What is frequency analysis, and how does it break the Caesar cipher?

Frequency analysis exploits the fact that in any language, certain letters appear more often — so the most frequent letter in ciphertext likely corresponds to the most common letter in the language.

How it works against Caesar:

1. Count the frequency of each letter in the ciphertext
2. The most frequent ciphertext letter probably maps to the most common plaintext letter (e.g., 'E' in English, 'E' in German)
3. The difference between these two letters reveals the shift key

Example: If 'H' is the most frequent letter in the ciphertext and 'E' is the most common letter in the language, the shift is $H - E = 3$.

Why this is devastating for monoalphabetic ciphers:

• Every instance of 'E' always maps to the same ciphertext letter
• With enough ciphertext, the frequency distribution of the original language shines through
• This works not just for Caesar but for any monoalphabetic substitution cipher

Why it fails against Vigenère: In a polyalphabetic cipher, 'E' maps to different ciphertext letters depending on position, which flattens the frequency distribution and hides the pattern.