Cryptology The Kappa Distribution for Random Texts

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Finally the same procedure for random texts. To this end we generate a 400000 character text by the built-in (pseudo-) random generator of Perl. Since the simulation might depend on the quality of the random generator we enhance the random text in the following way: We generate 8132 random letters by the cryptographically strong BBS-generator and use them as key for a Belaso encryption of our random text, repeating the key several times. In spite of this periodicity we may assume that the result gives a 400000 character random text of good quality.

Here is the text. This provides us with 2000 text pairs of length 100. The results are in the spreadsheet and in following figure and table.

Note that the values fit the theoretical values almost perfectly.

To get coincidence indices divide x-values by 100.

Distribution of κ for 2000 English text pairs of 100 letters

Minimum:	0.00
Median:	0.04		Mean value:	0.040
Maximum:	0.12		Standard dev:	0.020
1st quartile:	0.03		5% quantile:	0.010
3rd quartile:	0.05		95% quantile:	0.070