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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: bedway
cipher variations:
cfexbz dgfyca ehgzdb fihaec gjibfd
hkjcge ilkdhf jmleig knmfjh longki
mpohlj nqpimk orqjnl psrkom qtslpn
rutmqo svunrp twvosq uxwptr vyxqus
wzyrvt xazswu ybatxv zcbuyw adcvzx

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: bedway
Cipher: yvwdzb

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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: bedway

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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: bedway
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: bedway
Cipher: orqjnl

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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: bedway
Cipher: 215141251145

Extended Methods:
Method #1

Plaintext: bedway
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
b e d w a y 
2 5 4 2 1 4 
1 1 1 5 1 5 
They are then read out in rows:
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: bedway
Cipher: wiqavv

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Method #3

Plaintext: bedway
method variations:
vqfeqk qfeqkv feqkvq
eqkvqf qkvqfe kvqfeq

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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: bedway

all 720 cipher variations:
bedway bedwya bedawy bedayw bedyaw bedywa bewday bewdya bewady bewayd bewyad
bewyda beawdy beawyd beadwy beadyw beaydw beaywd beywad beywda beyawd beyadw
beydaw beydwa bdeway bdewya bdeawy bdeayw bdeyaw bdeywa bdweay bdweya bdwaey
bdwaye bdwyae bdwyea bdawey bdawye bdaewy bdaeyw bdayew bdaywe bdywae bdywea
bdyawe bdyaew bdyeaw bdyewa bwdeay bwdeya bwdaey bwdaye bwdyae bwdyea bweday
bwedya bweady bweayd bweyad bweyda bwaedy bwaeyd bwadey bwadye bwayde bwayed
bwyead bwyeda bwyaed bwyade bwydae bwydea badwey badwye badewy badeyw badyew
badywe bawdey bawdye bawedy baweyd bawyed bawyde baewdy baewyd baedwy baedyw
baeydw baeywd baywed baywde bayewd bayedw baydew baydwe bydwae bydwea bydawe
bydaew bydeaw bydewa bywdae bywdea bywade bywaed bywead byweda byawde byawed
byadwe byadew byaedw byaewd byewad byewda byeawd byeadw byedaw byedwa ebdway
ebdwya ebdawy ebdayw ebdyaw ebdywa ebwday ebwdya ebwady ebwayd ebwyad ebwyda
ebawdy ebawyd ebadwy ebadyw ebaydw ebaywd ebywad ebywda ebyawd ebyadw ebydaw
ebydwa edbway edbwya edbawy edbayw edbyaw edbywa edwbay edwbya edwaby edwayb
edwyab edwyba edawby edawyb edabwy edabyw edaybw edaywb edywab edywba edyawb
edyabw edybaw edybwa ewdbay ewdbya ewdaby ewdayb ewdyab ewdyba ewbday ewbdya
ewbady ewbayd ewbyad ewbyda ewabdy ewabyd ewadby ewadyb ewaydb ewaybd ewybad
ewybda ewyabd ewyadb ewydab ewydba eadwby eadwyb eadbwy eadbyw eadybw eadywb
eawdby eawdyb eawbdy eawbyd eawybd eawydb eabwdy eabwyd eabdwy eabdyw eabydw
eabywd eaywbd eaywdb eaybwd eaybdw eaydbw eaydwb eydwab eydwba eydawb eydabw
eydbaw eydbwa eywdab eywdba eywadb eywabd eywbad eywbda eyawdb eyawbd eyadwb
eyadbw eyabdw eyabwd eybwad eybwda eybawd eybadw eybdaw eybdwa debway debwya
debawy debayw debyaw debywa dewbay dewbya dewaby dewayb dewyab dewyba deawby
deawyb deabwy deabyw deaybw deaywb deywab deywba deyawb deyabw deybaw deybwa
dbeway dbewya dbeawy dbeayw dbeyaw dbeywa dbweay dbweya dbwaey dbwaye dbwyae
