 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: kyodai
Cipher: utqwcf

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Method #3

Plaintext: kyodai
method variations:
rusaqw usaqwr saqwru
aqwrus qwrusa wrusaq

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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: kyodai

all 720 cipher variations:
kyodai kyodia kyoadi kyoaid kyoiad kyoida kydoai kydoia kydaoi kydaio kydiao
kydioa kyadoi kyadio kyaodi kyaoid kyaiod kyaido kyidao kyidoa kyiado kyiaod
kyioad kyioda koydai koydia koyadi koyaid koyiad koyida kodyai kodyia kodayi
kodaiy kodiay kodiya koadyi koadiy koaydi koayid koaiyd koaidy koiday koidya
koiady koiayd koiyad koiyda kdoyai kdoyia kdoayi kdoaiy kdoiay kdoiya kdyoai
kdyoia kdyaoi kdyaio kdyiao kdyioa kdayoi kdayio kdaoyi kdaoiy kdaioy kdaiyo
kdiyao kdiyoa kdiayo kdiaoy kdioay kdioya kaodyi kaodiy kaoydi kaoyid kaoiyd
kaoidy kadoyi kadoiy kadyoi kadyio kadiyo kadioy kaydoi kaydio kayodi kayoid
kayiod kayido kaidyo kaidoy kaiydo kaiyod kaioyd kaiody kioday kiodya kioady
kioayd kioyad kioyda kidoay kidoya kidaoy kidayo kidyao kidyoa kiadoy kiadyo
kiaody kiaoyd kiayod kiaydo kiydao kiydoa kiyado kiyaod kiyoad kiyoda ykodai
ykodia ykoadi ykoaid ykoiad ykoida ykdoai ykdoia ykdaoi ykdaio ykdiao ykdioa
ykadoi ykadio ykaodi ykaoid ykaiod ykaido ykidao ykidoa ykiado ykiaod ykioad
ykioda yokdai yokdia yokadi yokaid yokiad yokida yodkai yodkia yodaki yodaik
yodiak yodika yoadki yoadik yoakdi yoakid yoaikd yoaidk yoidak yoidka yoiadk
yoiakd yoikad yoikda ydokai ydokia ydoaki ydoaik ydoiak ydoika ydkoai ydkoia
ydkaoi ydkaio ydkiao ydkioa ydakoi ydakio ydaoki ydaoik ydaiok ydaiko ydikao
ydikoa ydiako ydiaok ydioak ydioka yaodki yaodik yaokdi yaokid yaoikd yaoidk
yadoki yadoik yadkoi yadkio yadiko yadiok yakdoi yakdio yakodi yakoid yakiod
yakido yaidko yaidok yaikdo yaikod yaiokd yaiodk yiodak yiodka yioadk yioakd
yiokad yiokda yidoak yidoka yidaok yidako yidkao yidkoa yiadok yiadko yiaodk
yiaokd yiakod yiakdo yikdao yikdoa yikado yikaod yikoad yikoda oykdai oykdia
oykadi oykaid oykiad oykida oydkai oydkia oydaki oydaik oydiak oydika oyadki
oyadik oyakdi oyakid oyaikd oyaidk oyidak oyidka oyiadk oyiakd oyikad oyikda
okydai okydia okyadi okyaid okyiad okyida okdyai okdyia okdayi okdaiy okdiay
okdiya okadyi okadiy okaydi okayid okaiyd okaidy okiday okidya okiady okiayd
okiyad okiyda odkyai odkyia odkayi odkaiy odkiay odkiya odykai odykia odyaki
odyaik odyiak odyika odayki odayik odakyi odakiy odaiky odaiyk odiyak odiyka
odiayk odiaky odikay odikya oakdyi oakdiy oakydi oakyid oakiyd oakidy oadkyi
oadkiy oadyki oadyik oadiyk oadiky oaydki oaydik oaykdi oaykid oayikd oayidk
oaidyk oaidky oaiydk oaiykd oaikyd oaikdy oikday oikdya oikady oikayd oikyad
