Cryptanalyst’s Index of Coincidence

Index of coincidence measures how likely it is to draw two matching letters by choosing two random letters from a text.

Definition

Given a text of length nn using an alphabet consisting of cc letters and given the number of appearances fif_i for each letter ii, the Index of coincidence (IC) is defined by the sum:

IC=∑i=1cfi(fi−1)n(n−1)\text{IC} = \frac{\sum_{i=1}^cf_i(f_i-1)}{n(n-1)}

The normalized Index of coincidence can be obtained by multiplying the above IC\text{IC} by cc.

This article is a work in progress.

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