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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: octads
cipher variations:
pdubet qevcfu rfwdgv sgxehw thyfix
uizgjy vjahkz wkbila xlcjmb ymdknc
znelod aofmpe bpgnqf cqhorg dripsh
esjqti ftkruj gulsvk hvmtwl iwnuxm
jxovyn kypwzo lzqxap marybq nbszcr

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: octads
Cipher: lxgzwh

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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: octads

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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: octads
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: octads
Cipher: bpgnqf

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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: octads
Cipher: 433144114134

Extended Methods:
Method #1

Plaintext: octads
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
o c t a d s 
4 3 4 1 4 3 
3 1 4 1 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: octads
Cipher: odocdq

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Method #3

Plaintext: octads
method variations:
nqdqlt qdqltn dqltnq
qltnqd ltnqdq tnqdql

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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: octads

all 720 cipher variations:
octads octasd octdas octdsa octsda octsad ocatds ocatsd ocadts ocadst ocasdt
ocastd ocdats ocdast ocdtas ocdtsa ocdsta ocdsat ocsadt ocsatd ocsdat ocsdta
ocstda ocstad otcads otcasd otcdas otcdsa otcsda otcsad otacds otacsd otadcs
otadsc otasdc otascd otdacs otdasc otdcas otdcsa otdsca otdsac otsadc otsacd
otsdac otsdca otscda otscad oatcds oatcsd oatdcs oatdsc oatsdc oatscd oactds
oactsd oacdts oacdst oacsdt oacstd oadcts oadcst oadtcs oadtsc oadstc oadsct
oascdt oasctd oasdct oasdtc oastdc oastcd odtacs odtasc odtcas odtcsa odtsca
odtsac odatcs odatsc odacts odacst odasct odastc odcats odcast odctas odctsa
odcsta odcsat odsact odsatc odscat odscta odstca odstac ostadc ostacd ostdac
ostdca ostcda ostcad osatdc osatcd osadtc osadct osacdt osactd osdatc osdact
osdtac osdtca osdcta osdcat oscadt oscatd oscdat oscdta osctda osctad cotads
cotasd cotdas cotdsa cotsda cotsad coatds coatsd coadts coadst coasdt coastd
codats codast codtas codtsa codsta codsat cosadt cosatd cosdat cosdta costda
costad ctoads ctoasd ctodas ctodsa ctosda ctosad ctaods ctaosd ctados ctadso
ctasdo ctasod ctdaos ctdaso ctdoas ctdosa ctdsoa ctdsao ctsado ctsaod ctsdao
ctsdoa ctsoda ctsoad catods catosd catdos catdso catsdo catsod caotds caotsd
caodts caodst caosdt caostd cadots cadost cadtos cadtso cadsto cadsot casodt
casotd casdot casdto castdo castod cdtaos cdtaso cdtoas cdtosa cdtsoa cdtsao
cdatos cdatso cdaots cdaost cdasot cdasto cdoats cdoast cdotas cdotsa cdosta
cdosat cdsaot cdsato cdsoat cdsota cdstoa cdstao cstado cstaod cstdao cstdoa
cstoda cstoad csatdo csatod csadto csadot csaodt csaotd csdato csdaot csdtao
csdtoa csdota csdoat csoadt csoatd csodat csodta csotda csotad tcoads tcoasd
tcodas tcodsa tcosda tcosad tcaods tcaosd tcados tcadso tcasdo tcasod tcdaos
tcdaso tcdoas tcdosa tcdsoa tcdsao tcsado tcsaod tcsdao tcsdoa tcsoda tcsoad
tocads tocasd tocdas tocdsa tocsda tocsad toacds toacsd toadcs toadsc toasdc
