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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: toucra
cipher variations:
upvdsb vqwetc wrxfud xsygve ytzhwf
zuaixg avbjyh bwckzi cxdlaj dyembk
ezfncl fagodm gbhpen hciqfo idjrgp
jekshq kfltir lgmujs mhnvkt niowlu
ojpxmv pkqynw qlrzox rmsapy sntbqz

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: toucra
Cipher: glfxiz

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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: toucra

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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: toucra
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: toucra
Cipher: gbhpen

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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: toucra
Cipher: 444354312411

Extended Methods:
Method #1

Plaintext: toucra
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 u c r a 
4 4 5 3 2 1 
4 3 4 1 4 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: toucra
Cipher: tpbodd

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Method #3

Plaintext: toucra
method variations:
txofdq xofdqt ofdqtx
fdqtxo dqtxof qtxofd

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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: toucra

all 720 cipher variations:
toucra toucar tourca tourac touarc touacr tocura tocuar tocrua tocrau tocaru
tocaur torcua torcau toruca toruac torauc toracu toacru toacur toarcu toaruc
toaurc toaucr tuocra tuocar tuorca tuorac tuoarc tuoacr tucora tucoar tucroa
tucrao tucaro tucaor turcoa turcao turoca turoac turaoc turaco tuacro tuacor
tuarco tuaroc tuaorc tuaocr tcuora tcuoar tcuroa tcurao tcuaro tcuaor tcoura
tcouar tcorua tcorau tcoaru tcoaur tcroua tcroau tcruoa tcruao tcrauo tcraou
tcaoru tcaour tcarou tcaruo tcauro tcauor trucoa trucao truoca truoac truaoc
truaco trcuoa trcuao trcoua trcoau trcaou trcauo trocua trocau trouca trouac
troauc troacu tracou tracuo traocu traouc trauoc trauco taucro taucor taurco
tauroc tauorc tauocr tacuro tacuor tacruo tacrou tacoru tacour tarcuo tarcou
taruco taruoc tarouc tarocu taocru taocur taorcu taoruc taourc taoucr otucra
otucar oturca oturac otuarc otuacr otcura otcuar otcrua otcrau otcaru otcaur
otrcua otrcau otruca otruac otrauc otracu otacru otacur otarcu otaruc otaurc
otaucr outcra outcar outrca outrac outarc outacr ouctra ouctar oucrta oucrat
oucart oucatr ourcta ourcat ourtca ourtac ouratc ouract ouacrt ouactr ouarct
ouartc ouatrc ouatcr ocutra ocutar ocurta ocurat ocuart ocuatr octura octuar
octrua octrau octaru octaur ocrtua ocrtau ocruta ocruat ocraut ocratu ocatru
ocatur ocartu ocarut ocaurt ocautr oructa orucat orutca orutac oruatc oruact
orcuta orcuat orctua orctau orcatu orcaut ortcua ortcau ortuca ortuac ortauc
ortacu oractu oracut oratcu oratuc orautc orauct oaucrt oauctr oaurct oaurtc
oautrc oautcr oacurt oacutr oacrut oacrtu oactru oactur oarcut oarctu oaruct
oarutc oartuc oartcu oatcru oatcur oatrcu oatruc oaturc oatucr uotcra uotcar
uotrca uotrac uotarc uotacr uoctra uoctar uocrta uocrat uocart uocatr uorcta
uorcat uortca uortac uoratc uoract uoacrt uoactr uoarct uoartc uoatrc uoatcr
utocra utocar utorca utorac utoarc utoacr utcora utcoar utcroa utcrao utcaro
