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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: vindex
cipher variations:
wjoefy xkpfgz ylqgha zmrhib ansijc
botjkd cpukle dqvlmf erwmng fsxnoh
gtyopi huzpqj ivaqrk jwbrsl kxcstm
lydtun mzeuvo nafvwp obgwxq pchxyr
qdiyzs rejzat sfkabu tglbcv uhmcdw

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: vindex
Cipher: ermwvc

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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: vindex

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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: vindex
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: vindex
Cipher: ivaqrk

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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: vindex
Cipher: 154233415135

Extended Methods:
Method #1

Plaintext: vindex
method variations:

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

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Method #3

Plaintext: vindex
method variations:
umsvle msvleu svleum
vleums leumsv eumsvl

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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: vindex

all 720 cipher variations:
vindex vindxe vinedx vinexd vinxed vinxde vidnex vidnxe videnx videxn vidxen
vidxne viednx viedxn viendx vienxd viexnd viexdn vixden vixdne vixedn vixend
vixned vixnde vnidex vnidxe vniedx vniexd vnixed vnixde vndiex vndixe vndeix
vndexi vndxei vndxie vnedix vnedxi vneidx vneixd vnexid vnexdi vnxdei vnxdie
vnxedi vnxeid vnxied vnxide vdniex vdnixe vdneix vdnexi vdnxei vdnxie vdinex
vdinxe vdienx vdiexn vdixen vdixne vdeinx vdeixn vdenix vdenxi vdexni vdexin
vdxien vdxine vdxein vdxeni vdxnei vdxnie vendix vendxi venidx venixd venxid
venxdi vednix vednxi vedinx vedixn vedxin vedxni veidnx veidxn veindx veinxd
veixnd veixdn vexdin vexdni vexidn vexind vexnid vexndi vxndei vxndie vxnedi
vxneid vxnied vxnide vxdnei vxdnie vxdeni vxdein vxdien vxdine vxedni vxedin
vxendi vxenid vxeind vxeidn vxiden vxidne vxiedn vxiend vxined vxinde ivndex
ivndxe ivnedx ivnexd ivnxed ivnxde ivdnex ivdnxe ivdenx ivdexn ivdxen ivdxne
ivednx ivedxn ivendx ivenxd ivexnd ivexdn ivxden ivxdne ivxedn ivxend ivxned
ivxnde invdex invdxe invedx invexd invxed invxde indvex indvxe indevx indexv
indxev indxve inedvx inedxv inevdx inevxd inexvd inexdv inxdev inxdve inxedv
inxevd inxved inxvde idnvex idnvxe idnevx idnexv idnxev idnxve idvnex idvnxe
idvenx idvexn idvxen idvxne idevnx idevxn idenvx idenxv idexnv idexvn idxven
idxvne idxevn idxenv idxnev idxnve iendvx iendxv ienvdx ienvxd ienxvd ienxdv
iednvx iednxv iedvnx iedvxn iedxvn iedxnv ievdnx ievdxn ievndx ievnxd ievxnd
ievxdn iexdvn iexdnv iexvdn iexvnd iexnvd iexndv ixndev ixndve ixnedv ixnevd
ixnved ixnvde ixdnev ixdnve ixdenv ixdevn ixdven ixdvne ixednv ixedvn ixendv
ixenvd ixevnd ixevdn ixvden ixvdne ixvedn ixvend ixvned ixvnde nivdex nivdxe
nivedx nivexd nivxed nivxde nidvex nidvxe nidevx nidexv nidxev nidxve niedvx
niedxv nievdx nievxd niexvd niexdv nixdev nixdve nixedv nixevd nixved nixvde
nvidex nvidxe nviedx nviexd nvixed nvixde nvdiex nvdixe nvdeix nvdexi nvdxei
nvdxie nvedix nvedxi nveidx nveixd nvexid nvexdi nvxdei nvxdie nvxedi nvxeid
