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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: stuffy
cipher variations:
tuvggz uvwhha vwxiib wxyjjc xyzkkd
yzalle zabmmf abcnng bcdooh cdeppi
defqqj efgrrk fghssl ghittm hijuun
ijkvvo jklwwp klmxxq lmnyyr mnozzs
nopaat opqbbu pqrccv qrsddw rsteex

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: stuffy
Cipher: hgfuub

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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: stuffy

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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: stuffy
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: stuffy
Cipher: fghssl

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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: stuffy
Cipher: 344454121245

Extended Methods:
Method #1

Plaintext: stuffy
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
s t u f f y 
3 4 5 1 1 4 
4 4 4 2 2 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: stuffy
Cipher: seqtiw

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Method #3

Plaintext: stuffy
method variations:
tydbrp ydbrpt dbrpty
brptyd rptydb ptydbr

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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: stuffy

all 720 cipher variations:
stuffy stufyf stuffy stufyf stuyff stuyff stfufy stfuyf stffuy stffyu stfyfu
stfyuf stffuy stffyu stfufy stfuyf stfyuf stfyfu styffu styfuf styffu styfuf
styuff styuff sutffy sutfyf sutffy sutfyf sutyff sutyff suftfy suftyf suffty
suffyt sufyft sufytf suffty suffyt suftfy suftyf sufytf sufyft suyfft suyftf
suyfft suyftf suytff suytff sfutfy sfutyf sfufty sfufyt sfuyft sfuytf sftufy
sftuyf sftfuy sftfyu sftyfu sftyuf sfftuy sfftyu sffuty sffuyt sffyut sffytu
sfytfu sfytuf sfyftu sfyfut sfyuft sfyutf sfufty sfufyt sfutfy sfutyf sfuytf
sfuyft sffuty sffuyt sfftuy sfftyu sffytu sffyut sftfuy sftfyu sftufy sftuyf
sftyuf sftyfu sfyftu sfyfut sfytfu sfytuf sfyutf sfyuft syufft syuftf syufft
syuftf syutff syutff syfuft syfutf syffut syfftu syftfu syftuf syffut syfftu
syfuft syfutf syftuf syftfu sytffu sytfuf sytffu sytfuf sytuff sytuff tsuffy
tsufyf tsuffy tsufyf tsuyff tsuyff tsfufy tsfuyf tsffuy tsffyu tsfyfu tsfyuf
tsffuy tsffyu tsfufy tsfuyf tsfyuf tsfyfu tsyffu tsyfuf tsyffu tsyfuf tsyuff
tsyuff tusffy tusfyf tusffy tusfyf tusyff tusyff tufsfy tufsyf tuffsy tuffys
tufyfs tufysf tuffsy tuffys tufsfy tufsyf tufysf tufyfs tuyffs tuyfsf tuyffs
tuyfsf tuysff tuysff tfusfy tfusyf tfufsy tfufys tfuyfs tfuysf tfsufy tfsuyf
tfsfuy tfsfyu tfsyfu tfsyuf tffsuy tffsyu tffusy tffuys tffyus tffysu tfysfu
tfysuf tfyfsu tfyfus tfyufs tfyusf tfufsy tfufys tfusfy tfusyf tfuysf tfuyfs
tffusy tffuys tffsuy tffsyu tffysu tffyus tfsfuy tfsfyu tfsufy tfsuyf tfsyuf
tfsyfu tfyfsu tfyfus tfysfu tfysuf tfyusf tfyufs tyuffs tyufsf tyuffs tyufsf
tyusff tyusff tyfufs tyfusf tyffus tyffsu tyfsfu tyfsuf tyffus tyffsu tyfufs
tyfusf tyfsuf tyfsfu tysffu tysfuf tysffu tysfuf tysuff tysuff utsffy utsfyf
utsffy utsfyf utsyff utsyff utfsfy utfsyf utffsy utffys utfyfs utfysf utffsy
utffys utfsfy utfsyf utfysf utfyfs utyffs utyfsf utyffs utyfsf utysff utysff
ustffy ustfyf ustffy ustfyf ustyff ustyff usftfy usftyf usffty usffyt usfyft
