Vigenere cipher is a poly-alphabetic substitution system, created by Blaise de Vigenère. Using generally a key and a table, it allow replacing a letter by another one, which is not always the same.

Vigenere Cipher - dCode

Tag(s) : Cryptography,Poly-Alphabetic Cipher

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Vigenere cipher is a poly-alphabetic substitution system, created by Blaise de Vigenère. Using generally a key and a table, it allow replacing a letter by another one, which is not always the same.

Encryption with Vigenere uses a key made of letters (and an alphabet). There are several ways to achieve the ciphering manually :

**Vigenere Ciphering by adding letters**

In order to cipher a text, take the first letter of the message and the first letter of the key, add their value (letters have a value depending on their rank in the alphabet, starting with 0). The result of the addition modulo 26 (26=the number of letter in the alphabet) gives the rank of the ciphered letter.

Let the key be KEY and the alphabet ABCDEFGHIJKLMNOPQRSTUVWXYZ. One wants to crypt DCODE.

One take the first letters of the plaintext D (value = 3) and of the key K (value = 10) and add them (3+10=13), the letter with value 13 is N.

One continue with the next letter of the plaintext, and the next letter of the key. When arrived at the end of the key, go back to the first letter of the key.

DCODE

KEYKE

NGMNI is the ciphertext.

**Vigenere Cipher using a table**

In order to encrypt using Vigenere method, the easiest way is to have a double enrty grid, here is one (when the alphabet is ABCDEFGHIJKLMNOPQRSTUVWXYZ):

Let the key be KEY, and the plaintext DCODE.

One locates the first letter of the plaintext message in the first line of the table and the first letter of the key on the left column. The cipher letter is at the intersection.

One locates the letter D on the first row, and the letter K on the first column, the ciphered letter is the intersection cell N.

One continue with the next letter of the plaintext, and the next letter of the key. When arrived at the end of the key, go back to the first letter of the key.

NGMNI is the ciphertext.

Decryption requires a key (and an alphabet). As for encryption, two ways are possible.

**Decryption of Vigenere by substracting letters**

Let the key be KEY and the alphabet ABCDEFGHIJKLMNOPQRSTUVWXYZ. One chant to decrypt NGMNI.

To decrypt, take the first letter of the ciphertext and the first letter of the key, and substract their value (letters have a value equals to their position in the alphabet starting from 0). If the result is negative, add 26 (26=the number of letters in the alphabet), the result gives the rank of the plain letter.

One takes the first letters of the ciphertext N (value = 13) and the key K (value = 10) and substract them (13-10=3), the letter of value 3 is D.

One continues with the next letters of the message and the next letters of the key, when arrived at the end of the key, go back the the first key of the key.

NGMNI

KEYKE

DCODE is the plain text.

**Decryption of Vigenere with a table**

To decrypt Vigenere with a double entry table, one uses the folowing grid (case alphabet is ABCDEFGHIJKLMNOPQRSTUVWXYZ):

Let the key be KEY. One wants to decrypt NGMNI.

One locates the first letter of the key in the left column, and locates on the row the first letter of the ciphered message. Then go up in the column to read the first letter, it is the corresponding plain letter.

Locates the letter K on the first column, and on the row of it, find the cell of the letter N, the name of its column is D, it is the first letter of the plain message.

One continues with the next letters of the message and the next letters of the key, when arrived at the end of the key, go back the the first key of the key.

The original plain text is DCODE.

The ciphered message has an indice of coincidence between 0.4 and 0.5, lower when the key is long.

Most common techniques uses statistical methods in order to find the key length, then a simple frequency analysis allow to find the key.

**Kasiski test**

Kasiski test consists in finding repeating sequences of letters in the ciphered text.

ABC appears three times in the message ABCXYZABCKLMNOPQRSABC

The fact that repeating letters can be found means two things : either a same sequence of letter of the plaintext is crypted with the same part of the key, either different sequences letters are crypted with different parts of the key but they ends with the same crypted letters. this second possibility is poorly probable.

By analysing the gaps between two identical redunding sequences, one can find multiples of the key length. By analysing each gaps in term of number of letters, and by calculating divisors, one can deduct with a high probability the size of the key.

Positions of ABC are 0, 6 et 18, gaps are 6, 12 and 18 letters length, their most common divisors are 2, 3 and 6, so the key has an high probability to be 2, 3 or 6 letters long.

**Index of coincidence test**

The test using the indice of coincidence consists in taking one letter out of n in the ciphertext and calculate the IC. The higher it is, the higher the probability n is the key size.

Indeed, taking one letter every n where n is the key-length, ends with a sequence of letters that are always crypted using the same shift. The index of coincidence is then equals to the one of the plain text.

To get the key back, one has to decrypt the ciphered text with the plaintext as key. The key will appear repeated.

Vernam code is a particular case of Vigenere when the key-length is equal to the text-length. In this case, impossible to use any statistical method, it is even impossible to break if the key is made of random characters. However if the key has a meaning, a known plaintext attack can help.

Saint-Cyr slide is a tool that simplifies encryption and decryption with Vigenere. Constituted of two alphabet, sliding one on the other.

To crypt a letter, one has to slide the A above the letter of the key, the letter of the ciphertext correspond to the one accross from the other alphabet.

Blaise de Vigenère (1523-1596) was a French diplomate, he probably invented this cipher.

Caesar cipher is in fact a Vigenere cipher with a 1-letter long key. Vigenere code uses longer keys that allows the letters to be crypted in multiple ways. The frequencey analysis is no more anough to break a code.

1586

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- How to encrypt using Vigenere cipher?
- How to decrypt Vigenere cipher?
- How to recognize Vigenere ciphered text?
- How to decipher Vigenere without knowing the key?
- how to find the key when having both cipher and plaintext?
- What are the variants of the Vigenere cipher?
- What is the Vernam Cipher ?
- What is a Saint-Cyr slide ?
- Why the name Vigenere ?
- What are the advantages of the Vigenere cipher versur Caesar Cipher ?
- When Vigenere have been invented ?

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