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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: braize
cipher variations:
csbjaf dtckbg eudlch fvemdi gwfnej
hxgofk iyhpgl jziqhm kajrin lbksjo
mcltkp ndmulq oenvmr pfowns qgpxot
rhqypu sirzqv tjsarw uktbsx vlucty
wmvduz xnweva yoxfwb zpygxc aqzhyd

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: braize
Cipher: yizrav

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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: braize

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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: braize
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: braize
Cipher: oenvmr

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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: braize
Cipher: 212411425551

Extended Methods:
Method #1

Plaintext: braize
method variations:

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

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Method #3

Plaintext: braize
method variations:
fdqwzf dqwzff qwzffd
wzffdq zffdqw ffdqwz

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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: braize

all 720 cipher variations:
braize braiez brazie brazei braezi braeiz briaze briaez brizae brizea brieza
brieaz brziae brziea brzaie brzaei brzeai brzeia breiza breiaz brezia brezai
breazi breaiz barize bariez barzie barzei barezi bareiz bairze bairez baizre
baizer baiezr baierz bazire bazier bazrie bazrei bazeri bazeir baeizr baeirz
baezir baezri baerzi baeriz biarze biarez biazre biazer biaezr biaerz biraze
biraez birzae birzea bireza bireaz bizrae bizrea bizare bizaer bizear bizera
bierza bieraz biezra biezar bieazr biearz bzaire bzaier bzarie bzarei bzaeri
bzaeir bziare bziaer bzirae bzirea bziera bziear bzriae bzriea bzraie bzraei
bzreai bzreia bzeira bzeiar bzeria bzerai bzeari bzeair beaizr beairz beazir
beazri bearzi beariz beiazr beiarz beizar beizra beirza beiraz beziar bezira
bezair bezari bezrai bezria beriza beriaz berzia berzai berazi beraiz rbaize
rbaiez rbazie rbazei rbaezi rbaeiz rbiaze rbiaez rbizae rbizea rbieza rbieaz
rbziae rbziea rbzaie rbzaei rbzeai rbzeia rbeiza rbeiaz rbezia rbezai rbeazi
rbeaiz rabize rabiez rabzie rabzei rabezi rabeiz raibze raibez raizbe raizeb
raiezb raiebz razibe razieb razbie razbei razebi razeib raeizb raeibz raezib
raezbi raebzi raebiz riabze riabez riazbe riazeb riaezb riaebz ribaze ribaez
ribzae ribzea ribeza ribeaz rizbae rizbea rizabe rizaeb rizeab rizeba riebza
riebaz riezba riezab rieazb rieabz rzaibe rzaieb rzabie rzabei rzaebi rzaeib
rziabe rziaeb rzibae rzibea rzieba rzieab rzbiae rzbiea rzbaie rzbaei rzbeai
rzbeia rzeiba rzeiab rzebia rzebai rzeabi rzeaib reaizb reaibz reazib reazbi
reabzi reabiz reiazb reiabz reizab reizba reibza reibaz reziab reziba rezaib
rezabi rezbai rezbia rebiza rebiaz rebzia rebzai rebazi rebaiz arbize arbiez
arbzie arbzei arbezi arbeiz aribze aribez arizbe arizeb ariezb ariebz arzibe
arzieb arzbie arzbei arzebi arzeib areizb areibz arezib arezbi arebzi arebiz
abrize abriez abrzie abrzei abrezi abreiz abirze abirez abizre abizer abiezr
abierz abzire abzier abzrie abzrei abzeri abzeir abeizr abeirz abezir abezri
