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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: mercal
cipher variations:
nfsdbm ogtecn phufdo qivgep rjwhfq
skxigr tlyjhs umzkit vnalju wobmkv
xpcnlw yqdomx zrepny asfqoz btgrpa
cuhsqb dvitrc ewjusd fxkvte gylwuf
hzmxvg ianywh jbozxi kcpayj ldqbzk

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: mercal
Cipher: nvixzo

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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: mercal

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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: mercal
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: mercal
Cipher: zrepny

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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: mercal
Cipher: 235124311113

Extended Methods:
Method #1

Plaintext: mercal
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
m e r c a l 
2 5 2 3 1 1 
3 1 4 1 1 3 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: mercal
Cipher: wmacdl

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Method #3

Plaintext: mercal
method variations:
xfoaah foaahx oaahxf
aahxfo ahxfoa hxfoaa

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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: mercal

all 720 cipher variations:
mercal mercla meracl meralc merlac merlca mecral mecrla mecarl mecalr meclar
meclra meacrl meaclr mearcl mearlc mealrc mealcr melcar melcra melacr melarc
melrac melrca mrecal mrecla mreacl mrealc mrelac mrelca mrceal mrcela mrcael
mrcale mrclae mrclea mracel mracle mraecl mraelc mralec mralce mrlcae mrlcea
mrlace mrlaec mrleac mrleca mcreal mcrela mcrael mcrale mcrlae mcrlea mceral
mcerla mcearl mcealr mcelar mcelra mcaerl mcaelr mcarel mcarle mcalre mcaler
mclear mclera mclaer mclare mclrae mclrea marcel marcle marecl marelc marlec
marlce macrel macrle macerl macelr macler maclre maecrl maeclr maercl maerlc
maelrc maelcr malcer malcre malecr malerc malrec malrce mlrcae mlrcea mlrace
mlraec mlreac mlreca mlcrae mlcrea mlcare mlcaer mlcear mlcera mlacre mlacer
mlarce mlarec mlaerc mlaecr mlecar mlecra mleacr mlearc mlerac mlerca emrcal
emrcla emracl emralc emrlac emrlca emcral emcrla emcarl emcalr emclar emclra
emacrl emaclr emarcl emarlc emalrc emalcr emlcar emlcra emlacr emlarc emlrac
emlrca ermcal ermcla ermacl ermalc ermlac ermlca ercmal ercmla ercaml ercalm
erclam erclma eracml eraclm eramcl eramlc eralmc eralcm erlcam erlcma erlacm
erlamc erlmac erlmca ecrmal ecrmla ecraml ecralm ecrlam ecrlma ecmral ecmrla
ecmarl ecmalr ecmlar ecmlra ecamrl ecamlr ecarml ecarlm ecalrm ecalmr eclmar
eclmra eclamr eclarm eclram eclrma earcml earclm earmcl earmlc earlmc earlcm
eacrml eacrlm eacmrl eacmlr eaclmr eaclrm eamcrl eamclr eamrcl eamrlc eamlrc
eamlcr ealcmr ealcrm ealmcr ealmrc ealrmc ealrcm elrcam elrcma elracm elramc
elrmac elrmca elcram elcrma elcarm elcamr elcmar elcmra elacrm elacmr elarcm
elarmc elamrc elamcr elmcar elmcra elmacr elmarc elmrac elmrca remcal remcla
remacl remalc remlac remlca recmal recmla recaml recalm reclam reclma reacml
reaclm reamcl reamlc realmc realcm relcam relcma relacm relamc relmac relmca
rmecal rmecla rmeacl rmealc rmelac rmelca rmceal rmcela rmcael rmcale rmclae
