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 :

$$IC = \sum_{q=A}^{q=Z} \frac{n_q(n_q-1)}{n(n-1)}$$

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 :

Language	Index 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

CyberChef

https://www.dcode.fr/index-coincidencewww.dcode.fr