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I'm curious on how long this 25th word / passphrase should be to provide roughly the same level of security as the seed phrase.

Since the seedphrase is BIP 39 there's a set amount of words you can pick from whereas with a passphrase it's a bit different.

Basically, let's assume somebody got ahold of a seed phrase but not the passphrase. What would be a good password length to ensure they couldn't brute force it within reasonable amount of time

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If you're using a 24-word BIP-39 seed phrase, that encodes 256 bits of entropy. A passphrase also needs 256 bits of entropy to contribute the same level of security.

Estimating the entropy of a password is not straightforward, since it's not always obvious what the search space is, but if we limit ourselves to passwords generated in a well-defined way, some example password lengths can be given (rounded to nearest integer):

  • 77 random digits from 0 to 9
  • 54 random lowercase English characters
  • 45 random lowercase and uppercase English characters
  • 19 random words from a 10,000 long wordlist

If that sounds like a lot, it's because 256-bit security is very likely an overkill (see this answer on Information Security StackExchange). You might want to use a 12-word seed phrase, in which case you can cut the numbers above in half.

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  • Pefect, thank you. Was exactly the answer I was looking for Oct 21, 2021 at 4:56

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