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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: aequi
cipher variations:
bfrvj cgswk dhtxl eiuym fjvzn
gkwao hlxbp imycq jnzdr koaes
lpbft mqcgu nrdhv oseiw ptfjx
qugky rvhlz swima txjnb uykoc
vzlpd wamqe xbnrf ycosg zdpth

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: aequi
Cipher: zvjfr

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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: aequi

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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: aequi
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: aequi
Cipher: nrdhv

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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: aequi
Cipher: 1151145442

Extended Methods:
Method #1

Plaintext: aequi
method variations:

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

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Method #3

Plaintext: aequi
method variations:
vaytb aytbv ytbva
tbvay bvayt

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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: aequi

all 120 cipher variations:
aequi aeqiu aeuqi aeuiq aeiuq aeiqu aqeui aqeiu aquei aquie aqiue
aqieu auqei auqie aueqi aueiq auieq auiqe aique aiqeu aiuqe aiueq
aieuq aiequ eaqui eaqiu eauqi eauiq eaiuq eaiqu eqaui eqaiu equai
equia eqiua eqiau euqai euqia euaqi euaiq euiaq euiqa eiqua eiqau
eiuqa eiuaq eiauq eiaqu qeaui qeaiu qeuai qeuia qeiua qeiau qaeui
qaeiu qauei qauie qaiue qaieu quaei quaie queai queia quiea quiae
qiaue qiaeu qiuae qiuea qieua qieau ueqai ueqia ueaqi ueaiq ueiaq
ueiqa uqeai uqeia uqaei uqaie uqiae uqiea uaqei uaqie uaeqi uaeiq
uaieq uaiqe uiqae uiqea uiaqe uiaeq uieaq uieqa iequa ieqau ieuqa
ieuaq ieauq ieaqu iqeua iqeau iquea iquae iqaue iqaeu iuqea iuqae
iueqa iueaq iuaeq iuaqe iaque iaqeu iauqe iaueq iaeuq iaequ

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History of cryptography
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