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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: tyring
cipher variations:
uzsjoh vatkpi wbulqj xcvmrk ydwnsl
zexotm afypun bgzqvo charwp dibsxq
ejctyr fkduzs glevat hmfwbu ingxcv
johydw kpizex lqjafy mrkbgz nslcha
otmdib punejc qvofkd rwpgle sxqhmf

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: tyring
Cipher: gbirmt

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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: tyring

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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: tyring
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: tyring
Cipher: glevat

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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: tyring
Cipher: 444524423322

Extended Methods:
Method #1

Plaintext: tyring
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
t y r i n g 
4 4 2 4 3 2 
4 5 4 2 3 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: tyring
Cipher: trhyih

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Method #3

Plaintext: tyring
method variations:
tktmhr ktmhrt tmhrtk
mhrtkt hrtktm rtktmh

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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: tyring

all 720 cipher variations:
tyring tyrign tyrnig tyrngi tyrgni tyrgin tyirng tyirgn tyinrg tyingr tyignr
tyigrn tynirg tynigr tynrig tynrgi tyngri tyngir tyginr tygirn tygnir tygnri
tygrni tygrin trying tryign trynig tryngi trygni trygin triyng triygn trinyg
tringy trigny trigyn trniyg trnigy trnyig trnygi trngyi trngiy trginy trgiyn
trgniy trgnyi trgyni trgyin tiryng tirygn tirnyg tirngy tirgny tirgyn tiyrng
tiyrgn tiynrg tiyngr tiygnr tiygrn tinyrg tinygr tinryg tinrgy tingry tingyr
tigynr tigyrn tignyr tignry tigrny tigryn tnriyg tnrigy tnryig tnrygi tnrgyi
tnrgiy tniryg tnirgy tniyrg tniygr tnigyr tnigry tnyirg tnyigr tnyrig tnyrgi
tnygri tnygir tngiyr tngiry tngyir tngyri tngryi tngriy tgriny tgriyn tgrniy
tgrnyi tgryni tgryin tgirny tgiryn tginry tginyr tgiynr tgiyrn tgniry tgniyr
tgnriy tgnryi tgnyri tgnyir tgyinr tgyirn tgynir tgynri tgyrni tgyrin ytring
ytrign ytrnig ytrngi ytrgni ytrgin ytirng ytirgn ytinrg ytingr ytignr ytigrn
ytnirg ytnigr ytnrig ytnrgi ytngri ytngir ytginr ytgirn ytgnir ytgnri ytgrni
ytgrin yrting yrtign yrtnig yrtngi yrtgni yrtgin yritng yritgn yrintg yringt
yrignt yrigtn yrnitg yrnigt yrntig yrntgi yrngti yrngit yrgint yrgitn yrgnit
yrgnti yrgtni yrgtin yirtng yirtgn yirntg yirngt yirgnt yirgtn yitrng yitrgn
yitnrg yitngr yitgnr yitgrn yintrg yintgr yinrtg yinrgt yingrt yingtr yigtnr
yigtrn yigntr yignrt yigrnt yigrtn ynritg ynrigt ynrtig ynrtgi ynrgti ynrgit
ynirtg ynirgt ynitrg ynitgr ynigtr ynigrt yntirg yntigr yntrig yntrgi yntgri
yntgir yngitr yngirt yngtir yngtri yngrti yngrit ygrint ygritn ygrnit ygrnti
ygrtni ygrtin ygirnt ygirtn yginrt ygintr ygitnr ygitrn ygnirt ygnitr ygnrit
ygnrti ygntri ygntir ygtinr ygtirn ygtnir ygtnri ygtrni ygtrin ryting rytign
rytnig rytngi rytgni rytgin ryitng ryitgn ryintg ryingt ryignt ryigtn rynitg
rynigt ryntig ryntgi ryngti ryngit rygint rygitn rygnit rygnti rygtni rygtin
rtying rtyign rtynig rtyngi rtygni rtygin rtiyng rtiygn rtinyg rtingy rtigny