usfytf usffty usffyt usftfy usftyf usfytf usfyft usyfft usyftf usyfft usyftf
usytff usytff ufstfy ufstyf ufsfty ufsfyt ufsyft ufsytf uftsfy uftsyf uftfsy
uftfys uftyfs uftysf ufftsy ufftys uffsty uffsyt uffyst uffyts ufytfs ufytsf
ufyfts ufyfst ufysft ufystf ufsfty ufsfyt ufstfy ufstyf ufsytf ufsyft uffsty
uffsyt ufftsy ufftys uffyts uffyst uftfsy uftfys uftsfy uftsyf uftysf uftyfs
ufyfts ufyfst ufytfs ufytsf ufystf ufysft uysfft uysftf uysfft uysftf uystff
uystff uyfsft uyfstf uyffst uyffts uyftfs uyftsf uyffst uyffts uyfsft uyfstf
uyftsf uyftfs uytffs uytfsf uytffs uytfsf uytsff uytsff ftusfy ftusyf ftufsy
ftufys ftuyfs ftuysf ftsufy ftsuyf ftsfuy ftsfyu ftsyfu ftsyuf ftfsuy ftfsyu
ftfusy ftfuys ftfyus ftfysu ftysfu ftysuf ftyfsu ftyfus ftyufs ftyusf futsfy
futsyf futfsy futfys futyfs futysf fustfy fustyf fusfty fusfyt fusyft fusytf
fufsty fufsyt fuftsy fuftys fufyts fufyst fuysft fuystf fuyfst fuyfts fuytfs
fuytsf fsutfy fsutyf fsufty fsufyt fsuyft fsuytf fstufy fstuyf fstfuy fstfyu
fstyfu fstyuf fsftuy fsftyu fsfuty fsfuyt fsfyut fsfytu fsytfu fsytuf fsyftu
fsyfut fsyuft fsyutf ffusty ffusyt ffutsy ffutys ffuyts ffuyst ffsuty ffsuyt
ffstuy ffstyu ffsytu ffsyut fftsuy fftsyu fftusy fftuys fftyus fftysu ffystu
ffysut ffytsu ffytus ffyuts ffyust fyusft fyustf fyufst fyufts fyutfs fyutsf
fysuft fysutf fysfut fysftu fystfu fystuf fyfsut fyfstu fyfust fyfuts fyftus
fyftsu fytsfu fytsuf fytfsu fytfus fytufs fytusf ftufsy ftufys ftusfy ftusyf
ftuysf ftuyfs ftfusy ftfuys ftfsuy ftfsyu ftfysu ftfyus ftsfuy ftsfyu ftsufy
ftsuyf ftsyuf ftsyfu ftyfsu ftyfus ftysfu ftysuf ftyusf ftyufs futfsy futfys
futsfy futsyf futysf futyfs fuftsy fuftys fufsty fufsyt fufyst fufyts fusfty
fusfyt fustfy fustyf fusytf fusyft fuyfst fuyfts fuysft fuystf fuytsf fuytfs
ffutsy ffutys ffusty ffusyt ffuyst ffuyts fftusy fftuys fftsuy fftsyu fftysu
fftyus ffstuy ffstyu ffsuty ffsuyt ffsyut ffsytu ffytsu ffytus ffystu ffysut
ffyust ffyuts fsufty fsufyt fsutfy fsutyf fsuytf fsuyft fsfuty fsfuyt fsftuy
fsftyu fsfytu fsfyut fstfuy fstfyu fstufy fstuyf fstyuf fstyfu fsyftu fsyfut
fsytfu fsytuf fsyutf fsyuft fyufst fyufts fyusft fyustf fyutsf fyutfs fyfust
fyfuts fyfsut fyfstu fyftsu fyftus fysfut fysftu fysuft fysutf fystuf fystfu
fytfsu fytfus fytsfu fytsuf fytusf fytufs ytuffs ytufsf ytuffs ytufsf ytusff
ytusff ytfufs ytfusf ytffus ytffsu ytfsfu ytfsuf ytffus ytffsu ytfufs ytfusf
ytfsuf ytfsfu ytsffu ytsfuf ytsffu ytsfuf ytsuff ytsuff yutffs yutfsf yutffs
yutfsf yutsff yutsff yuftfs yuftsf yuffts yuffst yufsft yufstf yuffts yuffst
yuftfs yuftsf yufstf yufsft yusfft yusftf yusfft yusftf yustff yustff yfutfs
yfutsf yfufts yfufst yfusft yfustf yftufs yftusf yftfus yftfsu yftsfu yftsuf
yfftus yfftsu yffuts yffust yffsut yffstu yfstfu yfstuf yfsftu yfsfut yfsuft
yfsutf yfufts yfufst yfutfs yfutsf yfustf yfusft yffuts yffust yfftus yfftsu
yffstu yffsut yftfus yftfsu yftufs yftusf yftsuf yftsfu yfsftu yfsfut yfstfu
yfstuf yfsutf yfsuft ysufft ysuftf ysufft ysuftf ysutff ysutff ysfuft ysfutf
ysffut ysfftu ysftfu ysftuf ysffut ysfftu ysfuft ysfutf ysftuf ysftfu ystffu
ystfuf ystffu ystfuf ystuff ystuff

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History of cryptography
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