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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: bchase
cipher variations:
cdibtf dejcug efkdvh fglewi ghmfxj
hingyk ijohzl jkpiam klqjbn lmrkco
mnsldp notmeq opunfr pqvogs qrwpht
rsxqiu styrjv tuzskw uvatlx vwbumy
wxcvnz xydwoa yzexpb zafyqc abgzrd

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: bchase
Cipher: yxszhv

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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: bchase

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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: bchase
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: bchase
Cipher: opunfr

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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: bchase
Cipher: 213132113451

Extended Methods:
Method #1

Plaintext: bchase
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
b c h a s e 
2 3 3 1 3 5 
1 1 2 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: bchase
Cipher: mcxabd

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Method #3

Plaintext: bchase
method variations:
llblyf lblyfl blyfll
lyfllb yfllbl fllbly

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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: bchase

all 720 cipher variations:
bchase bchaes bchsae bchsea bchesa bcheas bcahse bcahes bcashe bcaseh bcaesh
bcaehs bcsahe bcsaeh bcshae bcshea bcseha bcseah bceash bceahs bcesah bcesha
bcehsa bcehas bhcase bhcaes bhcsae bhcsea bhcesa bhceas bhacse bhaces bhasce
bhasec bhaesc bhaecs bhsace bhsaec bhscae bhscea bhseca bhseac bheasc bheacs
bhesac bhesca bhecsa bhecas bahcse bahces bahsce bahsec bahesc bahecs bachse
baches bacshe bacseh bacesh bacehs basche basceh bashce bashec basehc basech
baecsh baechs baesch baeshc baehsc baehcs bshace bshaec bshcae bshcea bsheca
bsheac bsahce bsahec bsache bsaceh bsaech bsaehc bscahe bscaeh bschae bschea
bsceha bsceah bseach bseahc bsecah bsecha bsehca bsehac behasc behacs behsac
behsca behcsa behcas beahsc beahcs beashc beasch beacsh beachs besahc besach
beshac beshca bescha bescah becash becahs becsah becsha bechsa bechas cbhase
cbhaes cbhsae cbhsea cbhesa cbheas cbahse cbahes cbashe cbaseh cbaesh cbaehs
cbsahe cbsaeh cbshae cbshea cbseha cbseah cbeash cbeahs cbesah cbesha cbehsa
cbehas chbase chbaes chbsae chbsea chbesa chbeas chabse chabes chasbe chaseb
chaesb chaebs chsabe chsaeb chsbae chsbea chseba chseab cheasb cheabs chesab
chesba chebsa chebas cahbse cahbes cahsbe cahseb cahesb cahebs cabhse cabhes
cabshe cabseh cabesh cabehs casbhe casbeh cashbe casheb casehb casebh caebsh
caebhs caesbh caeshb caehsb caehbs cshabe cshaeb cshbae cshbea csheba csheab
csahbe csaheb csabhe csabeh csaebh csaehb csbahe csbaeh csbhae csbhea csbeha
csbeah cseabh cseahb csebah csebha csehba csehab cehasb cehabs cehsab cehsba
cehbsa cehbas ceahsb ceahbs ceashb ceasbh ceabsh ceabhs cesahb cesabh ceshab
ceshba cesbha cesbah cebash cebahs cebsah cebsha cebhsa cebhas hcbase hcbaes
hcbsae hcbsea hcbesa hcbeas hcabse hcabes hcasbe hcaseb hcaesb hcaebs hcsabe
hcsaeb hcsbae hcsbea hcseba hcseab hceasb hceabs hcesab hcesba hcebsa hcebas
hbcase hbcaes hbcsae hbcsea hbcesa hbceas hbacse hbaces hbasce hbasec hbaesc
