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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: ligman
cipher variations:
mjhnbo nkiocp oljpdq pmkqer qnlrfs
romsgt spnthu tqouiv urpvjw vsqwkx
wtrxly xusymz yvtzna zwuaob axvbpc
bywcqd czxdre dayesf ebzftg fcaguh
gdbhvi heciwj ifdjxk jgekyl khflzm

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: ligman
Cipher: ortnzm

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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: ligman

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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: ligman
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: ligman
Cipher: yvtzna

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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: ligman
Cipher: 134222231133

Extended Methods:
Method #1

Plaintext: ligman
method variations:

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

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Method #3

Plaintext: ligman
method variations:
sggclc ggclcs gclcsg
clcsgg lcsggc csggcl

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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: ligman

all 720 cipher variations:
ligman ligmna ligamn liganm lignam lignma limgan limgna limagn limang limnag
limnga liamgn liamng liagmn liagnm liangm lianmg linmag linmga linamg linagm
lingam lingma lgiman lgimna lgiamn lgianm lginam lginma lgmian lgmina lgmain
lgmani lgmnai lgmnia lgamin lgamni lgaimn lgainm lganim lganmi lgnmai lgnmia
lgnami lgnaim lgniam lgnima lmgian lmgina lmgain lmgani lmgnai lmgnia lmigan
lmigna lmiagn lmiang lminag lminga lmaign lmaing lmagin lmagni lmangi lmanig
lmniag lmniga lmnaig lmnagi lmngai lmngia lagmin lagmni lagimn laginm lagnim
lagnmi lamgin lamgni lamign laming lamnig lamngi laimgn laimng laigmn laignm
laingm lainmg lanmig lanmgi lanimg lanigm langim langmi lngmai lngmia lngami
lngaim lngiam lngima lnmgai lnmgia lnmagi lnmaig lnmiag lnmiga lnamgi lnamig
lnagmi lnagim lnaigm lnaimg lnimag lnimga lniamg lniagm lnigam lnigma ilgman
ilgmna ilgamn ilganm ilgnam ilgnma ilmgan ilmgna ilmagn ilmang ilmnag ilmnga
ilamgn ilamng ilagmn ilagnm ilangm ilanmg ilnmag ilnmga ilnamg ilnagm ilngam
ilngma iglman iglmna iglamn iglanm iglnam iglnma igmlan igmlna igmaln igmanl
igmnal igmnla igamln igamnl igalmn igalnm iganlm iganml ignmal ignmla ignaml
ignalm ignlam ignlma imglan imglna imgaln imganl imgnal imgnla imlgan imlgna
imlagn imlang imlnag imlnga imalgn imalng imagln imagnl imangl imanlg imnlag
imnlga imnalg imnagl imngal imngla iagmln iagmnl iaglmn iaglnm iagnlm iagnml
iamgln iamgnl iamlgn iamlng iamnlg iamngl ialmgn ialmng ialgmn ialgnm ialngm
ialnmg ianmlg ianmgl ianlmg ianlgm ianglm iangml ingmal ingmla ingaml ingalm
inglam inglma inmgal inmgla inmagl inmalg inmlag inmlga inamgl inamlg inagml
inaglm inalgm inalmg inlmag inlmga inlamg inlagm inlgam inlgma gilman gilmna
gilamn gilanm gilnam gilnma gimlan gimlna gimaln gimanl gimnal gimnla giamln
giamnl gialmn gialnm gianlm gianml ginmal ginmla ginaml ginalm ginlam ginlma
gliman glimna gliamn glianm glinam glinma glmian glmina glmain glmani glmnai
glmnia glamin glamni glaimn glainm glanim glanmi glnmai glnmia glnami glnaim
