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Monero seed phrases use 25 words, while Trezor Model T seed phrases have only 12 words. If you generate a Monero wallet using the Trezor, does that mean you're not getting a sufficiently strong private key?

(Monero draws its wordlist from 1626 possibilities instead of Trezor's 2048, but Monero's seed still has 10^40 times the number of combinations as Trezor's).

jtgrassie
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puzzler
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2 Answers2

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A Monero private key is any 256 bit number mod l and the seed phrase is deterministically derived from this private key. 24 words (the 25th is a checksum), from the dictionary in Monero, gives enough bits (257) to encode/decode from the 253 bit random private key.

As noted, the Trezor Model T uses a 12 word phrase with a dictionary which is only good enough for 128 bits (plus a checksum). This essentially limits the possible range of private keys.

Longer bit ranges are of course more desirable.

It's worth pointing out that both Trezor devices can be initialized with longer phrases [source]:

Note For advanced users: It is possible to generate 12, 18 or 24-word seeds on both Trezor devices. If you want to generate recovery seed with different length than default (e.g., 24 words on Trezor Model T), please see initialize device with trezorctl command.

Generating 24 words will give enough range to cover all possible Monero private keys.

jtgrassie
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Trezor's 12 seed word is still insanely secure. With 5,444,517,870,735,015,415,413,993,718,908,291,383,296 possible combinations, nobody is ever going to try and bruteforce a private key.

(Even if they wanted to, they'd have to sync it to the blockchain. Yuck!)

Dr-Bracket
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