rtigyn rtniyg rtnigy rtnyig rtnygi rtngyi rtngiy rtginy rtgiyn rtgniy rtgnyi
rtgyni rtgyin rityng ritygn ritnyg ritngy ritgny ritgyn riytng riytgn riyntg
riyngt riygnt riygtn rinytg rinygt rintyg rintgy ringty ringyt rigynt rigytn
rignyt rignty rigtny rigtyn rntiyg rntigy rntyig rntygi rntgyi rntgiy rnityg
rnitgy rniytg rniygt rnigyt rnigty rnyitg rnyigt rnytig rnytgi rnygti rnygit
rngiyt rngity rngyit rngyti rngtyi rngtiy rgtiny rgtiyn rgtniy rgtnyi rgtyni
rgtyin rgitny rgityn rginty rginyt rgiynt rgiytn rgnity rgniyt rgntiy rgntyi
rgnyti rgnyit rgyint rgyitn rgynit rgynti rgytni rgytin iyrtng iyrtgn iyrntg
iyrngt iyrgnt iyrgtn iytrng iytrgn iytnrg iytngr iytgnr iytgrn iyntrg iyntgr
iynrtg iynrgt iyngrt iyngtr iygtnr iygtrn iygntr iygnrt iygrnt iygrtn irytng
irytgn iryntg iryngt irygnt irygtn irtyng irtygn irtnyg irtngy irtgny irtgyn
irntyg irntgy irnytg irnygt irngyt irngty irgtny irgtyn irgnty irgnyt irgynt
irgytn itryng itrygn itrnyg itrngy itrgny itrgyn ityrng ityrgn itynrg ityngr
itygnr itygrn itnyrg itnygr itnryg itnrgy itngry itngyr itgynr itgyrn itgnyr
itgnry itgrny itgryn inrtyg inrtgy inrytg inrygt inrgyt inrgty intryg intrgy
intyrg intygr intgyr intgry inytrg inytgr inyrtg inyrgt inygrt inygtr ingtyr
ingtry ingytr ingyrt ingryt ingrty igrtny igrtyn igrnty igrnyt igrynt igrytn
igtrny igtryn igtnry igtnyr igtynr igtyrn igntry igntyr ignrty ignryt ignyrt
ignytr igytnr igytrn igyntr igynrt igyrnt igyrtn nyritg nyrigt nyrtig nyrtgi
nyrgti nyrgit nyirtg nyirgt nyitrg nyitgr nyigtr nyigrt nytirg nytigr nytrig
nytrgi nytgri nytgir nygitr nygirt nygtir nygtri nygrti nygrit nryitg nryigt
nrytig nrytgi nrygti nrygit nriytg nriygt nrityg nritgy nrigty nrigyt nrtiyg
nrtigy nrtyig nrtygi nrtgyi nrtgiy nrgity nrgiyt nrgtiy nrgtyi nrgyti nrgyit
nirytg nirygt nirtyg nirtgy nirgty nirgyt niyrtg niyrgt niytrg niytgr niygtr
niygrt nityrg nitygr nitryg nitrgy nitgry nitgyr nigytr nigyrt nigtyr nigtry
nigrty nigryt ntriyg ntrigy ntryig ntrygi ntrgyi ntrgiy ntiryg ntirgy ntiyrg
ntiygr ntigyr ntigry ntyirg ntyigr ntyrig ntyrgi ntygri ntygir ntgiyr ntgiry
ntgyir ntgyri ntgryi ntgriy ngrity ngriyt ngrtiy ngrtyi ngryti ngryit ngirty
ngiryt ngitry ngityr ngiytr ngiyrt ngtiry ngtiyr ngtriy ngtryi ngtyri ngtyir
ngyitr ngyirt ngytir ngytri ngyrti ngyrit gyrint gyritn gyrnit gyrnti gyrtni
gyrtin gyirnt gyirtn gyinrt gyintr gyitnr gyitrn gynirt gynitr gynrit gynrti
gyntri gyntir gytinr gytirn gytnir gytnri gytrni gytrin gryint gryitn grynit
grynti grytni grytin griynt griytn grinyt grinty gritny grityn grniyt grnity
grnyit grnyti grntyi grntiy grtiny grtiyn grtniy grtnyi grtyni grtyin girynt
girytn girnyt girnty girtny girtyn giyrnt giyrtn giynrt giyntr giytnr giytrn
ginyrt ginytr ginryt ginrty gintry gintyr gitynr gityrn gitnyr gitnry gitrny
gitryn gnriyt gnrity gnryit gnryti gnrtyi gnrtiy gniryt gnirty gniyrt gniytr
gnityr gnitry gnyirt gnyitr gnyrit gnyrti gnytri gnytir gntiyr gntiry gntyir
gntyri gntryi gntriy gtriny gtriyn gtrniy gtrnyi gtryni gtryin gtirny gtiryn
gtinry gtinyr gtiynr gtiyrn gtniry gtniyr gtnriy gtnryi gtnyri gtnyir gtyinr
gtyirn gtynir gtynri gtyrni gtyrin

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History of cryptography
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