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A while ago, I purchased Bitcoin and stored the corresponding 24-word private key. However, I am unable to recall the precise order of the words. I intentionally wrote them down in an unconventional manner to prevent potential theft if someone discovered my recovery sheet. Regrettably, I have now forgotten the correct order myself. It's frustrating.

The number of possible permutations is incredibly large! (24! = 620,448,401,733,239,439,360,000). Even if I were able to check one new permutation every second, it would still take millions of years...

So my question is: Have I calculated correctly? Is it practically impossible for me to retrieve my Bitcoin?

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    If you know like 7 or 8 of the right order from your 24-word mnemonic phrase and know some address that comes from your key and its path, then it is possible to recover your key back.
    – Romo
    Commented Jul 10, 2023 at 1:49
  • @Romo I'm afraid I may not possess enough bitcoin in that account to cover his expenses. Additionally, I'm perplexed as to why I am unable to select 24 random words from the BIP39 wordlist and gain entry to a new wallet on my Ledger/Trezor. It simply notifies me that the recovery sheet was incorrect. Shouldn't it instead grant access to an empty wallet? I assumed that all conceivable combinations from the wordlist would generate a functional wallet, independent of a hardware wallet generating the words for you. Perhaps there is some information there that could aid me in accessing my funds?
    – MyAlfred
    Commented Jul 10, 2023 at 23:46
  • ChatGPT helped me rewrite that comment. Just to make my points more clear
    – MyAlfred
    Commented Jul 10, 2023 at 23:49

2 Answers 2

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If you have a 24-word passphrase, without repeated words, and truly do not know the order anymore (as in: every order is equally likely), then it is practically infeasible to recover.

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  • And in that case there would be exactly 620,448,401,733,239,439,360,000 or 24! permutations right? Do i understand BIP39 correctly?
    – MyAlfred
    Commented Jul 9, 2023 at 20:46
  • Also is it just as hard to find/generate the public key/address. I don't remember how much Bitcoin there is in there.
    – MyAlfred
    Commented Jul 9, 2023 at 22:01
  • @MyAlfred Yes; perhaps it can be a bit less by taking the fact that BIP39 phrases have a checksum into account, but not much. And yes, if all you have is the phrase, computing the address requires finding the private key first. Commented Jul 9, 2023 at 22:12
  • @peter Alright. That makes sense! thanks
    – MyAlfred
    Commented Jul 9, 2023 at 22:15
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There are 24!=620,448,401,733,239,439,360,000 permutations, which is about 79 bits.

BIP39 phrases include 8 bits of checksum, but even computing that involves one SHA-256 hash per permutation. Modern GPUs achieve about 500 megahashes/sec, which would only get you 2^45 checks per day, taking more than 30 million cards*years just to calculate all checksums.

This unfortunately makes it safe to say it's absolutely infeasible to check every permutation.

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  • i suppose it would be difficult to hire a professional brute force it since i can't even prove how much bitcoin is in there since i don't know the public key?
    – MyAlfred
    Commented Jul 10, 2023 at 10:42
  • From a rough calculation using bitcoin network hash rate and block rewards, it would cost at least a double-digit number of bitcoins to produce that many hashes, just for the checksum calculations.
    – w123
    Commented Jul 10, 2023 at 10:58

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