glniam glnima gmlian gmlina gmlain gmlani gmlnai gmlnia gmilan gmilna gmialn
gmianl gminal gminla gmailn gmainl gmalin gmalni gmanli gmanil gmnial gmnila
gmnail gmnali gmnlai gmnlia galmin galmni galimn galinm galnim galnmi gamlin
gamlni gamiln gaminl gamnil gamnli gaimln gaimnl gailmn gailnm gainlm gainml
ganmil ganmli ganiml ganilm ganlim ganlmi gnlmai gnlmia gnlami gnlaim gnliam
gnlima gnmlai gnmlia gnmali gnmail gnmial gnmila gnamli gnamil gnalmi gnalim
gnailm gnaiml gnimal gnimla gniaml gnialm gnilam gnilma miglan miglna migaln
miganl mignal mignla milgan milgna milagn milang milnag milnga mialgn mialng
miagln miagnl miangl mianlg minlag minlga minalg minagl mingal mingla mgilan
mgilna mgialn mgianl mginal mginla mglian mglina mglain mglani mglnai mglnia
mgalin mgalni mgailn mgainl mganil mganli mgnlai mgnlia mgnali mgnail mgnial
mgnila mlgian mlgina mlgain mlgani mlgnai mlgnia mligan mligna mliagn mliang
mlinag mlinga mlaign mlaing mlagin mlagni mlangi mlanig mlniag mlniga mlnaig
mlnagi mlngai mlngia maglin maglni magiln maginl magnil magnli malgin malgni
malign maling malnig malngi mailgn mailng maigln maignl maingl mainlg manlig
manlgi manilg manigl mangil mangli mnglai mnglia mngali mngail mngial mngila
mnlgai mnlgia mnlagi mnlaig mnliag mnliga mnalgi mnalig mnagli mnagil mnaigl
mnailg mnilag mnilga mnialg mniagl mnigal mnigla aigmln aigmnl aiglmn aiglnm
aignlm aignml aimgln aimgnl aimlgn aimlng aimnlg aimngl ailmgn ailmng ailgmn
ailgnm ailngm ailnmg ainmlg ainmgl ainlmg ainlgm ainglm aingml agimln agimnl
agilmn agilnm aginlm aginml agmiln agminl agmlin agmlni agmnli agmnil aglmin
aglmni aglimn aglinm aglnim aglnmi agnmli agnmil agnlmi agnlim agnilm agniml
amgiln amginl amglin amglni amgnli amgnil amigln amignl amilgn amilng aminlg
amingl amlign amling amlgin amlgni amlngi amlnig amnilg amnigl amnlig amnlgi
amngli amngil algmin algmni algimn alginm algnim algnmi almgin almgni almign
alming almnig almngi alimgn alimng aligmn alignm alingm alinmg alnmig alnmgi
alnimg alnigm alngim alngmi angmli angmil anglmi anglim angilm angiml anmgli
anmgil anmlgi anmlig anmilg anmigl anlmgi anlmig anlgmi anlgim anligm anlimg
animlg animgl anilmg anilgm aniglm anigml nigmal nigmla nigaml nigalm niglam
niglma nimgal nimgla nimagl nimalg nimlag nimlga niamgl niamlg niagml niaglm
nialgm nialmg nilmag nilmga nilamg nilagm nilgam nilgma ngimal ngimla ngiaml
ngialm ngilam ngilma ngmial ngmila ngmail ngmali ngmlai ngmlia ngamil ngamli
ngaiml ngailm ngalim ngalmi nglmai nglmia nglami nglaim ngliam nglima nmgial
nmgila nmgail nmgali nmglai nmglia nmigal nmigla nmiagl nmialg nmilag nmilga
nmaigl nmailg nmagil nmagli nmalgi nmalig nmliag nmliga nmlaig nmlagi nmlgai
nmlgia nagmil nagmli nagiml nagilm naglim naglmi namgil namgli namigl namilg
namlig namlgi naimgl naimlg naigml naiglm nailgm nailmg nalmig nalmgi nalimg
naligm nalgim nalgmi nlgmai nlgmia nlgami nlgaim nlgiam nlgima nlmgai nlmgia
nlmagi nlmaig nlmiag nlmiga nlamgi nlamig nlagmi nlagim nlaigm nlaimg nlimag
nlimga nliamg nliagm nligam nligma

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History of cryptography
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