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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: fraire
cipher variations:
gsbjsf htcktg iudluh jvemvi kwfnwj
lxgoxk myhpyl nziqzm oajran pbksbo
qcltcp rdmudq senver tfowfs ugpxgt
vhqyhu wirziv xjsajw yktbkx zlucly
amvdmz bnwena coxfob dpygpc eqzhqd

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: fraire
Cipher: uizriv

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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: fraire
Cipher: AABAB BAAAA AAAAA ABAAA BAAAA 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: fraire
cipher variations:
gsbjsfqabzanaibpivkqbfqduybvylegblgtywbrwjiebher
smbxmzcubnuhmcbdcpwkbtkxhtcktgrbcabobjcqjwlrcgre
vzcwzmfhcmhuzxcsxkjfcifstncynadvcovindcedqxlculy
iudluhscdbcpckdrkxmsdhsfwadxangidnivaydtylkgdjgt
uodzobewdpwjoedferymdvmzjvemvitdecdqdleslynteitg
xbeybohjeojwbzeuzmlhekhuvpeapcfxeqxkpfegfsznewna
kwfnwjuefderemftmzoufjuhycfzcpikfpkxcafvanmifliv
wqfbqdgyfrylqgfhgtaofxoblxgoxkvfgefsfngunapvgkvi
zdgadqjlgqlydbgwbonjgmjwxrgcrehzgszmrhgihubpgypc
myhpylwghfgtgohvobqwhlwjaehberkmhrmzechxcpokhnkx
yshdsfiahtansihjivcqhzqdnziqzmxhighuhpiwpcrximxk
bficfslnisnafdiydqpliolyztietgjbiubotjikjwdriare
oajranyijhiviqjxqdsyjnylcgjdgtmojtobgejzerqmjpmz
aujfuhkcjvcpukjlkxesjbsfpbksbozjkijwjrkyretzkozm
dhkehunpkupchfkafsrnkqnabvkgvildkwdqvlkmlyftkctg
qcltcpakljkxkslzsfualpaneilfivoqlvqdiglbgtsolrob
cwlhwjmelxerwmlnmzgulduhrdmudqblmklyltmatgvbmqbo
fjmgjwprmwrejhmchutpmspcdxmixknfmyfsxnmonahvmevi
senvercmnlmzmunbuhwcnrcpgknhkxqsnxsfkindivuqntqd
eynjylognzgtyonpobiwnfwjtfowfsdnomnanvocvixdosdq
hloilyrtoytgljoejwvrourefzokzmphoahuzpoqpcjxogxk
ugpxgteopnobowpdwjyepterimpjmzsupzuhmkpfkxwspvsf
gaplanqipbivaqprqdkyphylvhqyhufpqopcpxqexkzfqufs
jnqknatvqavinlqglyxtqwtghbqmborjqcjwbrqsrelzqizm
wirzivgqrpqdqyrfylagrvgtkorlobuwrbwjomrhmzyurxuh
icrncpskrdkxcsrtsfmarjanxjsajwhrsqrerzsgzmbhswhu
lpsmpcvxscxkpnsinazvsyvijdsodqtlselydtsutgnbskbo
yktbkxistrsfsathancitxivmqtnqdwytdylqotjobawtzwj
ketperumtfmzeutvuhoctlcpzluclyjtustgtbuibodjuyjw
nruorexzuezmrpukpcbxuaxklfuqfsvnugnafvuwvipdumdq
amvdmzkuvtuhucvjcpekvzkxosvpsfyavfansqvlqdcyvbyl
mgvrgtwovhobgwvxwjqevnerbnwenalvwuvivdwkdqflwaly
ptwqtgzbwgbotrwmredzwczmnhwshuxpwipchxwyxkrfwofs
coxfobmwxvwjwexlergmxbmzquxruhacxhcpusxnsfeaxdan
oixtivyqxjqdiyxzylsgxpgtdpygpcnxywxkxfymfshnycna
rvysvibdyidqvtyotgfbyebopjyujwzrykrejzyazmthyqhu
eqzhqdoyzxylygzngtiozdobswztwjcezjerwuzpuhgczfcp
qkzvkxaszlsfkazbanuizrivfrairepzayzmzhaohujpaepc
txauxkdfakfsxvaqvihdagdqrlawlybtamtglbacbovjasjw

