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Ich bin oft in diesem Sub unterwegs, daher weiß ich, wie oft die Frage gestellt wird: “Wie hoch sind die Chancen/Wahrscheinlichkeit, dass jemand meine Startphrase errät?” Und wenn ich mich nicht irre, ist die Zahl etwas Astronomisches wie 2^256.
Aber ich habe noch nie jemanden gesehen, der die Frage im Sinne von “Wie hoch ist die Wahrscheinlichkeit, dass jemand JEDEN Seed-Phrase errät” beantwortet (nicht nur meine oder Ihre).
Und werden diese Wahrscheinlichkeiten nicht wahrscheinlicher, je mehr Leute Cold Wallets verwenden?
Schule dieser Anfänger pls
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First let’s talk about the odds of finding your seed phrase. Brute forcing wallets is impossible assuming true random number generation.
Why? Because even allowing for the checksum (which reduces the valid address space by 1/256), the odds of randomly finding your 24-word seed phrase by guessing 24 BIP39 words are approximately 1 in 1.16 x 10^77 . How hard is that to brute force? Well, if there were a supercomputer that could run through a trillion combinations per day, and the Earth had a billion such supercomputers all running 24/7 for 3 billion years, you would still only cover 10^33 combinations. So you need 10^44 such billion-supercomputer planets, or 100 million trillion trillion trillion such billion-supercomputer planets all running 24/7. Then if you just wait 3 billion years, you will finally have run through all the combinations. And the answer will be 42 🙂
*Clarifying expected value*
In fact the expected (mean) time to find a given wallet is precisely half the amount of time it would take to cover all the combinations, in this case 1.5 billion years average assuming you had access to 100 million trillion trillion trillion billion-supercomputer planets all running 24/7 for 1.5 billion years. However there is no guarantee after 1.5 billion, it may take up to 3 billion years before you are guaranteed to find it. And even if you did find it in 1.5 billion years, that is hardly any more feasible considering the impossible hardware requirements and having to wait 1.5 billion years to hopefully get lucky and find it early. I.e., it does not change the conclusion at all.
*Quantum computers*
Even the best quantum computers today would not put the slightest dent in the numbers quoted above.
“Google announced it has a quantum computer that is 100 million times faster than any classical computer in its lab.”
It is also important to note that that speed is for very specialized calculations optimized for quantum computing which brute forcing bip39 seed phrases probably would not fall into. But even if it did do this 100 million times faster, that doesn’t do shit against the numbers I’ve quoted above. Basically would change the final conclusion to something like this (dropping the leading 100 million):
If you had access to 1 billion of Google’s best quantum computer per planet, and somehow the brute force algorithm was optimized to take advantage of the 100 million factor speed boost, you would still need to run 1 trillion trillion trillion billion-supercomputer planets 24/7 for 3 billion years, instead of 100 million trillion trillion trillion such planets. Not any more feasible.
*Now, you want to consider the odds of finding any active seed phrase*
Just take 12 zeros off the above odds assuming there are 1 trillion wallets in use which of course there are not. This does not appreciably affect the above conclusions:
With Google’s best quantum computers looking for any active wallet you would still need to run 1 trillion trillion billion-supercomputer planets 24/7 for 3 billion years, instead of 100 million trillion trillion trillion such planets using conventional computers to find one wallet. And of course that assumes that the quantum computers are optimized for this problem which as we discussed above they currently are not. But even assuming that they are, this is not any more feasible even considering you would be happy to find anybody’s wallet not just your own.P.s. It is *possible* (optimistically) that this calculus could change within about 20 years, depending how development goes on quantum computers. However I would expect the Bitcoin developers to have updated the algorithms by then.
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Odds of guessing any phrase are still do small to prevent it from being seriously considered… There are only a few hundred million active addresses on Bitcoin+Eth, this is still nothing… (BTCRecover actually uses this property when trying to do a recovery where you don’t have any of the wallet addresses)
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Hello,
In order to make sure that the seed phrases generated by a Ledger are confidential, we have embedded a Random Number Generator (RNG) in the Secure Element. You can learn more about it [here](https://support.ledger.com/hc/en-us/articles/360010073520-Quality-of-randomness?docs=true)
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3blue1brown answers this very well:
In summary: Take a billion earths. Then pick a grain of sand from any of these earths. The chances of someone guessing your seed is still much much lower than two people picking the exact same grain of sand.
It’s not going to happen, no matter how many billions of people are picking sand for billions of years.
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