## 3.5 PRUNING FROM THE TABLE OF ISOMORPHS

We identify the repeated trials of the experiment *∈* with the generation of plaintext with letters in the generic alphabet by the *iid* language model with probabilities *π*(*i*) = Pr{*X* = *i*} for 0 ≤ *i* < *m*.

To test if the ciphertext *r*-gram *v* is an isomorph of the plaintext *u*, the ciphertext letter counts {*N*_{vi}} are compared to the plaintext letter probabilities using the *χ*^{2}-statistic:

Table 3.5 lists the count of 1-grams {*N*_{i}} and their frequencies *f*(*i*) = *N*_{i}/*n* in the ciphertext cipherEx3.1. Table 3.6 gives the probabilities {*π*(*i*)} of 1-grams derived from a large sample English language text. The plan is to now use the *χ*^{2}-test to associate the seven high-frequency ciphertext letters in Table 3.5:

**TABLE 3.5 Letter Counts and Frequencies in cipherEx3.1**

**TABLE 3.6 1-Gram English-Language Plaintext Probabilities**

with seven of the nine plaintext letters of highest probability from Table 3.6:

A correspondence between t, z, o, h and some subset of E, T, A, O, N, ...