Cryptorium

History

The Vigenère Cipher is named after the French diplomat Blaise de Vigenère, who described it in the 16th century, although it was known and used earlier by various cryptographers. The cipher was often mistakenly attributed to Vigenère for a long time, which is why it is sometimes called the "Vigenère Square" or "Vigenère Table." The cipher became renowned for its complexity compared to simple substitution ciphers, offering a much higher level of security through its use of a keyword or phrase to vary the encryption method.

Working

The Vigenère Cipher is a method of encrypting alphabetic text by using a series of different Caesar ciphers based on the letters of a keyword. This makes it a polyalphabetic substitution cipher, as opposed to monoalphabetic ciphers like the Caesar Cipher.

Polyalphabetic Cipher: Instead of shifting by a single fixed amount (as in the Caesar Cipher), the Vigenère Cipher shifts by a different amount for each letter of the plaintext, based on a keyword.

Key Concepts

Alphabet: Typically, the standard English alphabet of 26 letters is used.

Keyword: The keyword is a sequence of letters that determines the shift for each letter in the plaintext. The length of the keyword is crucial as it affects the encryption's complexity.

Algorithm

Encryption

Key Definition: Choose a keyword. The keyword should be repeated or truncated to match the length of the plaintext.

Encryption Formula:

E(p_i) = (p_i + k_i) mod 26
                

Where:

• E(p_i) is the encrypted letter.
• p_i is the position of the plaintext letter.
• k_i is the position of the keyword letter.

Example:

Plaintext: HELLO

Keyword: KEY (repeated to match the length of the plaintext: KEYKE)

Encryption:

H (7) + K (10) = 17 -> R
E (4) + E (4) = 8 -> I
L (11) + Y (24) = 35 mod 26 = 9 -> J
L (11) + K (10) = 21 -> V
O (14) + E (4) = 18 -> S
                

Encrypted Text: RIJVS

Decryption

Key Definition: Use the same keyword as in encryption.

Decryption Formula:

D(c_i) = (c_i - k_i + 26) mod 26
                

Where:

• D(c_i) is the decrypted letter.
• c_i is the position of the ciphertext letter.
• k_i is the position of the keyword letter.

Example:

Ciphertext: RIJVS

Keyword: KEY (repeated to match the length of the ciphertext: KEYKE)

Decryption:

R (17) - K (10) = 7 -> H
I (8) - E (4) = 4 -> E
J (9) - Y (24) = -15 + 26 = 11 -> L
V (21) - K (10) = 11 -> L
S (18) - E (4) = 14 -> O
                

Decrypted Text: HELLO

Summary

The Vigenère Cipher enhances the Caesar Cipher by employing a keyword to shift letters in a manner that is less predictable. This polyalphabetic approach makes it more secure than monoalphabetic ciphers, though it can still be vulnerable to frequency analysis if not used properly.