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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: precum
cipher variations:
qsfdvn rtgewo suhfxp tvigyq uwjhzr
vxkias wyljbt xzmkcu yanldv zbomew
acpnfx bdqogy cerphz dfsqia egtrjb
fhuskc givtld hjwume ikxvnf jlywog
kmzxph lnayqi mobzrj npcask oqdbtl

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: precum
Cipher: kivxfn

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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: precum

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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: precum
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: precum
Cipher: cerphz

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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: precum
Cipher: 532451315423

Extended Methods:
Method #1

Plaintext: precum
method variations:

Method #2
Bifid cipher
The message is converted to its coordinates in the usual manner, but they are written vertically beneath:
p r e c u m 
5 2 5 3 5 2 
3 4 1 1 4 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: precum
Cipher: kpksao

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Method #3

Plaintext: precum
method variations:
hylvix ylvixh lvixhy
vixhyl ixhylv xhylvi

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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: precum

all 720 cipher variations:
precum precmu preucm preumc premuc premcu prceum prcemu prcuem prcume prcmue
prcmeu prucem prucme pruecm pruemc prumec prumce prmcue prmceu prmuce prmuec
prmeuc prmecu percum percmu perucm perumc permuc permcu pecrum pecrmu pecurm
pecumr pecmur pecmru peucrm peucmr peurcm peurmc peumrc peumcr pemcur pemcru
pemucr pemurc pemruc pemrcu pcerum pcermu pceurm pceumr pcemur pcemru pcreum
pcremu pcruem pcrume pcrmue pcrmeu pcurem pcurme pcuerm pcuemr pcumer pcumre
pcmrue pcmreu pcmure pcmuer pcmeur pcmeru puecrm puecmr puercm puermc puemrc
puemcr pucerm pucemr pucrem pucrme pucmre pucmer purcem purcme purecm puremc
purmec purmce pumcre pumcer pumrce pumrec pumerc pumecr pmecur pmecru pmeucr
pmeurc pmeruc pmercu pmceur pmceru pmcuer pmcure pmcrue pmcreu pmucer pmucre
pmuecr pmuerc pmurec pmurce pmrcue pmrceu pmruce pmruec pmreuc pmrecu rpecum
rpecmu rpeucm rpeumc rpemuc rpemcu rpceum rpcemu rpcuem rpcume rpcmue rpcmeu
rpucem rpucme rpuecm rpuemc rpumec rpumce rpmcue rpmceu rpmuce rpmuec rpmeuc
rpmecu repcum repcmu repucm repumc repmuc repmcu recpum recpmu recupm recump
recmup recmpu reucpm reucmp reupcm reupmc reumpc reumcp remcup remcpu remucp
remupc rempuc rempcu rcepum rcepmu rceupm rceump rcemup rcempu rcpeum rcpemu
rcpuem rcpume rcpmue rcpmeu rcupem rcupme rcuepm rcuemp rcumep rcumpe rcmpue
rcmpeu rcmupe rcmuep rcmeup rcmepu ruecpm ruecmp ruepcm ruepmc ruempc ruemcp
rucepm rucemp rucpem rucpme rucmpe rucmep rupcem rupcme rupecm rupemc rupmec
rupmce rumcpe rumcep rumpce rumpec rumepc rumecp rmecup rmecpu rmeucp rmeupc
rmepuc rmepcu rmceup rmcepu rmcuep rmcupe rmcpue rmcpeu rmucep rmucpe rmuecp
rmuepc rmupec rmupce rmpcue rmpceu rmpuce rmpuec rmpeuc rmpecu erpcum erpcmu
erpucm erpumc erpmuc erpmcu ercpum ercpmu ercupm ercump ercmup ercmpu erucpm
erucmp erupcm erupmc erumpc erumcp ermcup ermcpu ermucp ermupc ermpuc ermpcu
