Variance of the Index of Coincidence

This concerns Friedman's Index of Coincidence (IC) in the
form (c/(N(N-1))) sum{n_i(n_i - 1), i = 1..c), as at
and in LANAKI at

Assuming the ciphertext alphabet has c letters that
occur (independently) with probabilities p_1,...,p_c,
the expected value of IC is c * sum(p_i^2, i=1..c).

I would like to know the formula for the variance of IC,
similarly as a function of c and p_1,...,p_c.


Relevant Pages

  • Re: Bayesian updating with multiple events.
    ... probabilities 2/5, etc. ... strings are equally likely. ... probabilities of the letters on cards 2 and 3. ... may not always be as informative as seeing the card ... ...
  • Re: A secure hand cipher?
    ... > Whenever a double letter occurs in the ciphertext, ... > For example, in your sample ciphertext, all double letters are ... > Progressing in this manner with a little known plaintext, ... the ciphertext alphabet can be approximated and eventually ...
  • Re: A secure hand cipher?
    ... >below that to spell out the ciphertext alphabet. ... >13th and 14th letters to divide the alphabet in half. ...