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: fraire
Cipher: senver

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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: fraire
Cipher: 122411422451

Extended Methods:
Method #1

Plaintext: fraire
method variations:
lwfowkqbltbpvgqyguamvdmz

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
f r a i r e 
1 2 1 4 2 5 
2 4 1 2 4 1 
They are then read out in rows:
121425241241
Then divided up into pairs again, and the pairs turned back into letters using the square:
Plain: fraire
Cipher: fqwrfd

Read more ...
Method #3

Plaintext: fraire
method variations:
gdqgya dqgyag qgyagd
gyagdq yagdqg agdqgy

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: fraire

all 720 cipher variations:
fraire fraier frarie frarei fraeri fraeir friare friaer frirae frirea friera
friear frriae frriea frraie frraei frreai frreia freira freiar freria frerai
freari freair farire farier farrie farrei fareri fareir fairre fairer fairre
fairer faierr faierr farire farier farrie farrei fareri fareir faeirr faeirr
faerir faerri faerri faerir fiarre fiarer fiarre fiarer fiaerr fiaerr firare
firaer firrae firrea firera firear firrae firrea firare firaer firear firera
fierra fierar fierra fierar fiearr fiearr fraire fraier frarie frarei fraeri
fraeir friare friaer frirae frirea friera friear frriae frriea frraie frraei
frreai frreia freira freiar freria frerai freari freair feairr feairr fearir
fearri fearri fearir feiarr feiarr feirar feirra feirra feirar feriar ferira
ferair ferari ferrai ferria ferira feriar ferria ferrai ferari ferair rfaire
rfaier rfarie rfarei rfaeri rfaeir rfiare rfiaer rfirae rfirea rfiera rfiear
rfriae rfriea rfraie rfraei rfreai rfreia rfeira rfeiar rferia rferai rfeari
rfeair rafire rafier rafrie rafrei raferi rafeir raifre raifer rairfe rairef
raierf raiefr rarife rarief rarfie rarfei rarefi rareif raeirf raeifr raerif
raerfi raefri raefir riafre riafer riarfe riaref riaerf riaefr rifare rifaer
rifrae rifrea rifera rifear rirfae rirfea rirafe riraef rireaf rirefa riefra
riefar rierfa rieraf riearf rieafr rraife rraief rrafie rrafei rraefi rraeif
rriafe rriaef rrifae rrifea rriefa rrieaf rrfiae rrfiea rrfaie rrfaei rrfeai
rrfeia rreifa rreiaf rrefia rrefai rreafi rreaif reairf reaifr rearif rearfi
reafri reafir reiarf reiafr reiraf reirfa reifra reifar reriaf rerifa reraif
rerafi rerfai rerfia refira refiar refria refrai refari refair arfire arfier
arfrie arfrei arferi arfeir arifre arifer arirfe ariref arierf ariefr arrife
arrief arrfie arrfei arrefi arreif areirf areifr arerif arerfi arefri arefir
afrire afrier afrrie afrrei afreri afreir afirre afirer afirre afirer afierr
afierr afrire afrier afrrie afrrei afreri afreir afeirr afeirr aferir aferri
aferri aferir aifrre aifrer aifrre aifrer aiferr aiferr airfre airfer airrfe
airref airerf airefr airrfe airref airfre airfer airefr airerf aierrf aierfr
aierrf aierfr aiefrr aiefrr arfire arfier arfrie arfrei arferi arfeir arifre