oikyda oidkay oidkya oidaky oidayk oidyak oidyka oiadky oiadyk oiakdy oiakyd
oiaykd oiaydk oiydak oiydka oiyadk oiyakd oiykad oiykda dyokai dyokia dyoaki
dyoaik dyoiak dyoika dykoai dykoia dykaoi dykaio dykiao dykioa dyakoi dyakio
dyaoki dyaoik dyaiok dyaiko dyikao dyikoa dyiako dyiaok dyioak dyioka doykai
doykia doyaki doyaik doyiak doyika dokyai dokyia dokayi dokaiy dokiay dokiya
doakyi doakiy doayki doayik doaiyk doaiky doikay doikya doiaky doiayk doiyak
doiyka dkoyai dkoyia dkoayi dkoaiy dkoiay dkoiya dkyoai dkyoia dkyaoi dkyaio
dkyiao dkyioa dkayoi dkayio dkaoyi dkaoiy dkaioy dkaiyo dkiyao dkiyoa dkiayo
dkiaoy dkioay dkioya daokyi daokiy daoyki daoyik daoiyk daoiky dakoyi dakoiy
dakyoi dakyio dakiyo dakioy daykoi daykio dayoki dayoik dayiok dayiko daikyo
daikoy daiyko daiyok daioyk daioky diokay diokya dioaky dioayk dioyak dioyka
dikoay dikoya dikaoy dikayo dikyao dikyoa diakoy diakyo diaoky diaoyk diayok
diayko diykao diykoa diyako diyaok diyoak diyoka ayodki ayodik ayokdi ayokid
ayoikd ayoidk aydoki aydoik aydkoi aydkio aydiko aydiok aykdoi aykdio aykodi
aykoid aykiod aykido ayidko ayidok ayikdo ayikod ayiokd ayiodk aoydki aoydik
aoykdi aoykid aoyikd aoyidk aodyki aodyik aodkyi aodkiy aodiky aodiyk aokdyi
aokdiy aokydi aokyid aokiyd aokidy aoidky aoidyk aoikdy aoikyd aoiykd aoiydk
adoyki adoyik adokyi adokiy adoiky adoiyk adyoki adyoik adykoi adykio adyiko
adyiok adkyoi adkyio adkoyi adkoiy adkioy adkiyo adiyko adiyok adikyo adikoy
adioky adioyk akodyi akodiy akoydi akoyid akoiyd akoidy akdoyi akdoiy akdyoi
akdyio akdiyo akdioy akydoi akydio akyodi akyoid akyiod akyido akidyo akidoy
akiydo akiyod akioyd akiody aiodky aiodyk aiokdy aiokyd aioykd aioydk aidoky
aidoyk aidkoy aidkyo aidyko aidyok aikdoy aikdyo aikody aikoyd aikyod aikydo
aiydko aiydok aiykdo aiykod aiyokd aiyodk iyodak iyodka iyoadk iyoakd iyokad
iyokda iydoak iydoka iydaok iydako iydkao iydkoa iyadok iyadko iyaodk iyaokd
iyakod iyakdo iykdao iykdoa iykado iykaod iykoad iykoda ioydak ioydka ioyadk
ioyakd ioykad ioykda iodyak iodyka iodayk iodaky iodkay iodkya ioadyk ioadky
ioaydk ioaykd ioakyd ioakdy iokday iokdya iokady iokayd iokyad iokyda idoyak
idoyka idoayk idoaky idokay idokya idyoak idyoka idyaok idyako idykao idykoa
idayok idayko idaoyk idaoky idakoy idakyo idkyao idkyoa idkayo idkaoy idkoay
idkoya iaodyk iaodky iaoydk iaoykd iaokyd iaokdy iadoyk iadoky iadyok iadyko
iadkyo iadkoy iaydok iaydko iayodk iayokd iaykod iaykdo iakdyo iakdoy iakydo
iakyod iakoyd iakody ikoday ikodya ikoady ikoayd ikoyad ikoyda ikdoay ikdoya
ikdaoy ikdayo ikdyao ikdyoa ikadoy ikadyo ikaody ikaoyd ikayod ikaydo ikydao
ikydoa ikyado ikyaod ikyoad ikyoda

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History of cryptography
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