Vigenère Cipher with Cryptanalysis

What Is the Vigenere Cipher

The Vigenere cipher is a polyalphabetic substitution cipher that uses a keyword to encrypt text with multiple different Caesar cipher shifts. Invented by Giovan Battista Bellaso in 1553 and later misattributed to Blaise de Vigenere, it was considered unbreakable for over 300 years — earning it the nickname "le chiffre indechiffrable" (the indecipherable cipher).

The Vigenere cipher represents a critical evolution in cryptographic history. By using multiple substitution alphabets instead of one, it defeats simple frequency analysis — the technique that trivially breaks Caesar and monoalphabetic substitution ciphers. Understanding the Vigenere cipher and how it was eventually broken teaches essential concepts about polyalphabetic encryption, key length analysis, and the ongoing arms race between codemakers and codebreakers.

How the Vigenere Cipher Works

Encryption uses a keyword that is repeated to match the length of the plaintext. Each keyword letter determines the Caesar shift for the corresponding plaintext letter:

Example with keyword "KEY":

Position	1	2	3	4	5	6	7	8	9
Plaintext	A	T	T	A	C	K	A	T	D
Keyword	K	E	Y	K	E	Y	K	E	Y
Shift	10	4	24	10	4	24	10	4	24
Ciphertext	K	X	R	K	G	I	K	X	B

Each letter is encrypted with a different shift, so the same plaintext letter (A) can encrypt to different ciphertext letters (K, K, K in this case because the keyword position happens to align — but with longer keywords, repetition decreases).

Breaking the Vigenere Cipher

The Vigenere cipher was broken in the 19th century using two techniques:

Kasiski Examination (1863)

Friedrich Kasiski observed that repeated sequences in ciphertext reveal the key length. If "THE" is encrypted at positions that align with the same keyword letters, the same ciphertext trigram appears. The distances between repetitions are multiples of the key length.

Index of Coincidence (1920)

William Friedman developed a statistical method that measures the probability that two randomly chosen letters from the ciphertext are the same. Natural language has a higher index of coincidence (~0.067 for English) than random text (~0.038). By testing different key lengths and measuring the IC of resulting groups, the correct key length produces groups with language-like IC values.

Common Use Cases

• Cryptography education: Learn the concept of polyalphabetic substitution and why it was a major advance over monoalphabetic ciphers
• Cryptanalysis practice: Practice Kasiski examination and index of coincidence analysis — fundamental statistical cryptanalysis techniques
• Historical cipher study: Understand the cipher that was considered unbreakable for three centuries and how it was eventually defeated
• CTF competitions: Vigenere ciphers appear frequently in Capture The Flag cybersecurity competitions
• Understanding modern encryption concepts: The principle of using a key to vary encryption across a message underlies modern stream ciphers and block cipher modes

Security Considerations

The Vigenere cipher provides no security for modern use. Its vulnerabilities include:

1. Key length reveals structure — Once the key length is determined (via Kasiski or IC), the cipher reduces to multiple independent Caesar ciphers, each trivially broken by frequency analysis
2. Key reuse is catastrophic — Using the same key for multiple messages provides exponentially more material for cryptanalysis
3. Short keys are especially weak — A 3-letter key provides only 17,576 possible keys, easily brute-forced even by hand
4. No diffusion — Each plaintext letter is encrypted independently, preserving statistical patterns within each key-position group