nvxied nvxide ndviex ndvixe ndveix ndvexi ndvxei ndvxie ndivex ndivxe ndievx
ndiexv ndixev ndixve ndeivx ndeixv ndevix ndevxi ndexvi ndexiv ndxiev ndxive
ndxeiv ndxevi ndxvei ndxvie nevdix nevdxi nevidx nevixd nevxid nevxdi nedvix
nedvxi nedivx nedixv nedxiv nedxvi neidvx neidxv neivdx neivxd neixvd neixdv
nexdiv nexdvi nexidv nexivd nexvid nexvdi nxvdei nxvdie nxvedi nxveid nxvied
nxvide nxdvei nxdvie nxdevi nxdeiv nxdiev nxdive nxedvi nxediv nxevdi nxevid
nxeivd nxeidv nxidev nxidve nxiedv nxievd nxived nxivde dinvex dinvxe dinevx
dinexv dinxev dinxve divnex divnxe divenx divexn divxen divxne dievnx dievxn
dienvx dienxv diexnv diexvn dixven dixvne dixevn dixenv dixnev dixnve dnivex
dnivxe dnievx dniexv dnixev dnixve dnviex dnvixe dnveix dnvexi dnvxei dnvxie
dnevix dnevxi dneivx dneixv dnexiv dnexvi dnxvei dnxvie dnxevi dnxeiv dnxiev
dnxive dvniex dvnixe dvneix dvnexi dvnxei dvnxie dvinex dvinxe dvienx dviexn
dvixen dvixne dveinx dveixn dvenix dvenxi dvexni dvexin dvxien dvxine dvxein
dvxeni dvxnei dvxnie denvix denvxi denivx denixv denxiv denxvi devnix devnxi
devinx devixn devxin devxni deivnx deivxn deinvx deinxv deixnv deixvn dexvin
dexvni dexivn dexinv dexniv dexnvi dxnvei dxnvie dxnevi dxneiv dxniev dxnive
dxvnei dxvnie dxveni dxvein dxvien dxvine dxevni dxevin dxenvi dxeniv dxeinv
dxeivn dxiven dxivne dxievn dxienv dxinev dxinve eindvx eindxv einvdx einvxd
einxvd einxdv eidnvx eidnxv eidvnx eidvxn eidxvn eidxnv eivdnx eivdxn eivndx
eivnxd eivxnd eivxdn eixdvn eixdnv eixvdn eixvnd eixnvd eixndv enidvx enidxv
enivdx enivxd enixvd enixdv endivx endixv endvix endvxi endxvi endxiv envdix
envdxi envidx envixd envxid envxdi enxdvi enxdiv enxvdi enxvid enxivd enxidv
ednivx ednixv ednvix ednvxi ednxvi ednxiv edinvx edinxv edivnx edivxn edixvn
edixnv edvinx edvixn edvnix edvnxi edvxni edvxin edxivn edxinv edxvin edxvni
edxnvi edxniv evndix evndxi evnidx evnixd evnxid evnxdi evdnix evdnxi evdinx
evdixn evdxin evdxni evidnx evidxn evindx evinxd evixnd evixdn evxdin evxdni
evxidn evxind evxnid evxndi exndvi exndiv exnvdi exnvid exnivd exnidv exdnvi
exdniv exdvni exdvin exdivn exdinv exvdni exvdin exvndi exvnid exvind exvidn
exidvn exidnv exivdn exivnd exinvd exindv xindev xindve xinedv xinevd xinved
xinvde xidnev xidnve xidenv xidevn xidven xidvne xiednv xiedvn xiendv xienvd
xievnd xievdn xivden xivdne xivedn xivend xivned xivnde xnidev xnidve xniedv
xnievd xnived xnivde xndiev xndive xndeiv xndevi xndvei xndvie xnediv xnedvi
xneidv xneivd xnevid xnevdi xnvdei xnvdie xnvedi xnveid xnvied xnvide xdniev
xdnive xdneiv xdnevi xdnvei xdnvie xdinev xdinve xdienv xdievn xdiven xdivne
xdeinv xdeivn xdeniv xdenvi xdevni xdevin xdvien xdvine xdvein xdveni xdvnei
xdvnie xendiv xendvi xenidv xenivd xenvid xenvdi xedniv xednvi xedinv xedivn
xedvin xedvni xeidnv xeidvn xeindv xeinvd xeivnd xeivdn xevdin xevdni xevidn
xevind xevnid xevndi xvndei xvndie xvnedi xvneid xvnied xvnide xvdnei xvdnie
xvdeni xvdein xvdien xvdine xvedni xvedin xvendi xvenid xveind xveidn xviden
xvidne xviedn xviend xvined xvinde

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History of cryptography
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