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.

Index of Coincidence - dCode

Tag(s) : Cryptanalysis

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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.

The **coincidence index** is an indicator used in cryptanalysis which makes it possible to evaluate the global distribution of letters in encrypted message for a given alphabet.

**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.

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 transposition cipher (letters were shuffled) or 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 \( 0.045 \pm 0.05 \)

For an non encrypted text, coincidence indexes are

English | 0.0667 | French | 0.0778 |
---|---|---|---|

German | 0.0762 | Spanish | 0.0770 |

Italian | 0.0738 | Russian | 0.0529 |

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 \( N=26 \)

Examples of codes in programming languages `// Python`

def ic(self):

num = 0.0

den = 0.0

for val in self.count.values():

i = val

num += i * (i - 1)

den += i

if (den == 0.0):

return 0.0

else:

return num / ( den * (den - 1))

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