Vigenère Cipher Explained: The Indecipherable Cipher?

The Vigenère Cipher is one of the most famous polyalphabetic substitution ciphers in history. Unlike the simple Caesar Cipher, it uses a keyword and multiple substitution alphabets, significantly increasing the difficulty of cracking it. For centuries, it was known as le chiffre indéchiffrable (the indecipherable cipher).

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1. What is the Vigenère Cipher?

The Vigenère Cipher is a method of encrypting alphabetic text by using a series of interwoven Caesar ciphers, based on the letters of a keyword. It belongs to the category of polyalphabetic ciphers.

In a Caesar cipher, every letter is shifted by the same amount (e.g., all letters shift by 3). In a Vigenère cipher, the shift amount changes for each letter of the plaintext, determined by a repeating keyword.

1.1 Key Features

Feature	Description
Type	Polyalphabetic Substitution Cipher
Core Tool	Vigenère Square (Tabula Recta)
Security	Stronger than Caesar, but broken in the 19th century
Key	Requires a keyword (passphrase)

2. History

Although named after Blaise de Vigenère, he was not the sole inventor.

• 1553: Giovan Battista Bellaso described an early polyalphabetic cipher based on a keyword.
• 1586: Blaise de Vigenère invented a stronger autokey cipher based on previous works.
• 19th Century: Due to historical misattribution, this polyalphabetic cipher became associated with Vigenère and was widely considered unbreakable until Friedrich Kasiski published a general method for deciphering it in 1863.

3. How It Works: The Vigenère Square

The core of the algorithm is the Vigenère Square (or Vigenère Table/Tabula Recta). It consists of the alphabet written out 26 times in different rows, each alphabet shifted cyclically to the left compared to the previous row.

3.1 The Table

  | A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
--+----------------------------------------------------
A | A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
B | B C D E F G H I J K L M N O P Q R S T U V W X Y Z A
C | C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
D | D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
...
Z | Z A B C D E F G H I J K L M N O P Q R S T U V W X Y

3.2 Encryption Process

Let’s encrypt the following:

• Plaintext: ATTACKATDAWN
• Keyword: LEMON

Step 1: Repeat the Keyword Repeat the keyword until it matches the length of the plaintext:

Plaintext: A T T A C K A T D A W N
Keyword:   L E M O N L E M O N L E

Step 2: Lookup and Encrypt For each letter, find the column corresponding to the plaintext letter and the row corresponding to the keyword letter. The intersection is the ciphertext letter.

1. 1st Letter: Plaintext A (Column) + Keyword L (Row) -> Intersection L
2. 2nd Letter: Plaintext T (Column) + Keyword E (Row) -> Intersection X
3. 3rd Letter: Plaintext T (Column) + Keyword M (Row) -> Intersection F

The result:

Plaintext:  A T T A C K A T D A W N
Keyword:    L E M O N L E M O N L E
Ciphertext: L X F O P V E F R N H R

3.3 Decryption Process

Decryption is the reverse of encryption.

1. Find the row corresponding to the keyword letter.
2. Scan across that row to find the ciphertext letter.
3. The column header of that letter is the plaintext.

Example for the first letter L with keyword L:

• Go to row L.
• Find L in that row.
• Look up to the column header -> A.

4. Breaking the Cipher

The Vigenère cipher is vulnerable because the keyword repeats.

4.1 Kasiski Examination

Published by Friedrich Kasiski in 1863, this method relies on searching for repeated strings of characters in the ciphertext. If a plaintext pattern repeats at a distance that is a multiple of the keyword length, the ciphertext will also repeat.

By analyzing the distances between repeated segments, cryptanalysts can determine the length of the keyword.

4.2 Friedman Test

William Friedman introduced the Index of Coincidence (IC). This statistical test allows cryptanalysts to estimate the keyword length by analyzing the frequency distribution of letters in the ciphertext, without needing repeated patterns.

Once the key length is known, the ciphertext can be broken down into multiple Caesar cipher columns, which can be solved individually using frequency analysis.

5. Conclusion

The Vigenère Cipher represents a significant milestone in cryptography. It demonstrates how simple substitution rules can be combined to create a complex system. While no longer secure against modern computing, understanding it is essential for grasping the evolution of encryption methods.

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