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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: quaggy
cipher variations:
rvbhhz swciia txdjjb uyekkc vzflld
wagmme xbhnnf ycioog zdjpph aekqqi
bflrrj cgmssk dhnttl eiouum fjpvvn
gkqwwo hlrxxp imsyyq jntzzr kouaas
lpvbbt mqwccu nrxddv osyeew ptzffx

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: quaggy
Cipher: jfzttb

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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: quaggy

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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: quaggy
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: quaggy
Cipher: dhnttl

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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: quaggy
Cipher: 145411222245

Extended Methods:
Method #1

Plaintext: quaggy
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
q u a g g y 
1 5 1 2 2 4 
4 4 1 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: quaggy
Cipher: vfrtfw

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Method #3

Plaintext: quaggy
method variations:
ydfgre dfgrey fgreyd
greydf reydfg eydfgr

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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: quaggy

all 720 cipher variations:
quaggy quagyg quaggy quagyg quaygg quaygg qugagy qugayg quggay quggya qugyga
qugyag quggay quggya qugagy qugayg qugyag qugyga quygga quygag quygga quygag
quyagg quyagg qauggy qaugyg qauggy qaugyg qauygg qauygg qagugy qaguyg qagguy
qaggyu qagygu qagyug qagguy qaggyu qagugy qaguyg qagyug qagygu qayggu qaygug
qayggu qaygug qayugg qayugg qgaugy qgauyg qgaguy qgagyu qgaygu qgayug qguagy
qguayg qgugay qgugya qguyga qguyag qgguay qgguya qggauy qggayu qggyau qggyua
qgyuga qgyuag qgygua qgygau qgyagu qgyaug qgaguy qgagyu qgaugy qgauyg qgayug
qgaygu qggauy qggayu qgguay qgguya qggyua qggyau qgugay qgugya qguagy qguayg
qguyag qguyga qgygua qgygau qgyuga qgyuag qgyaug qgyagu qyaggu qyagug qyaggu
qyagug qyaugg qyaugg qygagu qygaug qyggau qyggua qyguga qyguag qyggau qyggua
qygagu qygaug qyguag qyguga qyugga qyugag qyugga qyugag qyuagg qyuagg uqaggy
uqagyg uqaggy uqagyg uqaygg uqaygg uqgagy uqgayg uqggay uqggya uqgyga uqgyag
uqggay uqggya uqgagy uqgayg uqgyag uqgyga uqygga uqygag uqygga uqygag uqyagg
uqyagg uaqggy uaqgyg uaqggy uaqgyg uaqygg uaqygg uagqgy uagqyg uaggqy uaggyq
uagygq uagyqg uaggqy uaggyq uagqgy uagqyg uagyqg uagygq uayggq uaygqg uayggq
uaygqg uayqgg uayqgg ugaqgy ugaqyg ugagqy ugagyq ugaygq ugayqg ugqagy ugqayg
ugqgay ugqgya ugqyga ugqyag uggqay uggqya uggaqy uggayq uggyaq uggyqa ugyqga
ugyqag ugygqa ugygaq ugyagq ugyaqg ugagqy ugagyq ugaqgy ugaqyg ugayqg ugaygq
uggaqy uggayq uggqay uggqya uggyqa uggyaq ugqgay ugqgya ugqagy ugqayg ugqyag
ugqyga ugygqa ugygaq ugyqga ugyqag ugyaqg ugyagq uyaggq uyagqg uyaggq uyagqg
uyaqgg uyaqgg uygagq uygaqg uyggaq uyggqa uygqga uygqag uyggaq uyggqa uygagq
uygaqg uygqag uygqga uyqgga uyqgag uyqgga uyqgag uyqagg uyqagg auqggy auqgyg
auqggy auqgyg auqygg auqygg augqgy augqyg auggqy auggyq augygq augyqg auggqy
auggyq augqgy augqyg augyqg augygq auyggq auygqg auyggq auygqg auyqgg auyqgg
aquggy aqugyg aquggy aqugyg aquygg aquygg aqgugy aqguyg aqgguy aqggyu aqgygu
