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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: torpid
cipher variations:
upsqje vqtrkf wruslg xsvtmh ytwuni
zuxvoj avywpk bwzxql cxayrm dybzsn
ezcato fadbup gbecvq hcfdwr idgexs
jehfyt kfigzu lgjhav mhkibw niljcx
ojmkdy pknlez qlomfa rmpngb snqohc

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: torpid
Cipher: glikrw

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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: torpid

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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: torpid
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: torpid
Cipher: gbecvq

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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: torpid
Cipher: 444324534241

Extended Methods:
Method #1

Plaintext: torpid
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
t o r p i d 
4 4 2 5 4 4 
4 3 4 3 2 1 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: torpid
Cipher: twtoob

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Method #3

Plaintext: torpid
method variations:
thysrq hysrqt ysrqth
srqthy rqthys qthysr

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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: torpid

all 720 cipher variations:
torpid torpdi toripd toridp tordip tordpi toprid toprdi topird topidr topdir
topdri toiprd toipdr toirpd toirdp toidrp toidpr todpir todpri todipr todirp
todrip todrpi tropid tropdi troipd troidp trodip trodpi trpoid trpodi trpiod
trpido trpdio trpdoi tripod tripdo triopd triodp tridop tridpo trdpio trdpoi
trdipo trdiop trdoip trdopi tproid tprodi tpriod tprido tprdio tprdoi tporid
tpordi tpoird tpoidr tpodir tpodri tpiord tpiodr tpirod tpirdo tpidro tpidor
tpdoir tpdori tpdior tpdiro tpdrio tpdroi tirpod tirpdo tiropd tirodp tirdop
tirdpo tiprod tiprdo tipord tipodr tipdor tipdro tioprd tiopdr tiorpd tiordp
tiodrp tiodpr tidpor tidpro tidopr tidorp tidrop tidrpo tdrpio tdrpoi tdripo
tdriop tdroip tdropi tdprio tdproi tdpiro tdpior tdpoir tdpori tdipro tdipor
tdirpo tdirop tdiorp tdiopr tdopir tdopri tdoipr tdoirp tdorip tdorpi otrpid
otrpdi otripd otridp otrdip otrdpi otprid otprdi otpird otpidr otpdir otpdri
otiprd otipdr otirpd otirdp otidrp otidpr otdpir otdpri otdipr otdirp otdrip
otdrpi ortpid ortpdi ortipd ortidp ortdip ortdpi orptid orptdi orpitd orpidt
orpdit orpdti oriptd oripdt oritpd oritdp oridtp oridpt ordpit ordpti ordipt
orditp ordtip ordtpi oprtid oprtdi opritd opridt oprdit oprdti optrid optrdi
optird optidr optdir optdri opitrd opitdr opirtd opirdt opidrt opidtr opdtir
opdtri opditr opdirt opdrit opdrti oirptd oirpdt oirtpd oirtdp oirdtp oirdpt
oiprtd oiprdt oiptrd oiptdr oipdtr oipdrt oitprd oitpdr oitrpd oitrdp oitdrp
oitdpr oidptr oidprt oidtpr oidtrp oidrtp oidrpt odrpit odrpti odript odritp
odrtip odrtpi odprit odprti odpirt odpitr odptir odptri odiprt odiptr odirpt
odirtp oditrp oditpr odtpir odtpri odtipr odtirp odtrip odtrpi rotpid rotpdi
rotipd rotidp rotdip rotdpi roptid roptdi ropitd ropidt ropdit ropdti roiptd
roipdt roitpd roitdp roidtp roidpt rodpit rodpti rodipt roditp rodtip rodtpi
rtopid rtopdi rtoipd rtoidp rtodip rtodpi rtpoid rtpodi rtpiod rtpido rtpdio
