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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: laevis
cipher variations:
mbfwjt ncgxku odhylv peizmw qfjanx
rgkboy shlcpz timdqa ujnerb vkofsc
wlpgtd xmqhue ynrivf zosjwg aptkxh
bqulyi crvmzj dswnak etxobl fuypcm
gvzqdn hwareo ixbsfp jyctgq kzduhr

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: laevis
Cipher: ozverh

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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: laevis

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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: laevis
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: laevis
Cipher: ynrivf

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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: laevis
Cipher: 131151154234

Extended Methods:
Method #1

Plaintext: laevis
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
l a e v i s 
1 1 5 1 4 3 
3 1 1 5 2 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: laevis
Cipher: aeocvr

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Method #3

Plaintext: laevis
method variations:
cvaumd vaumdc aumdcv
umdcva mdcvau dcvaum

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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: laevis

all 720 cipher variations:
laevis laevsi laeivs laeisv laesiv laesvi laveis lavesi lavies lavise lavsie
lavsei laives laivse laievs laiesv laisev laisve lasvie lasvei lasive lasiev
laseiv lasevi leavis leavsi leaivs leaisv leasiv leasvi levais levasi levias
levisa levsia levsai leivas leivsa leiavs leiasv leisav leisva lesvia lesvai
lesiva lesiav lesaiv lesavi lveais lveasi lveias lveisa lvesia lvesai lvaeis
lvaesi lvaies lvaise lvasie lvasei lviaes lviase lvieas lviesa lvisea lvisae
lvsaie lvsaei lvsiae lvsiea lvseia lvseai lievas lievsa lieavs lieasv liesav
liesva liveas livesa livaes livase livsae livsea liaves liavse liaevs liaesv
liasev liasve lisvae lisvea lisave lisaev liseav liseva lsevia lsevai lseiva
lseiav lseaiv lseavi lsveia lsveai lsviea lsviae lsvaie lsvaei lsivea lsivae
lsieva lsieav lsiaev lsiave lsavie lsavei lsaive lsaiev lsaeiv lsaevi alevis
alevsi aleivs aleisv alesiv alesvi alveis alvesi alvies alvise alvsie alvsei
alives alivse alievs aliesv alisev alisve alsvie alsvei alsive alsiev alseiv
alsevi aelvis aelvsi aelivs aelisv aelsiv aelsvi aevlis aevlsi aevils aevisl
aevsil aevsli aeivls aeivsl aeilvs aeilsv aeislv aeisvl aesvil aesvli aesivl
aesilv aesliv aeslvi avelis avelsi aveils aveisl avesil avesli avleis avlesi
avlies avlise avlsie avlsei aviles avilse aviels aviesl avisel avisle avslie
avslei avsile avsiel avseil avseli aievls aievsl aielvs aielsv aieslv aiesvl
aivels aivesl aivles aivlse aivsle aivsel ailves ailvse ailevs ailesv ailsev
ailsve aisvle aisvel aislve aislev aiselv aisevl asevil asevli aseivl aseilv
aseliv aselvi asveil asveli asviel asvile asvlie asvlei asivel asivle asievl
asielv asilev asilve aslvie aslvei aslive asliev asleiv aslevi ealvis ealvsi
ealivs ealisv ealsiv ealsvi eavlis eavlsi eavils eavisl eavsil eavsli eaivls
eaivsl eailvs eailsv eaislv eaisvl easvil easvli easivl easilv easliv easlvi
elavis elavsi elaivs elaisv elasiv elasvi elvais elvasi elvias elvisa elvsia
elvsai elivas elivsa eliavs eliasv elisav elisva elsvia elsvai elsiva elsiav
elsaiv elsavi evlais evlasi evlias evlisa evlsia evlsai evalis evalsi evails
evaisl evasil evasli evials eviasl evilas evilsa evisla evisal evsail evsali
evsial evsila evslia evslai eilvas eilvsa eilavs eilasv eilsav eilsva eivlas
eivlsa eivals eivasl eivsal eivsla eiavls eiavsl eialvs eialsv eiaslv eiasvl
eisval eisvla eisavl eisalv eislav eislva eslvia eslvai esliva esliav eslaiv
eslavi esvlia esvlai esvila esvial esvail esvali esivla esival esilva esilav
esialv esiavl esavil esavli esaivl esailv esaliv esalvi vaelis vaelsi vaeils
vaeisl vaesil vaesli valeis valesi valies valise valsie valsei vailes vailse
vaiels vaiesl vaisel vaisle vaslie vaslei vasile vasiel vaseil vaseli vealis
vealsi veails veaisl veasil veasli velais velasi velias velisa velsia velsai
veilas veilsa veials veiasl veisal veisla veslia veslai vesila vesial vesail
vesali vleais vleasi vleias vleisa vlesia vlesai vlaeis vlaesi vlaies vlaise
vlasie vlasei vliaes vliase vlieas vliesa vlisea vlisae vlsaie vlsaei vlsiae
vlsiea vlseia vlseai vielas vielsa vieals vieasl viesal viesla vileas vilesa
vilaes vilase vilsae vilsea viales vialse viaels viaesl viasel viasle vislae
vislea visale visael viseal visela vselia vselai vseila vseial vseail vseali
vsleia vsleai vsliea vsliae vslaie vslaei vsilea vsilae vsiela vsieal vsiael
vsiale vsalie vsalei vsaile vsaiel vsaeil vsaeli iaevls iaevsl iaelvs iaelsv
iaeslv iaesvl iavels iavesl iavles iavlse iavsle iavsel ialves ialvse ialevs
ialesv ialsev ialsve iasvle iasvel iaslve iaslev iaselv iasevl ieavls ieavsl
iealvs iealsv ieaslv ieasvl ievals ievasl ievlas ievlsa ievsla ievsal ielvas
ielvsa ielavs ielasv ielsav ielsva iesvla iesval ieslva ieslav iesalv iesavl
iveals iveasl ivelas ivelsa ivesla ivesal ivaels ivaesl ivales ivalse ivasle
ivasel ivlaes ivlase ivleas ivlesa ivlsea ivlsae ivsale ivsael ivslae ivslea
ivsela ivseal ilevas ilevsa ileavs ileasv ilesav ilesva ilveas ilvesa ilvaes
ilvase ilvsae ilvsea ilaves ilavse ilaevs ilaesv ilasev ilasve ilsvae ilsvea
ilsave ilsaev ilseav ilseva isevla iseval iselva iselav isealv iseavl isvela
isveal isvlea isvlae isvale isvael islvea islvae isleva isleav islaev islave
isavle isavel isalve isalev isaelv isaevl saevil saevli saeivl saeilv saeliv
saelvi saveil saveli saviel savile savlie savlei saivel saivle saievl saielv
sailev sailve salvie salvei salive saliev saleiv salevi seavil seavli seaivl
seailv sealiv sealvi sevail sevali sevial sevila sevlia sevlai seival seivla
seiavl seialv seilav seilva selvia selvai seliva seliav selaiv selavi sveail
sveali sveial sveila svelia svelai svaeil svaeli svaiel svaile svalie svalei
sviael sviale svieal sviela svilea svilae svlaie svlaei svliae svliea svleia
svleai sieval sievla sieavl siealv sielav sielva siveal sivela sivael sivale
sivlae sivlea siavel siavle siaevl siaelv sialev sialve silvae silvea silave
silaev sileav sileva slevia slevai sleiva sleiav sleaiv sleavi slveia slveai
slviea slviae slvaie slvaei slivea slivae slieva slieav sliaev sliave slavie
slavei slaive slaiev slaeiv slaevi

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History of cryptography
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