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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: montag
cipher variations:
npoubh oqpvci prqwdj qsrxek rtsyfl
sutzgm tvuahn uwvbio vxwcjp wyxdkq
xzyelr yazfms zbagnt acbhou bdcipv
cedjqw dfekrx egflsy fhgmtz gihnua
hjiovb ikjpwc jlkqxd kmlrye lnmszf

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: montag
Cipher: nlmgzt

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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: montag

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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: montag
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: montag
Cipher: zbagnt

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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: montag
Cipher: 234333441122

Extended Methods:
Method #1

Plaintext: montag
method variations:

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

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Method #3

Plaintext: montag
method variations:
snsdfg nsdfgs sdfgsn
dfgsns fgsnsd gsnsdf

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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: montag

all 720 cipher variations:
montag montga monatg monagt mongat mongta motnag motnga motang motagn motgan
motgna moatng moatgn moantg moangt moagnt moagtn mogtan mogtna mogatn mogant
mognat mognta mnotag mnotga mnoatg mnoagt mnogat mnogta mntoag mntoga mntaog
mntago mntgao mntgoa mnatog mnatgo mnaotg mnaogt mnagot mnagto mngtao mngtoa
mngato mngaot mngoat mngota mtnoag mtnoga mtnaog mtnago mtngao mtngoa mtonag
mtonga mtoang mtoagn mtogan mtogna mtaong mtaogn mtanog mtango mtagno mtagon
mtgoan mtgona mtgaon mtgano mtgnao mtgnoa mantog mantgo manotg manogt mangot
mangto matnog matngo matong matogn matgon matgno maotng maotgn maontg maongt
maognt maogtn magton magtno magotn magont magnot magnto mgntao mgntoa mgnato
mgnaot mgnoat mgnota mgtnao mgtnoa mgtano mgtaon mgtoan mgtona mgatno mgaton
mganto mganot mgaont mgaotn mgotan mgotna mgoatn mgoant mgonat mgonta omntag
omntga omnatg omnagt omngat omngta omtnag omtnga omtang omtagn omtgan omtgna
omatng omatgn omantg omangt omagnt omagtn omgtan omgtna omgatn omgant omgnat
omgnta onmtag onmtga onmatg onmagt onmgat onmgta ontmag ontmga ontamg ontagm
ontgam ontgma onatmg onatgm onamtg onamgt onagmt onagtm ongtam ongtma ongatm
ongamt ongmat ongmta otnmag otnmga otnamg otnagm otngam otngma otmnag otmnga
otmang otmagn otmgan otmgna otamng otamgn otanmg otangm otagnm otagmn otgman
otgmna otgamn otganm otgnam otgnma oantmg oantgm oanmtg oanmgt oangmt oangtm
oatnmg oatngm oatmng oatmgn oatgmn oatgnm oamtng oamtgn oamntg oamngt oamgnt
oamgtn oagtmn oagtnm oagmtn oagmnt oagnmt oagntm ogntam ogntma ognatm ognamt
ognmat ognmta ogtnam ogtnma ogtanm ogtamn ogtman ogtmna ogatnm ogatmn ogantm
oganmt ogamnt ogamtn ogmtan ogmtna ogmatn ogmant ogmnat ogmnta nomtag nomtga
nomatg nomagt nomgat nomgta notmag notmga notamg notagm notgam notgma noatmg
noatgm noamtg noamgt noagmt noagtm nogtam nogtma nogatm nogamt nogmat nogmta
nmotag nmotga nmoatg nmoagt nmogat nmogta nmtoag nmtoga nmtaog nmtago nmtgao
nmtgoa nmatog nmatgo nmaotg nmaogt nmagot nmagto nmgtao nmgtoa nmgato nmgaot
