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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: metius
cipher variations:
nfujvt ogvkwu phwlxv qixmyw rjynzx
skzoay tlapbz umbqca vncrdb wodsec
xpetfd yqfuge zrgvhf ashwig btixjh
cujyki dvkzlj ewlamk fxmbnl gyncom
hzodpn iapeqo jbqfrp kcrgsq ldshtr

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: metius
Cipher: nvgrfh

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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: metius

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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: metius
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: metius
Cipher: zrgvhf

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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: metius
Cipher: 235144425434

Extended Methods:
Method #1

Plaintext: metius
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 t i u s 
2 5 4 4 5 3 
3 1 4 2 4 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: metius
Cipher: wtpcit

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Method #3

Plaintext: metius
method variations:
xqtwoi qtwoix twoixq
woixqt oixqtw ixqtwo

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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: metius

all 720 cipher variations:
metius metisu metuis metusi metsui metsiu meitus meitsu meiuts meiust meisut
meistu meuits meuist meutis meutsi meusti meusit mesiut mesitu mesuit mesuti
mestui mestiu mteius mteisu mteuis mteusi mtesui mtesiu mtieus mtiesu mtiues
mtiuse mtisue mtiseu mtuies mtuise mtueis mtuesi mtusei mtusie mtsiue mtsieu
mtsuie mtsuei mtseui mtseiu miteus mitesu mitues mituse mitsue mitseu mietus
mietsu mieuts mieust miesut miestu miuets miuest miutes miutse miuste miuset
miseut misetu misuet misute mistue misteu muties mutise muteis mutesi mutsei
mutsie muites muitse muiets muiest muiset muiste mueits mueist muetis muetsi
muesti muesit musiet musite museit museti mustei mustie mstiue mstieu mstuie
mstuei msteui msteiu msitue msiteu msiute msiuet msieut msietu msuite msuiet
msutie msutei msueti msueit mseiut mseitu mseuit mseuti msetui msetiu emtius
emtisu emtuis emtusi emtsui emtsiu emitus emitsu emiuts emiust emisut emistu
emuits emuist emutis emutsi emusti emusit emsiut emsitu emsuit emsuti emstui
emstiu etmius etmisu etmuis etmusi etmsui etmsiu etimus etimsu etiums etiusm
etisum etismu etuims etuism etumis etumsi etusmi etusim etsium etsimu etsuim
etsumi etsmui etsmiu eitmus eitmsu eitums eitusm eitsum eitsmu eimtus eimtsu
eimuts eimust eimsut eimstu eiumts eiumst eiutms eiutsm eiustm eiusmt eismut
eismtu eisumt eisutm eistum eistmu eutims eutism eutmis eutmsi eutsmi eutsim
euitms euitsm euimts euimst euismt euistm eumits eumist eumtis eumtsi eumsti
eumsit eusimt eusitm eusmit eusmti eustmi eustim estium estimu estuim estumi
estmui estmiu esitum esitmu esiutm esiumt esimut esimtu esuitm esuimt esutim
esutmi esumti esumit esmiut esmitu esmuit esmuti esmtui esmtiu temius temisu
temuis temusi temsui temsiu teimus teimsu teiums teiusm teisum teismu teuims
teuism teumis teumsi teusmi teusim tesium tesimu tesuim tesumi tesmui tesmiu
tmeius tmeisu tmeuis tmeusi tmesui tmesiu tmieus tmiesu tmiues tmiuse tmisue
tmiseu tmuies tmuise tmueis tmuesi tmusei tmusie tmsiue tmsieu tmsuie tmsuei
tmseui tmseiu timeus timesu timues timuse timsue timseu tiemus tiemsu tieums
tieusm tiesum tiesmu tiuems tiuesm tiumes tiumse tiusme tiusem tiseum tisemu
tisuem tisume tismue tismeu tumies tumise tumeis tumesi tumsei tumsie tuimes
tuimse tuiems tuiesm tuisem tuisme tueims tueism tuemis tuemsi tuesmi tuesim
tusiem tusime tuseim tusemi tusmei tusmie tsmiue tsmieu tsmuie tsmuei tsmeui
tsmeiu tsimue tsimeu tsiume tsiuem tsieum tsiemu tsuime tsuiem tsumie tsumei
tsuemi tsueim tseium tseimu tseuim tseumi tsemui tsemiu ietmus ietmsu ietums
ietusm ietsum ietsmu iemtus iemtsu iemuts iemust iemsut iemstu ieumts ieumst
ieutms ieutsm ieustm ieusmt iesmut iesmtu iesumt iesutm iestum iestmu itemus
itemsu iteums iteusm itesum itesmu itmeus itmesu itmues itmuse itmsue itmseu
itumes itumse ituems ituesm itusem itusme itsmue itsmeu itsume itsuem itseum
itsemu imteus imtesu imtues imtuse imtsue imtseu imetus imetsu imeuts imeust
imesut imestu imuets imuest imutes imutse imuste imuset imseut imsetu imsuet
imsute imstue imsteu iutmes iutmse iutems iutesm iutsem iutsme iumtes iumtse
iumets iumest iumset iumste iuemts iuemst iuetms iuetsm iuestm iuesmt iusmet
iusmte iusemt iusetm iustem iustme istmue istmeu istume istuem isteum istemu
ismtue ismteu ismute ismuet ismeut ismetu isumte isumet isutme isutem isuetm
isuemt isemut isemtu iseumt iseutm isetum isetmu uetims uetism uetmis uetmsi
uetsmi uetsim ueitms ueitsm ueimts ueimst ueismt ueistm uemits uemist uemtis
uemtsi uemsti uemsit uesimt uesitm uesmit uesmti uestmi uestim uteims uteism
utemis utemsi utesmi utesim utiems utiesm utimes utimse utisme utisem utmies
utmise utmeis utmesi utmsei utmsie utsime utsiem utsmie utsmei utsemi utseim
uitems uitesm uitmes uitmse uitsme uitsem uietms uietsm uiemts uiemst uiesmt
uiestm uimets uimest uimtes uimtse uimste uimset uisemt uisetm uismet uismte
uistme uistem umties umtise umteis umtesi umtsei umtsie umites umitse umiets
umiest umiset umiste umeits umeist umetis umetsi umesti umesit umsiet umsite
umseit umseti umstei umstie ustime ustiem ustmie ustmei ustemi usteim usitme
usitem usimte usimet usiemt usietm usmite usmiet usmtie usmtei usmeti usmeit
useimt useitm usemit usemti usetmi usetim setium setimu setuim setumi setmui
setmiu seitum seitmu seiutm seiumt seimut seimtu seuitm seuimt seutim seutmi
seumti seumit semiut semitu semuit semuti semtui semtiu steium steimu steuim
steumi stemui stemiu stieum stiemu stiuem stiume stimue stimeu stuiem stuime
stueim stuemi stumei stumie stmiue stmieu stmuie stmuei stmeui stmeiu siteum
sitemu situem situme sitmue sitmeu sietum sietmu sieutm sieumt siemut siemtu
siuetm siuemt siutem siutme siumte siumet simeut simetu simuet simute simtue
simteu sutiem sutime suteim sutemi sutmei sutmie suitem suitme suietm suiemt
suimet suimte sueitm sueimt suetim suetmi suemti suemit sumiet sumite sumeit
sumeti sumtei sumtie smtiue smtieu smtuie smtuei smteui smteiu smitue smiteu
smiute smiuet smieut smietu smuite smuiet smutie smutei smueti smueit smeiut
smeitu smeuit smeuti smetui smetiu

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History of cryptography
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