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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 [1]:

IC=i=1cfi(fi1)n(n1)\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.

See also



  1. Friedman, William F. (1922). "The index of coincidence and its applications in cryptography." Department of Ciphers. Publ 22. Geneva, Illinois, USA: Riverbank Laboratories. Download