Index of coincidence

The Index of Coincidence (IOC) is a statistical measure used in cryptography to analyze the randomness of a set of symbols.

A higher IOC value indicates a less random distribution of letters in the text and can be an indicator that a substitution cipher has been used. By comparing the IOC of a ciphertext to the expected IOC of plaintext in the same language, an attacker can make inferences about the encryption method used and use this information to break the cipher.

How it works ?

To calculate an index of coincidence for a mono-alphabetic substitution, here is the equation :

IC=∑q=Aq=Znq(nq−1)n(n−1)IC = \sum_{q=A}^{q=Z} \frac{n_q(n_q-1)}{n(n-1)}

n is a total amount of letters within the text

n_A is the amount of A

n_B is the amount of B etc.

Note: This techniques only works if the provided text is large enough.

Index of coincidence Table

Here is the "standard" indexes of coincidence for theses languages :

LanguageIndex of coincidence

English

0,0667

Serbian

0,0643

Swedish

0,0644

Esperanto

0,0690

Greek

0,0691

Norvégien

0,0694

Norwegian

0,0707

Finnish

0,0737

Italian

0,0738

Portuguese

0,0745

Arab

0,0758

German

0,0762

Hebrew

0,0768

Spanish

0,0770

Japanese

0,0772

French

0,0778

Dutch

0,0798

malaysian

0,0852

Russian

0,0529

Resources

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