arifer arirfe ariref arierf ariefr arrife arrief arrfie arrfei arrefi arreif
areirf areifr arerif arerfi arefri arefir aefirr aefirr aefrir aefrri aefrri
aefrir aeifrr aeifrr aeirfr aeirrf aeirrf aeirfr aerifr aerirf aerfir aerfri
aerrfi aerrif aerirf aerifr aerrif aerrfi aerfri aerfir irafre irafer irarfe
iraref iraerf iraefr irfare irfaer irfrae irfrea irfera irfear irrfae irrfea
irrafe irraef irreaf irrefa irefra irefar irerfa ireraf irearf ireafr iarfre
iarfer iarrfe iarref iarerf iarefr iafrre iafrer iafrre iafrer iaferr iaferr
iarfre iarfer iarrfe iarref iarerf iarefr iaefrr iaefrr iaerfr iaerrf iaerrf
iaerfr ifarre ifarer ifarre ifarer ifaerr ifaerr ifrare ifraer ifrrae ifrrea
ifrera ifrear ifrrae ifrrea ifrare ifraer ifrear ifrera iferra iferar iferra
iferar ifearr ifearr irafre irafer irarfe iraref iraerf iraefr irfare irfaer
irfrae irfrea irfera irfear irrfae irrfea irrafe irraef irreaf irrefa irefra
irefar irerfa ireraf irearf ireafr ieafrr ieafrr iearfr iearrf iearrf iearfr
iefarr iefarr iefrar iefrra iefrra iefrar ierfar ierfra ierafr ierarf ierraf
ierrfa ierfra ierfar ierrfa ierraf ierarf ierafr rraife rraief rrafie rrafei
rraefi rraeif rriafe rriaef rrifae rrifea rriefa rrieaf rrfiae rrfiea rrfaie
rrfaei rrfeai rrfeia rreifa rreiaf rrefia rrefai rreafi rreaif rarife rarief
rarfie rarfei rarefi rareif rairfe rairef raifre raifer raiefr raierf rafire
rafier rafrie rafrei raferi rafeir raeifr raeirf raefir raefri raerfi raerif
riarfe riaref riafre riafer riaefr riaerf rirafe riraef rirfae rirfea rirefa
rireaf rifrae rifrea rifare rifaer rifear rifera rierfa rieraf riefra riefar
rieafr riearf rfaire rfaier rfarie rfarei rfaeri rfaeir rfiare rfiaer rfirae
rfirea rfiera rfiear rfriae rfriea rfraie rfraei rfreai rfreia rfeira rfeiar
rferia rferai rfeari rfeair reaifr reairf reafir reafri rearfi rearif reiafr
reiarf reifar reifra reirfa reiraf refiar refira refair refari refrai refria
rerifa reriaf rerfia rerfai rerafi reraif erairf eraifr erarif erarfi erafri
erafir eriarf eriafr eriraf erirfa erifra erifar erriaf errifa erraif errafi
errfai errfia erfira erfiar erfria erfrai erfari erfair earirf earifr earrif
earrfi earfri earfir eairrf eairfr eairrf eairfr eaifrr eaifrr earirf earifr
earrif earrfi earfri earfir eafirr eafirr eafrir eafrri eafrri eafrir eiarrf
eiarfr eiarrf eiarfr eiafrr eiafrr eirarf eirafr eirraf eirrfa eirfra eirfar
eirraf eirrfa eirarf eirafr eirfar eirfra eifrra eifrar eifrra eifrar eifarr
eifarr erairf eraifr erarif erarfi erafri erafir eriarf eriafr eriraf erirfa
erifra erifar erriaf errifa erraif errafi errfai errfia erfira erfiar erfria
erfrai erfari erfair efairr efairr efarir efarri efarri efarir efiarr efiarr
efirar efirra efirra efirar efriar efrira efrair efrari efrrai efrria efrira
efriar efrria efrrai efrari efrair

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History of cryptography
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