Trigram
- A trigram may also refer to Ba gua, a philosophical concept in ancient China. It may also refer to a three-letter acronym.
Trigrams are a special case of the n-gram, where n is 3. They are often used in natural language processing for doing statistical analysis of texts.
Frequency
A typical cryptanalytic frequency analysis finds that the 16 most common character-level trigrams in English are:[1]
| Rank | Trigram |
|---|---|
| 1 | the |
| 2 | and |
| 3 | tha |
| 4 | ent |
| 5 | ing |
| 6 | ion |
| 7 | tio |
| 8 | for |
| 9 | nde |
| 10 | has |
| 11 | nce |
| 12 | edt |
| 13 | tis |
| 14 | oft |
| 15 | sth |
| 16 | men |
Because encrypted messages sent by telegraph often omit punctuation and spaces, cryptographic frequency analysis of such messages includes trigrams that straddle word boundaries. This causes trigrams such as "edt" to occur frequently, even though it may never occur in any one word of those messages.
Examples
The sentence "the quick red fox jumps over the lazy brown dog" has the following word level trigrams:
the quick red quick red fox red fox jumps fox jumps over jumps over the over the lazy the lazy brown lazy brown dog
And the word-level trigram "the quick red" has the following character-level trigrams (where an underscore "_" marks a space):
the he_ e_q _qu qui uic ick ck_ k_r _re red
References
- ↑ Lewand, Robert (2000). Cryptological Mathematics. The Mathematical Association of America. p. 36. ISBN 978-0-88385-719-9. Table also available from pages.central.edu