hbaecs hbsace hbsaec hbscae hbscea hbseca hbseac hbeasc hbeacs hbesac hbesca
hbecsa hbecas habcse habces habsce habsec habesc habecs hacbse hacbes hacsbe
hacseb hacesb hacebs hascbe hasceb hasbce hasbec hasebc hasecb haecsb haecbs
haescb haesbc haebsc haebcs hsbace hsbaec hsbcae hsbcea hsbeca hsbeac hsabce
hsabec hsacbe hsaceb hsaecb hsaebc hscabe hscaeb hscbae hscbea hsceba hsceab
hseacb hseabc hsecab hsecba hsebca hsebac hebasc hebacs hebsac hebsca hebcsa
hebcas heabsc heabcs heasbc heascb heacsb heacbs hesabc hesacb hesbac hesbca
hescba hescab hecasb hecabs hecsab hecsba hecbsa hecbas achbse achbes achsbe
achseb achesb achebs acbhse acbhes acbshe acbseh acbesh acbehs acsbhe acsbeh
acshbe acsheb acsehb acsebh acebsh acebhs acesbh aceshb acehsb acehbs ahcbse
ahcbes ahcsbe ahcseb ahcesb ahcebs ahbcse ahbces ahbsce ahbsec ahbesc ahbecs
ahsbce ahsbec ahscbe ahsceb ahsecb ahsebc ahebsc ahebcs ahesbc ahescb ahecsb
ahecbs abhcse abhces abhsce abhsec abhesc abhecs abchse abches abcshe abcseh
abcesh abcehs absche absceh abshce abshec absehc absech abecsh abechs abesch
abeshc abehsc abehcs ashbce ashbec ashcbe ashceb ashecb ashebc asbhce asbhec
asbche asbceh asbech asbehc ascbhe ascbeh aschbe ascheb ascehb ascebh asebch
asebhc asecbh asechb asehcb asehbc aehbsc aehbcs aehsbc aehscb aehcsb aehcbs
aebhsc aebhcs aebshc aebsch aebcsh aebchs aesbhc aesbch aeshbc aeshcb aeschb
aescbh aecbsh aecbhs aecsbh aecshb aechsb aechbs schabe schaeb schbae schbea
scheba scheab scahbe scaheb scabhe scabeh scaebh scaehb scbahe scbaeh scbhae
scbhea scbeha scbeah sceabh sceahb scebah scebha scehba scehab shcabe shcaeb
shcbae shcbea shceba shceab shacbe shaceb shabce shabec shaebc shaecb shbace
shbaec shbcae shbcea shbeca shbeac sheabc sheacb shebac shebca shecba shecab
sahcbe sahceb sahbce sahbec sahebc sahecb sachbe sacheb sacbhe sacbeh sacebh
sacehb sabche sabceh sabhce sabhec sabehc sabech saecbh saechb saebch saebhc
saehbc saehcb sbhace sbhaec sbhcae sbhcea sbheca sbheac sbahce sbahec sbache
sbaceh sbaech sbaehc sbcahe sbcaeh sbchae sbchea sbceha sbceah sbeach sbeahc
sbecah sbecha sbehca sbehac sehabc sehacb sehbac sehbca sehcba sehcab seahbc
seahcb seabhc seabch seacbh seachb sebahc sebach sebhac sebhca sebcha sebcah
secabh secahb secbah secbha sechba sechab echasb echabs echsab echsba echbsa
echbas ecahsb ecahbs ecashb ecasbh ecabsh ecabhs ecsahb ecsabh ecshab ecshba
ecsbha ecsbah ecbash ecbahs ecbsah ecbsha ecbhsa ecbhas ehcasb ehcabs ehcsab
ehcsba ehcbsa ehcbas ehacsb ehacbs ehascb ehasbc ehabsc ehabcs ehsacb ehsabc
ehscab ehscba ehsbca ehsbac ehbasc ehbacs ehbsac ehbsca ehbcsa ehbcas eahcsb
eahcbs eahscb eahsbc eahbsc eahbcs eachsb eachbs eacshb eacsbh eacbsh eacbhs
easchb eascbh eashcb eashbc easbhc easbch eabcsh eabchs eabsch eabshc eabhsc
eabhcs eshacb eshabc eshcab eshcba eshbca eshbac esahcb esahbc esachb esacbh
esabch esabhc escahb escabh eschab eschba escbha escbah esbach esbahc esbcah
esbcha esbhca esbhac ebhasc ebhacs ebhsac ebhsca ebhcsa ebhcas ebahsc ebahcs
ebashc ebasch ebacsh ebachs ebsahc ebsach ebshac ebshca ebscha ebscah ebcash
ebcahs ebcsah ebcsha ebchsa ebchas

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History of cryptography
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