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cathedr

flagitavissemque

parteque

graybeal

parramon

ultraspherical


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: sprag
cipher variations:
tqsbh urtci vsudj wtvek xuwfl
yvxgm zwyhn axzio byajp czbkq
daclr ebdms fcent gdfou hegpv
ifhqw jgirx khjsy liktz mjlua
nkmvb olnwc pmoxd qnpye roqzf

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: sprag
Cipher: hkizt

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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: sprag
Cipher: BAAAB ABBBA BAAAA AAAAA AABBA

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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: sprag
cipher variations:
tqsbhduabtnyibfxcqbrhgybdrkgbplswbnvwebz
famblpeubxzicbjjmkbvurtcievbcuozjcgydrcs
ihzceslhcqmtxcowxfcagbncmqfvcyajdckknlcw
vsudjfwcdvpakdhzesdtjiadftmidrnuydpxygdb
hcodnrgwdzbkedllomdxwtvekgxdewqbleiafteu
kjbegunjesovzeqyzhecidpeoshxeaclfemmpney
xuwflhyefxrcmfjbgufvlkcfhvokftpwafrzaifd
jeqfptiyfbdmgfnnqofzyvxgmizfgysdngkchvgw
mldgiwplguqxbgsabjgekfrgqujzgcenhgoorpga
zwyhnjaghzteohldiwhxnmehjxqmhvrychtbckhf
lgshrvkahdfoihppsqhbaxziokbhiaufpimejxiy
onfikyrniwszdiucdligmhtiswlbiegpjiqqtric
byajplcijbvgqjnfkyjzpogjlzsojxtaejvdemjh
niujtxmcjfhqkjrrusjdczbkqmdjkcwhrkoglzka
qphkmatpkyubfkwefnkiojvkuyndkgirlkssvtke
daclrnekldxislphmalbrqilnbuqlzvcglxfgolj
pkwlvzoelhjsmlttwulfebdmsoflmeyjtmqinbmc
srjmocvrmawdhmyghpmkqlxmwapfmiktnmuuxvmg
fcentpgmnfzkunrjocndtsknpdwsnbxeinzhiqnl
rmynxbqgnjluonvvywnhgdfouqhnogalvoskpdoe
utloqextocyfjoaijromsnzoycrhokmvpowwzxoi
hegpvriophbmwptlqepfvumprfyupdzgkpbjkspn
toapzdsiplnwqpxxaypjifhqwsjpqicnxqumrfqg
wvnqsgzvqeahlqckltqoupbqaetjqmoxrqyybzqk
jgirxtkqrjdoyrvnsgrhxworthawrfbimrdlmurp
vqcrbfukrnpysrzzcarlkhjsyulrskepzswothsi
yxpsuibxsgcjnsemnvsqwrdscgvlsoqztsaadbsm
liktzvmstlfqatxpuitjzyqtvjcythdkotfnowtr
xsetdhwmtprautbbectnmjluawntumgrbuyqvjuk
azruwkdzuielpugopxusytfueixnuqsbvuccfduo
nkmvbxouvnhscvzrwkvlbasvxleavjfmqvhpqyvt
zugvfjyovrtcwvddgevpolnwcypvwoitdwasxlwm
cbtwymfbwkgnrwiqrzwuavhwgkzpwsudxweehfwq
pmoxdzqwxpjuexbtymxndcuxzngcxlhosxjrsaxv
bwixhlaqxtveyxffigxrqnpyearxyqkvfycuznyo
edvyaohdymiptykstbywcxjyimbryuwfzyggjhys
roqzfbsyzrlwgzdvaozpfewzbpieznjquzltuczx
dykzjncszvxgazhhkiztspragctzasmxhaewbpaq
gfxacqjfaokrvamuvdayezlakodtawyhbaiiljau

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: sprag
Cipher: fcent

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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: sprag
Cipher: 3453241122

Extended Methods:
Method #1

Plaintext: sprag
method variations:
xuwfmczblrhegqwnkmvb

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
s p r a g 
3 5 2 1 2 
4 3 4 1 2 
They are then read out in rows:
3521243412
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: sprag
Cipher: xbrsf

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Method #3

Plaintext: sprag
method variations:
yhdfm hdfmy dfmyh
fmyhd myhdf

Read more ...[RUS] , [EN]

 

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: sprag

all 120 cipher variations:
sprag sprga sparg spagr spgar spgra srpag srpga srapg sragp srgap
srgpa sarpg sargp saprg sapgr sagpr sagrp sgrap sgrpa sgarp sgapr
sgpar sgpra psrag psrga psarg psagr psgar psgra prsag prsga prasg
prags prgas prgsa parsg pargs pasrg pasgr pagsr pagrs pgras pgrsa
pgars pgasr pgsar pgsra rpsag rpsga rpasg rpags rpgas rpgsa rspag
rspga rsapg rsagp rsgap rsgpa raspg rasgp rapsg rapgs ragps ragsp
rgsap rgspa rgasp rgaps rgpas rgpsa aprsg aprgs apsrg apsgr apgsr
apgrs arpsg arpgs arspg arsgp argsp argps asrpg asrgp asprg aspgr
asgpr asgrp agrsp agrps agsrp agspr agpsr agprs gpras gprsa gpars
gpasr gpsar gpsra grpas grpsa graps grasp grsap grspa garps garsp
gaprs gapsr gaspr gasrp gsrap gsrpa gsarp gsapr gspar gspra

Read more ...[1] , [2] , [3]

History of cryptography
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