Cancel a substitution
Frequency analysis
The method that breaks all simple substitution ciphers was described in the 9th century by the Arab scholar Al-Kindi. It is disarmingly simple.
The principle
- Count how many times each letter appears in the ciphertext.
- Compare this frequency distribution with that of the target language.
- Establish the most likely correspondences, then refine them.
French frequencies
| Letter | Frequency |
|---|---|
| E | ~15 % |
| A | ~8% |
| S | ~8% |
| I | ~7% |
| N | ~7% |
| T | ~7% |
E dominates by a wide margin: in a reasonably long French text, it is almost always the most frequent letter.
In practice
In an encrypted message of a few hundred letters, the most frequent letter is almost certainly E. We replace it, and partial words emerge:
_E _E___GE E_T _L_IR
From there, we can gradually work out LE MESSAGE EST CLAIR. Each correct guess reveals further possibilities: the analysis speeds up of its own accord.
A realistic limitation
The method requires sufficient data. With just three words, the frequencies are meaningless and the attack fails. This is why very short messages hold out — not because of the strength of the cipher, but due to a lack of usable statistics.
Key takeaway: it is not the key size that provides protection, but the absence of structure in the ciphertext.