Variance of the Index of Coincidence
 From: "r.e.s." <r.s@xxxxxxxxxxxxxxxx>
 Date: Thu, 04 Jan 2007 02:40:59 GMT
This concerns Friedman's Index of Coincidence (IC) in the
form (c/(N(N1))) sum{n_i(n_i  1), i = 1..c), as at
http://en.wikipedia.org/wiki/Index_of_coincidence
and in LANAKI at
http://www.und.nodak.edu/org/crypto/crypto/
lanaki.crypt.class/docs/misc/indexofcoincidencenote
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.
.
 FollowUps:
 Re: Variance of the Index of Coincidence
 From: Douglas A. Gwyn
 Re: Variance of the Index of Coincidence
 Prev by Date: Re: Encryption key longer than text to encrypt
 Next by Date: Re: Encryption key longer than text to encrypt
 Previous by thread: Re: Number theoretic functions
 Next by thread: Re: Variance of the Index of Coincidence
 Index(es):
Relevant Pages