rtpdoi rtipod rtipdo rtiopd rtiodp rtidop rtidpo rtdpio rtdpoi rtdipo rtdiop
rtdoip rtdopi rptoid rptodi rptiod rptido rptdio rptdoi rpotid rpotdi rpoitd
rpoidt rpodit rpodti rpiotd rpiodt rpitod rpitdo rpidto rpidot rpdoit rpdoti
rpdiot rpdito rpdtio rpdtoi ritpod ritpdo ritopd ritodp ritdop ritdpo riptod
riptdo ripotd ripodt ripdot ripdto rioptd riopdt riotpd riotdp riodtp riodpt
ridpot ridpto ridopt ridotp ridtop ridtpo rdtpio rdtpoi rdtipo rdtiop rdtoip
rdtopi rdptio rdptoi rdpito rdpiot rdpoit rdpoti rdipto rdipot rditpo rditop
rdiotp rdiopt rdopit rdopti rdoipt rdoitp rdotip rdotpi portid portdi poritd
poridt pordit pordti potrid potrdi potird potidr potdir potdri poitrd poitdr
poirtd poirdt poidrt poidtr podtir podtri poditr podirt podrit podrti protid
protdi proitd proidt prodit prodti prtoid prtodi prtiod prtido prtdio prtdoi
pritod pritdo priotd priodt pridot pridto prdtio prdtoi prdito prdiot prdoit
prdoti ptroid ptrodi ptriod ptrido ptrdio ptrdoi ptorid ptordi ptoird ptoidr
ptodir ptodri ptiord ptiodr ptirod ptirdo ptidro ptidor ptdoir ptdori ptdior
ptdiro ptdrio ptdroi pirtod pirtdo pirotd pirodt pirdot pirdto pitrod pitrdo
pitord pitodr pitdor pitdro piotrd piotdr piortd piordt piodrt piodtr pidtor
pidtro pidotr pidort pidrot pidrto pdrtio pdrtoi pdrito pdriot pdroit pdroti
pdtrio pdtroi pdtiro pdtior pdtoir pdtori pditro pditor pdirto pdirot pdiort
pdiotr pdotir pdotri pdoitr pdoirt pdorit pdorti iorptd iorpdt iortpd iortdp
iordtp iordpt ioprtd ioprdt ioptrd ioptdr iopdtr iopdrt iotprd iotpdr iotrpd
iotrdp iotdrp iotdpr iodptr iodprt iodtpr iodtrp iodrtp iodrpt iroptd iropdt
irotpd irotdp irodtp irodpt irpotd irpodt irptod irptdo irpdto irpdot irtpod
irtpdo irtopd irtodp irtdop irtdpo irdpto irdpot irdtpo irdtop irdotp irdopt
iprotd iprodt iprtod iprtdo iprdto iprdot iportd ipordt ipotrd ipotdr ipodtr
ipodrt iptord iptodr iptrod iptrdo iptdro iptdor ipdotr ipdort ipdtor ipdtro
ipdrto ipdrot itrpod itrpdo itropd itrodp itrdop itrdpo itprod itprdo itpord
itpodr itpdor itpdro itoprd itopdr itorpd itordp itodrp itodpr itdpor itdpro
itdopr itdorp itdrop itdrpo idrpto idrpot idrtpo idrtop idrotp idropt idprto
idprot idptro idptor idpotr idport idtpro idtpor idtrpo idtrop idtorp idtopr
idoptr idoprt idotpr idotrp idortp idorpt dorpit dorpti doript doritp dortip
dortpi doprit doprti dopirt dopitr doptir doptri doiprt doiptr doirpt doirtp
doitrp doitpr dotpir dotpri dotipr dotirp dotrip dotrpi dropit dropti droipt
droitp drotip drotpi drpoit drpoti drpiot drpito drptio drptoi dripot dripto
driopt driotp dritop dritpo drtpio drtpoi drtipo drtiop drtoip drtopi dproit
dproti dpriot dprito dprtio dprtoi dporit dporti dpoirt dpoitr dpotir dpotri
dpiort dpiotr dpirot dpirto dpitro dpitor dptoir dptori dptior dptiro dptrio
dptroi dirpot dirpto diropt dirotp dirtop dirtpo diprot diprto diport dipotr
diptor diptro dioprt dioptr diorpt diortp diotrp diotpr ditpor ditpro ditopr
ditorp ditrop ditrpo dtrpio dtrpoi dtripo dtriop dtroip dtropi dtprio dtproi
dtpiro dtpior dtpoir dtpori dtipro dtipor dtirpo dtirop dtiorp dtiopr dtopir
dtopri dtoipr dtoirp dtorip dtorpi

Read more ...[1] , [2] , [3]

History of cryptography
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