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Index of Coincidence

Tool to compute coincidence index. Index of Coincidence is a cryptanalysis technique studying the probability of finding repeating letters in an encrypted text. A text in English language has a coincidence index of 0.0667.

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Index of Coincidence -

Tag(s) : Cryptanalysis

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# Index of Coincidence

## Cryptanalysis using Index of Coincidence

Tool to compute coincidence index. Index of Coincidence is a cryptanalysis technique studying the probability of finding repeating letters in an encrypted text. A text in English language has a coincidence index of 0.0667.

### How to use Index of Coincidence?

For a given ciphered message, the value for the index of coincidence allows to filter the list of ciphering methods to use. It is one of the first cryptanalysis technique.

If the Index of coincidence is high (close to $$0.070$$), i.e. similar to plain text, then the message has probably been crypted using a monoalphabetic substitution (a letter can be replaced by only one other).

If the Index of coincidence is low (close to $$0.0385$$), i.e. similar to a random text, then the message has probably been crypted using a polyalphabetic cipher (a letter can be replaced by multiple other ones).

The more the coincidence count is low, the more alphabets have been used.

Example: Vigenere cipher with a key of length 4 to 8 letters have an IC of about $$0.045 \pm 0.01$$

### How to calculate a coincidence index?

Index of coincidence uses the formula:

$$IC = \sum_{i=A}^{i=Z} \frac{n_{i}(n_{i}-1)}{N(N-1)}$$

with $$n_i$$ the number of occurrences of the letter $$i$$ in the text and $$N$$ the total number of letters.

### What are values of IC among languages?

For an non encrypted texte.

 English French 0.0667 0.0778 0.0762 0.077 0.0738 0.0529

### What is a random text?

A text where each letter has the same probability of appearance than another, IC is then of $$1/N$$ (where $$N$$ is the number of letters in the alphabet)

Example: $$IC = 0.0385$$ for $$N=26$$