aberzi aberiz aibrze aibrez aibzre aibzer aibezr aiberz airbze airbez airzbe
airzeb airezb airebz aizrbe aizreb aizbre aizber aizebr aizerb aierzb aierbz
aiezrb aiezbr aiebzr aiebrz azbire azbier azbrie azbrei azberi azbeir azibre
aziber azirbe azireb azierb aziebr azribe azrieb azrbie azrbei azrebi azreib
azeirb azeibr azerib azerbi azebri azebir aebizr aebirz aebzir aebzri aebrzi
aebriz aeibzr aeibrz aeizbr aeizrb aeirzb aeirbz aezibr aezirb aezbir aezbri
aezrbi aezrib aerizb aeribz aerzib aerzbi aerbzi aerbiz irabze irabez irazbe
irazeb iraezb iraebz irbaze irbaez irbzae irbzea irbeza irbeaz irzbae irzbea
irzabe irzaeb irzeab irzeba irebza irebaz irezba irezab ireazb ireabz iarbze
iarbez iarzbe iarzeb iarezb iarebz iabrze iabrez iabzre iabzer iabezr iaberz
iazbre iazber iazrbe iazreb iazerb iazebr iaebzr iaebrz iaezbr iaezrb iaerzb
iaerbz ibarze ibarez ibazre ibazer ibaezr ibaerz ibraze ibraez ibrzae ibrzea
ibreza ibreaz ibzrae ibzrea ibzare ibzaer ibzear ibzera iberza iberaz ibezra
ibezar ibeazr ibearz izabre izaber izarbe izareb izaerb izaebr izbare izbaer
izbrae izbrea izbera izbear izrbae izrbea izrabe izraeb izreab izreba izebra
izebar izerba izerab izearb izeabr ieabzr ieabrz ieazbr ieazrb iearzb iearbz
iebazr iebarz iebzar iebzra iebrza iebraz iezbar iezbra iezabr iezarb iezrab
iezrba ierbza ierbaz ierzba ierzab ierazb ierabz zraibe zraieb zrabie zrabei
zraebi zraeib zriabe zriaeb zribae zribea zrieba zrieab zrbiae zrbiea zrbaie
zrbaei zrbeai zrbeia zreiba zreiab zrebia zrebai zreabi zreaib zaribe zarieb
zarbie zarbei zarebi zareib zairbe zaireb zaibre zaiber zaiebr zaierb zabire
zabier zabrie zabrei zaberi zabeir zaeibr zaeirb zaebir zaebri zaerbi zaerib
ziarbe ziareb ziabre ziaber ziaebr ziaerb zirabe ziraeb zirbae zirbea zireba
zireab zibrae zibrea zibare zibaer zibear zibera zierba zierab ziebra ziebar
zieabr ziearb zbaire zbaier zbarie zbarei zbaeri zbaeir zbiare zbiaer zbirae
zbirea zbiera zbiear zbriae zbriea zbraie zbraei zbreai zbreia zbeira zbeiar
zberia zberai zbeari zbeair zeaibr zeairb zeabir zeabri zearbi zearib zeiabr
zeiarb zeibar zeibra zeirba zeirab zebiar zebira zebair zebari zebrai zebria
zeriba zeriab zerbia zerbai zerabi zeraib eraizb eraibz erazib erazbi erabzi
erabiz eriazb eriabz erizab erizba eribza eribaz erziab erziba erzaib erzabi
erzbai erzbia erbiza erbiaz erbzia erbzai erbazi erbaiz earizb earibz earzib
earzbi earbzi earbiz eairzb eairbz eaizrb eaizbr eaibzr eaibrz eazirb eazibr
eazrib eazrbi eazbri eazbir eabizr eabirz eabzir eabzri eabrzi eabriz eiarzb
eiarbz eiazrb eiazbr eiabzr eiabrz eirazb eirabz eirzab eirzba eirbza eirbaz
eizrab eizrba eizarb eizabr eizbar eizbra eibrza eibraz eibzra eibzar eibazr
eibarz ezairb ezaibr ezarib ezarbi ezabri ezabir eziarb eziabr ezirab ezirba
ezibra ezibar ezriab ezriba ezraib ezrabi ezrbai ezrbia ezbira ezbiar ezbria
ezbrai ezbari ezbair ebaizr ebairz ebazir ebazri ebarzi ebariz ebiazr ebiarz
ebizar ebizra ebirza ebiraz ebziar ebzira ebzair ebzari ebzrai ebzria ebriza
ebriaz ebrzia ebrzai ebrazi ebraiz

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History of cryptography
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