utcaor utrcoa utrcao utroca utroac utraoc utraco utacro utacor utarco utaroc
utaorc utaocr uctora uctoar uctroa uctrao uctaro uctaor ucotra ucotar ucorta
ucorat ucoart ucoatr ucrota ucroat ucrtoa ucrtao ucrato ucraot ucaort ucaotr
ucarot ucarto ucatro ucator urtcoa urtcao urtoca urtoac urtaoc urtaco urctoa
urctao urcota urcoat urcaot urcato urocta urocat urotca urotac uroatc uroact
uracot uracto uraoct uraotc uratoc uratco uatcro uatcor uatrco uatroc uatorc
uatocr uactro uactor uacrto uacrot uacort uacotr uarcto uarcot uartco uartoc
uarotc uaroct uaocrt uaoctr uaorct uaortc uaotrc uaotcr coutra coutar courta
courat couart couatr cotura cotuar cotrua cotrau cotaru cotaur cortua cortau
coruta coruat coraut coratu coatru coatur coartu coarut coaurt coautr cuotra
cuotar cuorta cuorat cuoart cuoatr cutora cutoar cutroa cutrao cutaro cutaor
curtoa curtao curota curoat curaot curato cuatro cuator cuarto cuarot cuaort
cuaotr ctuora ctuoar cturoa cturao ctuaro ctuaor ctoura ctouar ctorua ctorau
ctoaru ctoaur ctroua ctroau ctruoa ctruao ctrauo ctraou ctaoru ctaour ctarou
ctaruo ctauro ctauor crutoa crutao cruota cruoat cruaot cruato crtuoa crtuao
crtoua crtoau crtaou crtauo crotua crotau crouta crouat croaut croatu cratou
cratuo craotu craout crauot crauto cautro cautor caurto caurot cauort cauotr
caturo catuor catruo catrou catoru catour cartuo cartou caruto caruot carout
carotu caotru caotur caortu caorut caourt caoutr roucta roucat routca routac
rouatc rouact rocuta rocuat roctua roctau rocatu rocaut rotcua rotcau rotuca
rotuac rotauc rotacu roactu roacut roatcu roatuc roautc roauct ruocta ruocat
ruotca ruotac ruoatc ruoact rucota rucoat ructoa ructao rucato rucaot rutcoa
rutcao rutoca rutoac rutaoc rutaco ruacto ruacot ruatco ruatoc ruaotc ruaoct
rcuota rcuoat rcutoa rcutao rcuato rcuaot rcouta rcouat rcotua rcotau rcoatu
rcoaut rctoua rctoau rctuoa rctuao rctauo rctaou rcaotu rcaout rcatou rcatuo
rcauto rcauot rtucoa rtucao rtuoca rtuoac rtuaoc rtuaco rtcuoa rtcuao rtcoua
rtcoau rtcaou rtcauo rtocua rtocau rtouca rtouac rtoauc rtoacu rtacou rtacuo
rtaocu rtaouc rtauoc rtauco raucto raucot rautco rautoc rauotc rauoct racuto
racuot ractuo ractou racotu racout ratcuo ratcou ratuco ratuoc ratouc ratocu
raoctu raocut raotcu raotuc raoutc raouct aoucrt aouctr aourct aourtc aoutrc
aoutcr aocurt aocutr aocrut aocrtu aoctru aoctur aorcut aorctu aoruct aorutc
aortuc aortcu aotcru aotcur aotrcu aotruc aoturc aotucr auocrt auoctr auorct
auortc auotrc auotcr aucort aucotr aucrot aucrto auctro auctor aurcot aurcto
auroct aurotc aurtoc aurtco autcro autcor autrco autroc autorc autocr acuort
acuotr acurot acurto acutro acutor acourt acoutr acorut acortu acotru acotur
acrout acrotu acruot acruto acrtuo acrtou actoru actour actrou actruo acturo
actuor arucot aructo aruoct aruotc arutoc arutco arcuot arcuto arcout arcotu
arctou arctuo arocut aroctu arouct aroutc arotuc arotcu artcou artcuo artocu
artouc artuoc artuco atucro atucor aturco aturoc atuorc atuocr atcuro atcuor
atcruo atcrou atcoru atcour atrcuo atrcou atruco atruoc atrouc atrocu atocru
atocur atorcu atoruc atourc atoucr

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History of cryptography
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