toascd todacs todasc todcas todcsa todsca todsac tosadc tosacd tosdac tosdca
toscda toscad taocds taocsd taodcs taodsc taosdc taoscd tacods tacosd tacdos
tacdso tacsdo tacsod tadcos tadcso tadocs tadosc tadsoc tadsco tascdo tascod
tasdco tasdoc tasodc tasocd tdoacs tdoasc tdocas tdocsa tdosca tdosac tdaocs
tdaosc tdacos tdacso tdasco tdasoc tdcaos tdcaso tdcoas tdcosa tdcsoa tdcsao
tdsaco tdsaoc tdscao tdscoa tdsoca tdsoac tsoadc tsoacd tsodac tsodca tsocda
tsocad tsaodc tsaocd tsadoc tsadco tsacdo tsacod tsdaoc tsdaco tsdoac tsdoca
tsdcoa tsdcao tscado tscaod tscdao tscdoa tscoda tscoad actods actosd actdos
actdso actsdo actsod acotds acotsd acodts acodst acosdt acostd acdots acdost
acdtos acdtso acdsto acdsot acsodt acsotd acsdot acsdto acstdo acstod atcods
atcosd atcdos atcdso atcsdo atcsod atocds atocsd atodcs atodsc atosdc atoscd
atdocs atdosc atdcos atdcso atdsco atdsoc atsodc atsocd atsdoc atsdco atscdo
atscod aotcds aotcsd aotdcs aotdsc aotsdc aotscd aoctds aoctsd aocdts aocdst
aocsdt aocstd aodcts aodcst aodtcs aodtsc aodstc aodsct aoscdt aosctd aosdct
aosdtc aostdc aostcd adtocs adtosc adtcos adtcso adtsco adtsoc adotcs adotsc
adocts adocst adosct adostc adcots adcost adctos adctso adcsto adcsot adsoct
adsotc adscot adscto adstco adstoc astodc astocd astdoc astdco astcdo astcod
asotdc asotcd asodtc asodct asocdt asoctd asdotc asdoct asdtoc asdtco asdcto
asdcot ascodt ascotd ascdot ascdto asctdo asctod dctaos dctaso dctoas dctosa
dctsoa dctsao dcatos dcatso dcaots dcaost dcasot dcasto dcoats dcoast dcotas
dcotsa dcosta dcosat dcsaot dcsato dcsoat dcsota dcstoa dcstao dtcaos dtcaso
dtcoas dtcosa dtcsoa dtcsao dtacos dtacso dtaocs dtaosc dtasoc dtasco dtoacs
dtoasc dtocas dtocsa dtosca dtosac dtsaoc dtsaco dtsoac dtsoca dtscoa dtscao
datcos datcso datocs datosc datsoc datsco dactos dactso dacots dacost dacsot
dacsto daocts daocst daotcs daotsc daostc daosct dascot dascto dasoct dasotc
dastoc dastco dotacs dotasc dotcas dotcsa dotsca dotsac doatcs doatsc doacts
doacst doasct doastc docats docast doctas doctsa docsta docsat dosact dosatc
doscat doscta dostca dostac dstaoc dstaco dstoac dstoca dstcoa dstcao dsatoc
dsatco dsaotc dsaoct dsacot dsacto dsoatc dsoact dsotac dsotca dsocta dsocat
dscaot dscato dscoat dscota dsctoa dsctao sctado sctaod sctdao sctdoa sctoda
sctoad scatdo scatod scadto scadot scaodt scaotd scdato scdaot scdtao scdtoa
scdota scdoat scoadt scoatd scodat scodta scotda scotad stcado stcaod stcdao
stcdoa stcoda stcoad stacdo stacod stadco stadoc staodc staocd stdaco stdaoc
stdcao stdcoa stdoca stdoac stoadc stoacd stodac stodca stocda stocad satcdo
satcod satdco satdoc satodc satocd sactdo sactod sacdto sacdot sacodt sacotd
sadcto sadcot sadtco sadtoc sadotc sadoct saocdt saoctd saodct saodtc saotdc
saotcd sdtaco sdtaoc sdtcao sdtcoa sdtoca sdtoac sdatco sdatoc sdacto sdacot
sdaoct sdaotc sdcato sdcaot sdctao sdctoa sdcota sdcoat sdoact sdoatc sdocat
sdocta sdotca sdotac sotadc sotacd sotdac sotdca sotcda sotcad soatdc soatcd
soadtc soadct soacdt soactd sodatc sodact sodtac sodtca sodcta sodcat socadt
socatd socdat socdta soctda soctad

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History of cryptography
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