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.
Trigram Frequency in Turkish Language
The frequeny of most common letter trigrams in Turkish are illustrated below [2]
lar 0.00816 rin 0.00292 rın 0.00247 lan 0.00208 bir 0.00702 den 0.00288 ınd 0.00243 ığı 0.00208 ler 0.00622 ama 0.00282 eni 0.00238 adı 0.00203 eri 0.00529 nde 0.00281 ada 0.00236 sın 0.00201 arı 0.00515 edi 0.00270 ile 0.00230 sin 0.00197 yor 0.00422 anı 0.00267 ind 0.00225 esi 0.00194 ara 0.00359 ası 0.00258 ala 0.00223 yle 0.00194 nda 0.00350 dan 0.00256 nın 0.00214 ken 0.00193 ini 0.00336 nla 0.00255 anl 0.00213 rdu 0.00192 ını 0.00311 aya 0.00255 kar 0.00209 ele 0.00190
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
- ↑ Sefik Ilkin Serengil. Attacking Turkish Texts Encrypted by Homophonic Cipher. MSc thesis, Galatasaray University, 2011.
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