Search for a tool
Affine Cipher

Tool to decrypt/encrypt with Affine automatically. The Affine cipher uses a encrypting function with additions and multiplication (as the mathematical affine function) which convert a letter (of value x in a 26 letters alphabet) into another letter with value (ax + b) modulo 26.

Results

Affine Cipher -

Tag(s) : Cryptography,Substitution Cipher

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!


Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Affine Cipher tool. Thank you.

This page is using the new English version of dCode, please make comments !

Affine Cipher

Sponsored ads

Affine Decoder








Also on dCode: Hill CipherCaesar Cipher


Affine Encoder







Also on dCode: Hill CipherCaesar Cipher


Tool to decrypt/encrypt with Affine automatically. The Affine cipher uses a encrypting function with additions and multiplication (as the mathematical affine function) which convert a letter (of value x in a 26 letters alphabet) into another letter with value (ax + b) modulo 26.

Answers to Questions

How to encrypt using Affine cipher

Encryption uses a classic alphabet, and two integers, called coefficients or keys A and B.

Let the alphabet be ABCDEFGHIJKLMNOPQRSTUVWXYZ and keys A=5, B=3. We want to code DCODE.

For each letter of the alphabet is associated to the value of its position in the alphabethref.

Beginning with 0, then A = 0, B = 1, Z = 25, but if one wants A = 1, ... Y = 25, Z = 0, then use ZABCDEFGHIJKLMNOPQRSTUVWXY.

For each letter (of value x) of the plain text, is associated a value y, resulting of the affine function y = A*x+B mod 26 (with 26 is the alphabet size)

For D (x=3), y = A*3+B = 5*3+3 = 18

For O (x=14), y = A*14+B = 5*14+3 = 73 = 21 mod 26

For each value y, corresponds a letter with the same position in the alphabethref, it is the ciphered letter.

For D (y=18), corresponds letter S (position 18).

For O (y=21), corresponds letter V (position 21).

The Affine cipher text is the replacement of the letters by the new ones.

DCODE becomes SNVSX

How to decrypt Affine cipher

Le decryption needs to know the 2 keys A and B and the alphabet.

Let the ciphered message be SNVSX and A=5, B=3 as keys

For each letter of the alphabet corresponds the value of its position in the alphabethref.

With the alphabet ABCDEFGHIJKLMNOPQRSTUVWXYZ, beginning with 0, A = 0, B = 1, Z = 25. There is also but A = 1, ... Y = 25 and Z = 0 with the alphabet ZABCDEFGHIJKLMNOPQRSTUVWXY.

For each letter (of value y) of the message, corresponds a value x, result of the inverse function x = A'*(y-B) mod 26 (with 26 is the alphabet size)

The value A' is an integer such as A*A' = 1 mod 26 (with 26 is the alphabet size). To find A', one has to calculate a modular inversehref.

A coefficient A' for A = 5 with an alphabet size of 26 is 21. Because 5 * 21 = 105 = 1 mod 26.

For S (y=18), x = A'*(18-B) = 21*(18-3) = 315 mod 26 = 3

For each value x, corresponds a letter with the same position in the alphabethref: the coded letter.

For S (x=3), corresponds the letter D (position 3).

The plain text is the replacement of all characters with calculated new letters.

The original plain text is DCODE.

How to recognize an Affine ciphered text?

The ciphered have an index of coincidencehref similar to the language of the plain text.

How to decipher Affine without coefficient?

One can crack Affine and find the coefficients by bruteforcing all possible A and B coefficients. Use the Brute-force attack option.

>If the alphabet is 26 characters long, then A coefficient has only 12 possible values, and B has 26 values, so there are only 312 test to try.

How to compute A' value?

You have to calculate the modular inversehref of A modulo the length of the alphabet.

How to compute B' value?

B' has the same value as B.

What are the A' values?

The value of A' depends on A but also on the alphabet's length, if it is a classic one, it is 26 characters long. The values of A' are then:

A = 1, A' = 1

A = 3, A' = 9

A = 5, A' = 21

A = 7, A' = 15

A = 9, A' = 3

A = 11, A' = 19

A = 15, A' = 7

A = 17, A' = 23

A = 19, A' = 11

A = 21, A' = 5

A = 23, A' = 17

A = 25, A' = 25

When Affine have been invented ?

No date of known author.

Why is there a constraint on the value of A?

The Bezout's theorem indicates that A' only exists if A and 26 (alphabet length) are coprimehref. This limits A values to 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 et 25 (if the alphabet is 26 characters long)

Can I use a key A not coprime with 26?

Yes, but an automatic decryption process becomes impossible, a single ciphered letter will have multiple plain letters possible.

Can I use a negative value for A?

Yes, but it exists a positive corresponding value, a value of A = -1 is equals to a value of A = 25 (because 25 = -1 mod 26).

Is there a limitation on B value?

No, B can take any value.

Ask a new question

Source code

dCode retains ownership of the source code of the script Affine Cipher. Except explicit open source licence (free / freeware), any algorithm, applet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any snippet or function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in PHP (or Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Affine Cipher script for offline use, for you, your company or association, see you on contact page !

Questions / Comments


Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Affine Cipher tool. Thank you.


Source : http://www.dcode.fr/affine-cipher
© 2016 dCode — The ultimate 'toolkit' website to solve every problem. dCode