Breaking the Vigenère Cipher
Cryptanalysis techniques for the Vigenère cipher — Kasiski examination, index of coincidence, and frequency analysis.
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Tags: Vigenère cipher cryptanalysis, break Vigenere cipher, Kasiski test cipher
Breaking the Vigenère Cipher Part of our complete guide to this topic — see the full series. Called le chiffre indéchiffrable for 300 years, the Vigenère cipher was cracked by two people working independently using the same insight: the repeating keyword creates statistical regularities that reveal both the key length and the key itself. --- All the tools discussed here are available for free at theproductguy.in — client-side, no sign-up required. The Three-Step Attack Detect key length — Kasiski test or index of coincidence Recover each key letter — frequency analysis on each column Decrypt — Vigenère decode with the recovered key --- Step 1: Detecting Key Length with the Kasiski Test Friedrich Kasiski published this technique in 1863 (though Charles Babbage likely discovered it earlier…
Frequently Asked Questions
How do I break a Vigenère cipher?
Breaking Vigenère requires two steps. First, determine the key length using the Kasiski test (look for repeated sequences and find the GCD of distances between them) or the index of coincidence (try different assumed key lengths and measure how English-like each column looks). Second, once the key length is known, each column of the ciphertext is a Caesar cipher — apply frequency analysis to recover each key letter.
What is the Kasiski test?
The Kasiski test finds the key length by locating 3-character (or longer) sequences that appear more than once in the ciphertext. Repeated sequences likely occur when the same plaintext fragment aligns with the same part of the keyword. The distances between repeated occurrences are multiples of the key length. Computing the GCD of all such distances gives the most likely key length.
How does index of coincidence help crack a cipher?
The index of coincidence (IC) measures letter frequency inequality. English text has IC ≈ 0.065 because some letters (E, T, A) are far more common than others. A random sequence has IC ≈ 0.038. If you split a Vigenère ciphertext into L columns (one per key letter) and each column has IC ≈ 0.065, then L is the correct key length — the columns are Caesar ciphers over English text.
What key length reveals the most about a Vigenère cipher?
Shorter key lengths are easier to break because each Caesar sub-cipher has more letters to analyze. For frequency analysis to be reliable, each column needs at least 20–30 characters. A key length of 3 against a 100-character ciphertext gives ~33 characters per column — enough for decent frequency analysis. A key length of 10 gives only ~10 characters — much harder to analyze reliably.
What tools automate Vigenère decryption?
Several tools automate Vigenère cryptanalysis: CyberChef has a Vigenère decode recipe and a 'find key length' step. dcode.fr's Vigenère solver attempts automatic decryption. The Python cryptography library quipqiup can solve general substitution ciphers. For CTF purposes, writing a custom Python script using the Kasiski test and frequency analysis is often faster and more educational.
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