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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: alixe
cipher variations:
bmjyf cnkzg dolah epmbi fqncj
grodk hspel itqfm jurgn kvsho
lwtip mxujq nyvkr ozwls paxmt
qbynu rczov sdapw tebqx ufcry
vgdsz wheta xifub yjgvc zkhwd

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: alixe
Cipher: zorcv

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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: alixe
Cipher: AAAAA ABABA ABAAA BABAB AABAA

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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: alixe
cipher variations:
bmjyfbizsnbepmvbafgdbwvalbslutbkrijbghcr
bcxwzbynqhbudkpbqtexcnkzgcjatocfqnwcbghe
cxwbmctmvuclsjkchidscdyxaczoricvelqcrufy
dolahdkbupdgroxdchifdyxcndunwvdmtkldijet
dezybdapsjdwfmrdsvgzepmbielcvqehspyedijg
ezydoevoxwenulmejkfuefazcebqtkexgnsetwha
fqncjfmdwrfitqzfejkhfazepfwpyxfovmnfklgv
fgbadfcrulfyhotfuxibgrodkgnexsgjuragfkli
gbafqgxqzygpwnoglmhwghcbegdsvmgzipugvyjc
hspelhofythkvsbhglmjhcbgrhyrazhqxophmnix
hidcfhetwnhajqvhwzkditqfmipgzuilwtcihmnk
idchsizsbairypqinojyijedgifuxoibkrwixale
jurgnjqhavjmxudjinoljeditjatcbjszqrjopkz
jkfehjgvypjclsxjybmfkvshokribwknyvekjopm
kfejukbudcktarskpqlaklgfikhwzqkdmtykzcng
lwtiplsjcxlozwflkpqnlgfkvlcvedlubstlqrmb
lmhgjlixarlenuzladohmxujqmtkdympaxgmlqro
mhglwmdwfemvctumrsncmnihkmjybsmfovambepi
nyvkrnuleznqbyhnmrspnihmxnexgfnwduvnstod
nojilnkzctngpwbncfqjozwlsovmfaorczionstq
ojinyofyhgoxevwotupeopkjmoladuohqxcodgrk
paxmtpwngbpsdajpoturpkjozpgzihpyfwxpuvqf
pqlknpmbevpirydpehslqbynuqxohcqtebkqpuvs
qlkpaqhajiqzgxyqvwrgqrmloqncfwqjszeqfitm
rczovrypidrufclrqvwtrmlqbribkjrahyzrwxsh
rsnmprodgxrktafrgjunsdapwszqjesvgdmsrwxu
snmrcsjclksbizasxytistonqspehyslubgshkvo
tebqxtarkftwhentsxyvtonsdtkdmltcjabtyzuj
tuportqfiztmvchtilwpufcryubslguxifoutyzw
upoteulenmudkbcuzavkuvqpsurgjaunwdiujmxq
vgdszvctmhvyjgpvuzaxvqpufvmfonvelcdvabwl
vwrqtvshkbvoxejvknyrwhetawduniwzkhqwvaby
wrqvgwngpowfmdewbcxmwxsruwtilcwpyfkwlozs
xifubxevojxalirxwbczxsrwhxohqpxgnefxcdyn
xytsvxujmdxqzglxmpatyjgvcyfwpkybmjsyxcda
ytsxiypirqyhofgydezoyzutwyvkneyrahmynqbu
zkhwdzgxqlzcnktzydebzutyjzqjsrzipghzefap
zavuxzwlofzsbinzorcvalixeahyrmadoluazefc
avuzkarktsajqhiafgbqabwvyaxmpgatcjoapsdw

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: alixe
Cipher: nyvkr

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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: alixe
Cipher: 1113423551

Extended Methods:
Method #1

Plaintext: alixe
method variations:
fqocklvthpqaynuvfdsz

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
a l i x e 
1 1 4 3 5 
1 3 2 5 1 
They are then read out in rows:
1143513251
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: alixe
Cipher: aoehe

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Method #3

Plaintext: alixe
method variations:
asmza smzaa mzaas
zaasm aasmz

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: alixe

all 120 cipher variations:
alixe aliex alxie alxei alexi aleix ailxe ailex aixle aixel aiexl
aielx axile axiel axlie axlei axeli axeil aeixl aeilx aexil aexli
aelxi aelix laixe laiex laxie laxei laexi laeix liaxe liaex lixae
lixea liexa lieax lxiae lxiea lxaie lxaei lxeai lxeia leixa leiax
lexia lexai leaxi leaix ilaxe ilaex ilxae ilxea ilexa ileax ialxe
ialex iaxle iaxel iaexl iaelx ixale ixael ixlae ixlea ixela ixeal
ieaxl iealx iexal iexla ielxa ielax xliae xliea xlaie xlaei xleai
xleia xilae xilea xiale xiael xieal xiela xaile xaiel xalie xalei
xaeli xaeil xeial xeila xeail xeali xelai xelia elixa eliax elxia
elxai elaxi elaix eilxa eilax eixla eixal eiaxl eialx exila exial
exlia exlai exali exail eaixl eailx eaxil eaxli ealxi ealix

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

History of cryptography
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