eprcum eprcmu eprucm eprumc eprmuc eprmcu epcrum epcrmu epcurm epcumr epcmur
epcmru epucrm epucmr epurcm epurmc epumrc epumcr epmcur epmcru epmucr epmurc
epmruc epmrcu ecprum ecprmu ecpurm ecpumr ecpmur ecpmru ecrpum ecrpmu ecrupm
ecrump ecrmup ecrmpu ecurpm ecurmp ecuprm ecupmr ecumpr ecumrp ecmrup ecmrpu
ecmurp ecmupr ecmpur ecmpru eupcrm eupcmr euprcm euprmc eupmrc eupmcr eucprm
eucpmr eucrpm eucrmp eucmrp eucmpr eurcpm eurcmp eurpcm eurpmc eurmpc eurmcp
eumcrp eumcpr eumrcp eumrpc eumprc eumpcr empcur empcru empucr empurc empruc
emprcu emcpur emcpru emcupr emcurp emcrup emcrpu emucpr emucrp emupcr emuprc
emurpc emurcp emrcup emrcpu emrucp emrupc emrpuc emrpcu crepum crepmu creupm
creump cremup crempu crpeum crpemu crpuem crpume crpmue crpmeu crupem crupme
cruepm cruemp crumep crumpe crmpue crmpeu crmupe crmuep crmeup crmepu cerpum
cerpmu cerupm cerump cermup cermpu ceprum ceprmu cepurm cepumr cepmur cepmru
ceuprm ceupmr ceurpm ceurmp ceumrp ceumpr cempur cempru cemupr cemurp cemrup
cemrpu cperum cpermu cpeurm cpeumr cpemur cpemru cpreum cpremu cpruem cprume
cprmue cprmeu cpurem cpurme cpuerm cpuemr cpumer cpumre cpmrue cpmreu cpmure
cpmuer cpmeur cpmeru cueprm cuepmr cuerpm cuermp cuemrp cuempr cuperm cupemr
cuprem cuprme cupmre cupmer curpem curpme curepm curemp curmep curmpe cumpre
cumper cumrpe cumrep cumerp cumepr cmepur cmepru cmeupr cmeurp cmerup cmerpu
cmpeur cmperu cmpuer cmpure cmprue cmpreu cmuper cmupre cmuepr cmuerp cmurep
cmurpe cmrpue cmrpeu cmrupe cmruep cmreup cmrepu urecpm urecmp urepcm urepmc
urempc uremcp urcepm urcemp urcpem urcpme urcmpe urcmep urpcem urpcme urpecm
urpemc urpmec urpmce urmcpe urmcep urmpce urmpec urmepc urmecp uercpm uercmp
uerpcm uerpmc uermpc uermcp uecrpm uecrmp uecprm uecpmr uecmpr uecmrp uepcrm
uepcmr ueprcm ueprmc uepmrc uepmcr uemcpr uemcrp uempcr uemprc uemrpc uemrcp
ucerpm ucermp uceprm ucepmr ucempr ucemrp ucrepm ucremp ucrpem ucrpme ucrmpe
ucrmep ucprem ucprme ucperm ucpemr ucpmer ucpmre ucmrpe ucmrep ucmpre ucmper
ucmepr ucmerp upecrm upecmr upercm upermc upemrc upemcr upcerm upcemr upcrem
upcrme upcmre upcmer uprcem uprcme uprecm upremc uprmec uprmce upmcre upmcer
upmrce upmrec upmerc upmecr umecpr umecrp umepcr umeprc umerpc umercp umcepr
umcerp umcper umcpre umcrpe umcrep umpcer umpcre umpecr umperc umprec umprce
umrcpe umrcep umrpce umrpec umrepc umrecp mrecup mrecpu mreucp mreupc mrepuc
mrepcu mrceup mrcepu mrcuep mrcupe mrcpue mrcpeu mrucep mrucpe mruecp mruepc
mrupec mrupce mrpcue mrpceu mrpuce mrpuec mrpeuc mrpecu mercup mercpu merucp
merupc merpuc merpcu mecrup mecrpu mecurp mecupr mecpur mecpru meucrp meucpr
meurcp meurpc meuprc meupcr mepcur mepcru mepucr mepurc mepruc meprcu mcerup
mcerpu mceurp mceupr mcepur mcepru mcreup mcrepu mcruep mcrupe mcrpue mcrpeu
mcurep mcurpe mcuerp mcuepr mcuper mcupre mcprue mcpreu mcpure mcpuer mcpeur
mcperu muecrp muecpr muercp muerpc mueprc muepcr mucerp mucepr mucrep mucrpe
mucpre mucper murcep murcpe murecp murepc murpec murpce mupcre mupcer muprce
muprec muperc mupecr mpecur mpecru mpeucr mpeurc mperuc mpercu mpceur mpceru
mpcuer mpcure mpcrue mpcreu mpucer mpucre mpuecr mpuerc mpurec mpurce mprcue
mprceu mpruce mpruec mpreuc mprecu

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History of cryptography
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