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I read that back then, you had entropies of 128 bit instead of 256. Like 12 vs 24 word mnemonic seed phrases. Are their wallets easier to brute force than other ones?

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The secp256k1 curve provides 128 bits of security, so as long as your source of entropy is good (indinsintguishable from uniformly random), anything over 128 bits gives you no benefit at all. I don't know which CSPRNGs were used back in the day and how they were seeded, but the fact that Satoshi's coins remain untouched to this day would indicate that the keys were in fact generated securely.

Side note, 24-word mnemonics aren't more secure that 12-word mnemonics either. As far as I'm aware, the reason for their existence is that you can safely type them into an untrusted device in a random order (as determined by a connected hardware wallet which itself has limited input capabilities). There are about 279 permutations of 24 words, which is a markedly lower security level than 128 bits, but still out of reach in the foreseeable future for all but the most dedicated attackers, and can be further improved by typing in a few words not part of the original mnemonic. Compare that with 12 words which only have 479,001,600 (about 229) permutations, trivially crackable on any modern PC.

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  • This is correct, 24 word would only be more difficult to crack if you actually had to crack the words. The attack is to find a private key given a public key, and the public key as you suggested provides 128bit security on the 256k curve. bitcoin.stackexchange.com/questions/110145/… bitcoin.stackexchange.com/questions/117348/…
    – Poseidon
    Apr 28, 2023 at 1:28
  • Thanks for this answer. I don't really understand it thoug. It sounds like you could rather just go with 12 words. I thought it had something to do with anyone knowing your public key, having it easier to get to your private key (brute force, but with less tries). Why 2<sup>79</sup>? I understand 2048<sup>24</sup> (BIP 39).
    – codepleb
    May 1, 2023 at 22:13
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    24! ≈ 2^79 (the number of permutations of 24 words). May 1, 2023 at 22:45
  • Why 24!? You can have words twice in a BIP39 seed phrase.
    – codepleb
    May 4, 2023 at 8:59
  • Yes, for a seed phrase with repeated words the number of distinct permutations of its words will be lower. Jan 3 at 16:13

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