aqgyug aqgguy aqggyu aqgugy aqguyg aqgyug aqgygu aqyggu aqygug aqyggu aqygug
aqyugg aqyugg agqugy agquyg agqguy agqgyu agqygu agqyug aguqgy aguqyg agugqy
agugyq aguygq aguyqg agguqy agguyq aggquy aggqyu aggyqu aggyuq agyugq agyuqg
agyguq agygqu agyqgu agyqug agqguy agqgyu agqugy agquyg agqyug agqygu aggquy
aggqyu agguqy agguyq aggyuq aggyqu agugqy agugyq aguqgy aguqyg aguyqg aguygq
agyguq agygqu agyugq agyuqg agyqug agyqgu ayqggu ayqgug ayqggu ayqgug ayqugg
ayqugg aygqgu aygqug ayggqu aygguq aygugq ayguqg ayggqu aygguq aygqgu aygqug
ayguqg aygugq ayuggq ayugqg ayuggq ayugqg ayuqgg ayuqgg guaqgy guaqyg guagqy
guagyq guaygq guayqg guqagy guqayg guqgay guqgya guqyga guqyag gugqay gugqya
gugaqy gugayq gugyaq gugyqa guyqga guyqag guygqa guygaq guyagq guyaqg gauqgy
gauqyg gaugqy gaugyq gauygq gauyqg gaqugy gaquyg gaqguy gaqgyu gaqygu gaqyug
gagquy gagqyu gaguqy gaguyq gagyuq gagyqu gayqgu gayqug gaygqu gayguq gayugq
gayuqg gqaugy gqauyg gqaguy gqagyu gqaygu gqayug gquagy gquayg gqugay gqugya
gquyga gquyag gqguay gqguya gqgauy gqgayu gqgyau gqgyua gqyuga gqyuag gqygua
gqygau gqyagu gqyaug ggaquy ggaqyu ggauqy ggauyq ggayuq ggayqu ggqauy ggqayu
ggquay ggquya ggqyua ggqyau gguqay gguqya gguaqy gguayq gguyaq gguyqa ggyqua
ggyqau ggyuqa ggyuaq ggyauq ggyaqu gyaqgu gyaqug gyagqu gyaguq gyaugq gyauqg
gyqagu gyqaug gyqgau gyqgua gyquga gyquag gygqau gygqua gygaqu gygauq gyguaq
gyguqa gyuqga gyuqag gyugqa gyugaq gyuagq gyuaqg guagqy guagyq guaqgy guaqyg
guayqg guaygq gugaqy gugayq gugqay gugqya gugyqa gugyaq guqgay guqgya guqagy
guqayg guqyag guqyga guygqa guygaq guyqga guyqag guyaqg guyagq gaugqy gaugyq
gauqgy gauqyg gauyqg gauygq gaguqy gaguyq gagquy gagqyu gagyqu gagyuq gaqguy
gaqgyu gaqugy gaquyg gaqyug gaqygu gaygqu gayguq gayqgu gayqug gayuqg gayugq
ggauqy ggauyq ggaquy ggaqyu ggayqu ggayuq gguaqy gguayq gguqay gguqya gguyqa
gguyaq ggquay ggquya ggqauy ggqayu ggqyau ggqyua ggyuqa ggyuaq ggyqua ggyqau
ggyaqu ggyauq gqaguy gqagyu gqaugy gqauyg gqayug gqaygu gqgauy gqgayu gqguay
gqguya gqgyua gqgyau gqugay gqugya gquagy gquayg gquyag gquyga gqygua gqygau
gqyuga gqyuag gqyaug gqyagu gyagqu gyaguq gyaqgu gyaqug gyauqg gyaugq gygaqu
gygauq gygqau gygqua gyguqa gyguaq gyqgau gyqgua gyqagu gyqaug gyquag gyquga
gyugqa gyugaq gyuqga gyuqag gyuaqg gyuagq yuaggq yuagqg yuaggq yuagqg yuaqgg
yuaqgg yugagq yugaqg yuggaq yuggqa yugqga yugqag yuggaq yuggqa yugagq yugaqg
yugqag yugqga yuqgga yuqgag yuqgga yuqgag yuqagg yuqagg yauggq yaugqg yauggq
yaugqg yauqgg yauqgg yagugq yaguqg yagguq yaggqu yagqgu yagqug yagguq yaggqu
yagugq yaguqg yagqug yagqgu yaqggu yaqgug yaqggu yaqgug yaqugg yaqugg ygaugq
ygauqg ygaguq ygagqu ygaqgu ygaqug yguagq yguaqg ygugaq ygugqa yguqga yguqag
ygguaq ygguqa yggauq yggaqu yggqau yggqua ygquga ygquag ygqgua ygqgau ygqagu
ygqaug ygaguq ygagqu ygaugq ygauqg ygaqug ygaqgu yggauq yggaqu ygguaq ygguqa
yggqua yggqau ygugaq ygugqa yguagq yguaqg yguqag yguqga ygqgua ygqgau ygquga
ygquag ygqaug ygqagu yqaggu yqagug yqaggu yqagug yqaugg yqaugg yqgagu yqgaug
yqggau yqggua yqguga yqguag yqggau yqggua yqgagu yqgaug yqguag yqguga yqugga
yqugag yqugga yqugag yquagg yquagg

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History of cryptography
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