rmclea rmacel rmacle rmaecl rmaelc rmalec rmalce rmlcae rmlcea rmlace rmlaec
rmleac rmleca rcmeal rcmela rcmael rcmale rcmlae rcmlea rcemal rcemla rceaml
rcealm rcelam rcelma rcaeml rcaelm rcamel rcamle rcalme rcalem rcleam rclema
rclaem rclame rclmae rclmea ramcel ramcle ramecl ramelc ramlec ramlce racmel
racmle raceml racelm raclem raclme raecml raeclm raemcl raemlc raelmc raelcm
ralcem ralcme ralecm ralemc ralmec ralmce rlmcae rlmcea rlmace rlmaec rlmeac
rlmeca rlcmae rlcmea rlcame rlcaem rlceam rlcema rlacme rlacem rlamce rlamec
rlaemc rlaecm rlecam rlecma rleacm rleamc rlemac rlemca cermal cermla ceraml
ceralm cerlam cerlma cemral cemrla cemarl cemalr cemlar cemlra ceamrl ceamlr
cearml cearlm cealrm cealmr celmar celmra celamr celarm celram celrma cremal
cremla creaml crealm crelam crelma crmeal crmela crmael crmale crmlae crmlea
cramel cramle craeml craelm cralem cralme crlmae crlmea crlame crlaem crleam
crlema cmreal cmrela cmrael cmrale cmrlae cmrlea cmeral cmerla cmearl cmealr
cmelar cmelra cmaerl cmaelr cmarel cmarle cmalre cmaler cmlear cmlera cmlaer
cmlare cmlrae cmlrea carmel carmle careml carelm carlem carlme camrel camrle
camerl camelr camler camlre caemrl caemlr caerml caerlm caelrm caelmr calmer
calmre calemr calerm calrem calrme clrmae clrmea clrame clraem clream clrema
clmrae clmrea clmare clmaer clmear clmera clamre clamer clarme clarem claerm
claemr clemar clemra cleamr clearm cleram clerma aercml aerclm aermcl aermlc
aerlmc aerlcm aecrml aecrlm aecmrl aecmlr aeclmr aeclrm aemcrl aemclr aemrcl
aemrlc aemlrc aemlcr aelcmr aelcrm aelmcr aelmrc aelrmc aelrcm arecml areclm
aremcl aremlc arelmc arelcm arceml arcelm arcmel arcmle arclme arclem armcel
armcle armecl armelc armlec armlce arlcme arlcem arlmce arlmec arlemc arlecm
acreml acrelm acrmel acrmle acrlme acrlem acerml acerlm acemrl acemlr acelmr
acelrm acmerl acmelr acmrel acmrle acmlre acmler aclemr aclerm aclmer aclmre
aclrme aclrem amrcel amrcle amrecl amrelc amrlec amrlce amcrel amcrle amcerl
amcelr amcler amclre amecrl ameclr amercl amerlc amelrc amelcr amlcer amlcre
amlecr amlerc amlrec amlrce alrcme alrcem alrmce alrmec alremc alrecm alcrme
alcrem alcmre alcmer alcemr alcerm almcre almcer almrce almrec almerc almecr
alecmr alecrm alemcr alemrc alermc alercm lercam lercma leracm leramc lermac
lermca lecram lecrma lecarm lecamr lecmar lecmra leacrm leacmr learcm learmc
leamrc leamcr lemcar lemcra lemacr lemarc lemrac lemrca lrecam lrecma lreacm
lreamc lremac lremca lrceam lrcema lrcaem lrcame lrcmae lrcmea lracem lracme
lraecm lraemc lramec lramce lrmcae lrmcea lrmace lrmaec lrmeac lrmeca lcream
lcrema lcraem lcrame lcrmae lcrmea lceram lcerma lcearm lceamr lcemar lcemra
lcaerm lcaemr lcarem lcarme lcamre lcamer lcmear lcmera lcmaer lcmare lcmrae
lcmrea larcem larcme larecm laremc larmec larmce lacrem lacrme lacerm lacemr
lacmer lacmre laecrm laecmr laercm laermc laemrc laemcr lamcer lamcre lamecr
lamerc lamrec lamrce lmrcae lmrcea lmrace lmraec lmreac lmreca lmcrae lmcrea
lmcare lmcaer lmcear lmcera lmacre lmacer lmarce lmarec lmaerc lmaecr lmecar
lmecra lmeacr lmearc lmerac lmerca

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History of cryptography
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