Twelve ordinary words do not look like much protection. In fact, it would be absurd to try guessing them. This guide, part of our section on what a recovery phrase is, walks through the numbers.
The numbers
Each word is one of 2,048. So the number of possible lists is enormous. Because of the checksum, only 1 in 16 of 12-word lists is valid, which leaves 2^128 real phrases.
| Phrase | Possible phrases | Written out |
|---|---|---|
| 12 words | 2^128 | About 340 undecillion |
| 24 words | 2^256 | About 116 quattuorvigintillion |
How long would guessing take?
Imagine that every person on Earth, about 8 billion people, had a computer checking a billion phrases each second. That is 8 quintillion checks a second. Going through all 12-word phrases would still take around a trillion years. The universe is about 14 billion years old.
Checking phrases is also slowed down by the 2,048 hashing rounds in the standard.
But the attacker only needs one match
Yes, and it makes no difference. There are far too few real wallets, compared with possible phrases, for chance to matter. Random collisions are not a practical risk.
When guessing does work
| Situation | Why it fails |
|---|---|
| You chose the words yourself | Humans are predictable |
| Words from a song or book | Attackers try these |
| A flawed wallet or generator | Limited real randomness |
| Only a few words are missing | The search is small |
| All the words known, in the wrong order | A computer can try the orderings |
This last one surprises people. Hiding your phrase by shuffling it gives little protection: 12 known words have about 479 million possible orders, and a computer can test them quickly. See splitting a phrase and hiding a phrase.
How phrases really get stolen
- Typing the words into a fake wallet site.
- Handing them to fake support.
- Photos and cloud backups. See storing a phrase digitally.
- Malware and screen recorders.
- Someone finding the paper.
- Pre-generated phrases from a seller.
None of those involve guessing. Focus your effort there, starting with common scams.