nmgoat nmgota ntmoag ntmoga ntmaog ntmago ntmgao ntmgoa ntomag ntomga ntoamg
ntoagm ntogam ntogma ntaomg ntaogm ntamog ntamgo ntagmo ntagom ntgoam ntgoma
ntgaom ntgamo ntgmao ntgmoa namtog namtgo namotg namogt namgot namgto natmog
natmgo natomg natogm natgom natgmo naotmg naotgm naomtg naomgt naogmt naogtm
nagtom nagtmo nagotm nagomt nagmot nagmto ngmtao ngmtoa ngmato ngmaot ngmoat
ngmota ngtmao ngtmoa ngtamo ngtaom ngtoam ngtoma ngatmo ngatom ngamto ngamot
ngaomt ngaotm ngotam ngotma ngoatm ngoamt ngomat ngomta tonmag tonmga tonamg
tonagm tongam tongma tomnag tomnga tomang tomagn tomgan tomgna toamng toamgn
toanmg toangm toagnm toagmn togman togmna togamn toganm tognam tognma tnomag
tnomga tnoamg tnoagm tnogam tnogma tnmoag tnmoga tnmaog tnmago tnmgao tnmgoa
tnamog tnamgo tnaomg tnaogm tnagom tnagmo tngmao tngmoa tngamo tngaom tngoam
tngoma tmnoag tmnoga tmnaog tmnago tmngao tmngoa tmonag tmonga tmoang tmoagn
tmogan tmogna tmaong tmaogn tmanog tmango tmagno tmagon tmgoan tmgona tmgaon
tmgano tmgnao tmgnoa tanmog tanmgo tanomg tanogm tangom tangmo tamnog tamngo
tamong tamogn tamgon tamgno taomng taomgn taonmg taongm taognm taogmn tagmon
tagmno tagomn tagonm tagnom tagnmo tgnmao tgnmoa tgnamo tgnaom tgnoam tgnoma
tgmnao tgmnoa tgmano tgmaon tgmoan tgmona tgamno tgamon tganmo tganom tgaonm
tgaomn tgoman tgomna tgoamn tgoanm tgonam tgonma aontmg aontgm aonmtg aonmgt
aongmt aongtm aotnmg aotngm aotmng aotmgn aotgmn aotgnm aomtng aomtgn aomntg
aomngt aomgnt aomgtn aogtmn aogtnm aogmtn aogmnt aognmt aogntm anotmg anotgm
anomtg anomgt anogmt anogtm antomg antogm antmog antmgo antgmo antgom anmtog
anmtgo anmotg anmogt anmgot anmgto angtmo angtom angmto angmot angomt angotm
atnomg atnogm atnmog atnmgo atngmo atngom atonmg atongm atomng atomgn atogmn
atognm atmong atmogn atmnog atmngo atmgno atmgon atgomn atgonm atgmon atgmno
atgnmo atgnom amntog amntgo amnotg amnogt amngot amngto amtnog amtngo amtong
amtogn amtgon amtgno amotng amotgn amontg amongt amognt amogtn amgton amgtno
amgotn amgont amgnot amgnto agntmo agntom agnmto agnmot agnomt agnotm agtnmo
agtnom agtmno agtmon agtomn agtonm agmtno agmton agmnto agmnot agmont agmotn
agotmn agotnm agomtn agomnt agonmt agontm gontam gontma gonatm gonamt gonmat
gonmta gotnam gotnma gotanm gotamn gotman gotmna goatnm goatmn goantm goanmt
goamnt goamtn gomtan gomtna gomatn gomant gomnat gomnta gnotam gnotma gnoatm
gnoamt gnomat gnomta gntoam gntoma gntaom gntamo gntmao gntmoa gnatom gnatmo
gnaotm gnaomt gnamot gnamto gnmtao gnmtoa gnmato gnmaot gnmoat gnmota gtnoam
gtnoma gtnaom gtnamo gtnmao gtnmoa gtonam gtonma gtoanm gtoamn gtoman gtomna
gtaonm gtaomn gtanom gtanmo gtamno gtamon gtmoan gtmona gtmaon gtmano gtmnao
gtmnoa gantom gantmo ganotm ganomt ganmot ganmto gatnom gatnmo gatonm gatomn
gatmon gatmno gaotnm gaotmn gaontm gaonmt gaomnt gaomtn gamton gamtno gamotn
gamont gamnot gamnto gmntao gmntoa gmnato gmnaot gmnoat gmnota gmtnao gmtnoa
gmtano gmtaon gmtoan gmtona gmatno gmaton gmanto gmanot gmaont gmaotn gmotan
gmotna gmoatn gmoant gmonat gmonta

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History of cryptography
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