Cryptology Bigram Scores

a7Hzq .#5r< kÜ\as TâÆK$ ûj(Ö2 ñw%h: Úk{4R f~`z8 ¤˜Æ+Ô „&¢Dø

Theoretical Values for Random Bigrams

From the known probabilities of the single letters we can calculate the probabilities of randomly combined bigrams and then the expected conditional bigram-weights. This is done in the mathematical version of this section.

From this we deduce: When we independently select two letters with the probabilities given by the language, form a bigram by them, and take its conditional bigram weight, the expected values are:

These are also the values we expect when testing two columns of a columnar cipher that don't fit together.

Theoretical Values for True Bigrams

For true bigrams we do the same, but select the second letter according to the conditional bigram probability given the first letter. (This comes down to choosing the complete bigram at once according to the bigram probabilities of the language, see the mathematical part of this section.) We deduce the expected values for the bigram weights:

These are also the values we expect when testing two columns of a columnar cipher that fit together.

Empirical Values for English, German, and French