dbwyea dbawey dbawye dbaewy dbaeyw dbayew dbaywe dbywae dbywea dbyawe dbyaew
dbyeaw dbyewa dwbeay dwbeya dwbaey dwbaye dwbyae dwbyea dwebay dwebya dweaby
dweayb dweyab dweyba dwaeby dwaeyb dwabey dwabye dwaybe dwayeb dwyeab dwyeba
dwyaeb dwyabe dwybae dwybea dabwey dabwye dabewy dabeyw dabyew dabywe dawbey
dawbye daweby daweyb dawyeb dawybe daewby daewyb daebwy daebyw daeybw daeywb
dayweb daywbe dayewb dayebw daybew daybwe dybwae dybwea dybawe dybaew dybeaw
dybewa dywbae dywbea dywabe dywaeb dyweab dyweba dyawbe dyaweb dyabwe dyabew
dyaebw dyaewb dyewab dyewba dyeawb dyeabw dyebaw dyebwa wedbay wedbya wedaby
wedayb wedyab wedyba webday webdya webady webayd webyad webyda weabdy weabyd
weadby weadyb weaydb weaybd weybad weybda weyabd weyadb weydab weydba wdebay
wdebya wdeaby wdeayb wdeyab wdeyba wdbeay wdbeya wdbaey wdbaye wdbyae wdbyea
wdabey wdabye wdaeby wdaeyb wdayeb wdaybe wdybae wdybea wdyabe wdyaeb wdyeab
wdyeba wbdeay wbdeya wbdaey wbdaye wbdyae wbdyea wbeday wbedya wbeady wbeayd
wbeyad wbeyda wbaedy wbaeyd wbadey wbadye wbayde wbayed wbyead wbyeda wbyaed
wbyade wbydae wbydea wadbey wadbye wadeby wadeyb wadyeb wadybe wabdey wabdye
wabedy wabeyd wabyed wabyde waebdy waebyd waedby waedyb waeydb waeybd waybed
waybde wayebd wayedb waydeb waydbe wydbae wydbea wydabe wydaeb wydeab wydeba
wybdae wybdea wybade wybaed wybead wybeda wyabde wyabed wyadbe wyadeb wyaedb
wyaebd wyebad wyebda wyeabd wyeadb wyedab wyedba aedwby aedwyb aedbwy aedbyw
aedybw aedywb aewdby aewdyb aewbdy aewbyd aewybd aewydb aebwdy aebwyd aebdwy
aebdyw aebydw aebywd aeywbd aeywdb aeybwd aeybdw aeydbw aeydwb adewby adewyb
adebwy adebyw adeybw adeywb adweby adweyb adwbey adwbye adwybe adwyeb adbwey
adbwye adbewy adbeyw adbyew adbywe adywbe adyweb adybwe adybew adyebw adyewb
awdeby awdeyb awdbey awdbye awdybe awdyeb awedby awedyb awebdy awebyd aweybd
aweydb awbedy awbeyd awbdey awbdye awbyde awbyed awyebd awyedb awybed awybde
awydbe awydeb abdwey abdwye abdewy abdeyw abdyew abdywe abwdey abwdye abwedy
abweyd abwyed abwyde abewdy abewyd abedwy abedyw abeydw abeywd abywed abywde
abyewd abyedw abydew abydwe aydwbe aydweb aydbwe aydbew aydebw aydewb aywdbe
aywdeb aywbde aywbed aywebd aywedb aybwde aybwed aybdwe aybdew aybedw aybewd
ayewbd ayewdb ayebwd ayebdw ayedbw ayedwb yedwab yedwba yedawb yedabw yedbaw
yedbwa yewdab yewdba yewadb yewabd yewbad yewbda yeawdb yeawbd yeadwb yeadbw
yeabdw yeabwd yebwad yebwda yebawd yebadw yebdaw yebdwa ydewab ydewba ydeawb
ydeabw ydebaw ydebwa ydweab ydweba ydwaeb ydwabe ydwbae ydwbea ydaweb ydawbe
ydaewb ydaebw ydabew ydabwe ydbwae ydbwea ydbawe ydbaew ydbeaw ydbewa ywdeab
ywdeba ywdaeb ywdabe ywdbae ywdbea ywedab ywedba yweadb yweabd ywebad ywebda
ywaedb ywaebd ywadeb ywadbe ywabde ywabed ywbead ywbeda ywbaed ywbade ywbdae
ywbdea yadweb yadwbe yadewb yadebw yadbew yadbwe yawdeb yawdbe yawedb yawebd
yawbed yawbde yaewdb yaewbd yaedwb yaedbw yaebdw yaebwd yabwed yabwde yabewd
yabedw yabdew yabdwe ybdwae ybdwea ybdawe ybdaew ybdeaw ybdewa ybwdae ybwdea
ybwade ybwaed ybwead ybweda ybawde ybawed ybadwe ybadew ybaedw ybaewd ybewad
ybewda ybeawd ybeadw ybedaw ybedwa

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History of cryptography
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