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whyever

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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: quate
cipher variations:
rvbuf swcvg txdwh uyexi vzfyj
wagzk xbhal ycibm zdjcn aekdo
bflep cgmfq dhngr eiohs fjpit
gkqju hlrkv imslw jntmx kouny
lpvoz mqwpa nrxqb osyrc ptzsd

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: quate
Cipher: jfzgv

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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: quate
Cipher: ABBBB BAABB AAAAA BAABA 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: quate
cipher variations:
rvbufxjbgndxbsvjlbedpzbqlvnbcthpbajndbmr
trbyzzfbkhftbwplhbixswcvgykchoeyctwkmcfe
qacrmwocduiqcbkoecnsusczaagcligucxqmicjy
txdwhzldipfzduxlndgfrbdsnxpdevjrdclpfdot
vtdabbhdmjhvdyrnjdkzuyexiamejqgaevymoehg
scetoyqefwksedmqgepuwuebccienkiwezsokela
vzfyjbnfkrhbfwznpfihtdfupzrfgxltfenrhfqv
xvfcddjfoljxfatplfmbwagzkcoglsicgxaoqgji
uegvqasghymugfosigrwywgdeekgpmkygbuqmgnc
xbhaldphmtjdhybprhkjvfhwrbthiznvhgptjhsx
zxhefflhqnlzhcvrnhodycibmeqinukeizcqsilk
wgixscuijaowihqukityayifggmiromaidwsoipe
zdjcnfrjovlfjadrtjmlxhjytdvjkbpxjirvljuz
bzjghhnjspnbjextpjqfaekdogskpwmgkbesuknm
yikzuewklcqykjswmkvacakhiioktqockfyuqkrg
bflephtlqxnhlcftvlonzjlavfxlmdrzlktxnlwb
dblijjplurpdlgzvrlshcgmfqiumryoimdguwmpo
akmbwgymnesamluyomxcecmjkkqmvsqemhawsmti
dhngrjvnszpjnehvxnqpblncxhznoftbnmvzpnyd
fdnkllrnwtrfnibxtnujeiohskwotaqkofiwyorq
cmodyiaopguconwaqozegeolmmsoxusgojcyuovk
fjpitlxpubrlpgjxzpsrdnpezjbpqhvdpoxbrpaf
hfpmnntpyvthpkdzvpwlgkqjumyqvcsmqhkyaqts
eoqfakcqriweqpycsqbgigqnoouqzwuiqleawqxm
hlrkvnzrwdtnrilzbrutfprgbldrsjxfrqzdtrch
jhroppvraxvjrmfbxrynimslwoasxeuosjmacsvu
gqshcmestkygsraeusdikispqqwsbywksngcyszo
jntmxpbtyfvptknbdtwvhrtidnftulzhtsbfvtej
ljtqrrxtczxltohdztapkounyqcuzgwquloceuxw
isujeoguvmaiutcgwufkmkurssyudaymupieaubq
lpvozrdvahxrvmpdfvyxjtvkfphvwnbjvudhxvgl
nlvsttzvebznvqjfbvcrmqwpasewbiyswnqegwzy
kuwlgqiwxockwveiywhmomwtuuawfcaowrkgcwds
nrxqbtfxcjztxorfhxazlvxmhrjxypdlxwfjzxin
pnxuvvbxgdbpxslhdxetosyrcugydkauypsgiyba
mwyniskyzqemyxgkayjoqoyvwwcyhecqytmieyfu
ptzsdvhzelbvzqthjzcbnxzojtlzarfnzyhlbzkp
rpzwxxdzifdrzunjfzgvquatewiafmcwaruikadc
oyapkumabsgoazimcalqsqaxyyeajgesavokgahw

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: quate
Cipher: dhngr

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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: quate
Cipher: 1454114451

Extended Methods:
Method #1

Plaintext: quate
method variations:
vzfykaeldpfkqiulpvoz

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
q u a t e 
1 5 1 4 5 
4 4 1 4 1 
They are then read out in rows:
1514544141
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: quate
Cipher: vqudd

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Method #3

Plaintext: quate
method variations:
ydqya dqyay qyayd
yaydq aydqy

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: quate

all 120 cipher variations:
quate quaet qutae qutea queta queat qaute qauet qatue qateu qaetu
qaeut qtaue qtaeu qtuae qtuea qteua qteau qeatu qeaut qetau qetua
qeuta qeuat uqate uqaet uqtae uqtea uqeta uqeat uaqte uaqet uatqe
uateq uaetq uaeqt utaqe utaeq utqae utqea uteqa uteaq ueatq ueaqt
uetaq uetqa ueqta ueqat auqte auqet autqe auteq auetq aueqt aqute
aquet aqtue aqteu aqetu aqeut atque atqeu atuqe atueq ateuq atequ
aeqtu aequt aetqu aetuq aeutq aeuqt tuaqe tuaeq tuqae tuqea tueqa
tueaq tauqe taueq taque taqeu taequ taeuq tqaue tqaeu tquae tquea
tqeua tqeau teaqu teauq teqau tequa teuqa teuaq euatq euaqt eutaq
eutqa euqta euqat eautq eauqt eatuq eatqu eaqtu eaqut etauq etaqu
etuaq etuqa etqua etqau eqatu eqaut eqtau eqtua equta equat

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

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