Are satoshis private keys easier to find than modern ones (given proper security in both cases)?

Question

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?

Answer 1

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.