Vigenere Cipher

The Vigenère cipher is a polyalphabetic encryption algorithm invented by the French cryptologist Blaise de Vigenère in the 16th century. It is based on a shift cipher to which is added the use of a keyword that changes the shift at each step.

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.

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.

Vigenere Cipher using a table

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

Locate the first letter of the plaintext message in the first row of the table and the first letter of the key on the left column. The cipher letter is at the intersection.

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.

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

Decryption of Vigenere by subtracting letters

To decrypt, take the first letter of the ciphertext and the first letter of the key, and subtract their value (letters have a value equal 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.

Continue 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.

Decryption of Vigenere with a table

To decrypt Vigenere with a double entry square table, use the following grid (case alphabet is ABCDEFGHIJKLMNOPQRSTUVWXYZ):

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.

Continue 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.

Following a Vigenere encryption, the message has a coincidence index which decreases between 0.05 and 0.04 depending on the length of the key, it decreases towards 0.04 the longer the key is.

Most common keyless techniques use statistical methods in order to find the key length, then a simple frequency analysis allows to find the key.

Kasiski test

Kasiski test consists in finding repeating sequences of letters in the ciphertext.

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

Index of coincidence test

The test using the index 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.

When encrypting, the key is added to the plain text to get encrypted text. So, from the encrypted text, subtract the plain text to get the key.

Multiple variants exists, as Beaufort Cipher, Vigenere Autoclave, Vernam Cipher

In order to make Vigenere resistant to attacks, the coder must determine the most secure encryption key possible. All attacks are based on detections of key repetitions, so to avoid this pitfall, it is necessary to use a key as long as possible so that it does not repeat, or even longer than the size of the text to encrypt. This is the case of the Vernam cipher.

The variant by running key uses a key length at least equal to that of the text. This technique makes it possible to secure Vigénère's cipher as Kasiski's attack is no longer valid.

To get a long enough key, it is common to use a long book or other message. The use of this kind of key then opens the possibility of other attacks, by probable word and / or by analysis of the frequencies of the characters if the message is long enough.

In the particular case where the entire key is made up of random characters (see Vernam one time pad), then the message becomes completely unbreakable by any method of cryptanalysis (unconditional security).

By using a disordered alphabet, or with a key that modifies the traditional Latin alphabet, then the majority of the tools of cryptanalysis become useless and the Vigenère cipher is then resistant to classical attacks.

Saint-Cyr slide is a rule-shaped instrument, a tool that simplifies manual encryption and decryption of a message encrypted with Vigenere. Its fixed part consists of the alphabet, and its sliding mobile part is a double alphabet.

To encrypt a letter, move the slider so that the A of the fixed part matches the letter of the key. Then look at the letter of the mobile part directly below the letter of the plain message written on the fixed part.

Blaise de Vigenère (1523-1596) was a French diplomat.

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 frequency analysis is no more enough to break a code.

Blaise de Vigenère wrote a treatise describing this cipher in 1586. A full reedition is available here (affiliate link) However another treatise from 1553 by Giovan Battista Bellaso already described a very similar system.