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Bitcoin => Bitcoin Discussion => Topic started by: pbies on February 14, 2024, 07:13:10 AM



Title: What was the method? - Bitcoin puzzles
Post by: pbies on February 14, 2024, 07:13:10 AM
Guys,

if puzzles over 66 were found because of public keys available,
what was the process to find the private keys when knowing the pubkeys?

EDIT: what differs known public key and unknown for getting privkeys?

Thanks


Title: Re: What was the method? - Bitcoin puzzles
Post by: BlackBoss_ on February 14, 2024, 07:21:11 AM
if puzzles over 66 were found because of public keys available,
what was the process to find the private keys when knowing the pubkeys?
You can not find a private key from a public key just like can not find a public key from a public address.

Private key > Public Key > Public address. Two steps are all one way, you can not do the reversed steps.

Keys and addresses (https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch04_keys.adoc).
https://www.oreilly.com/api/v2/epubs/9781491902639/files/images/msbt_0401.png (https://www.oreilly.com/library/view/mastering-bitcoin/9781491902639/ch04.html?_gl=1*1raffl5*_ga*MjA2NTMzNzE0NC4xNzA3ODk1MzI1*_ga_092EL089CH*MTcwNzg5NTMyNS4xLjEuMTcwNzg5NTM0OS4zNi4wLjA.#private_public_keys)


Title: Re: What was the method? - Bitcoin puzzles
Post by: pbies on February 14, 2024, 07:30:21 AM
if puzzles over 66 were found because of public keys available,
what was the process to find the private keys when knowing the pubkeys?
You can not find a private key from a public key just like can not find a public key from a public address.

Private key > Public Key > Public address. Two steps are all one way, you can not do the reversed steps.

Keys and addresses (https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch04_keys.adoc).
https://www.oreilly.com/api/v2/epubs/9781491902639/files/images/msbt_0401.png (https://www.oreilly.com/library/view/mastering-bitcoin/9781491902639/ch04.html?_gl=1*1raffl5*_ga*MjA2NTMzNzE0NC4xNzA3ODk1MzI1*_ga_092EL089CH*MTcwNzg5NTMyNS4xLjEuMTcwNzg5NTM0OS4zNi4wLjA.#private_public_keys)

I know that.

Question was different, your answer is off-topic.


Title: Re: What was the method? - Bitcoin puzzles
Post by: apogio on February 14, 2024, 10:39:02 AM
Guys,

if puzzles over 66 were found because of public keys available,
what was the process to find the private keys when knowing the pubkeys?

EDIT: what differs known public key and unknown for getting privkeys?

Thanks

What are these puzzles you are refering to? I am not aware of puzzles like this, where you are given a public key and you need to derive the private key.

If an attacker wanted to find a private key from the corresponding public key, what they would need to do would be to solve the ECDLP. Check this post for further info by o_e_l_e_o: https://bitcointalk.org/index.php?topic=5393030.msg63258028#msg63258028

There is a very good tool discussed here: https://bitcointalk.org/index.php?topic=5244940.0



Title: Re: What was the method? - Bitcoin puzzles
Post by: BlackHatCoiner on February 14, 2024, 11:52:10 AM
what was the process to find the private keys when knowing the pubkeys?
As of today, there are two well-known algorithms for this process. Baby-step, giant-step, and Pollard’s rho.

EDIT: what differs known public key and unknown for getting privkeys?
In both BSGS and Pollard's rho, you need to perform operations on the elliptic curve, which requires to know the actual points involved. You can't run these algorithms based on the hash of the public key. And since both have time complexity O(sqrt(N)), you have an orders of magnitude advantage on working out private keys of known pubic keys.

You can not find a private key from a public key just like can not find a public key from a public address.
You can actually perform a reversal from public key to private by reversing the modular multiplications which produced the public key; it's just very computationally expensive, and considered infeasible for very long numbers like 256 bits. In mentioned puzzles, the puzzle makers have deliberately generated insecure keys, to encourage finders from attempting to break them. It's a smart way to know the progress in breaking the elliptic curve's security.

What are these puzzles you are refering to?
They're probably referring to these: https://bitcointalk.org/index.php?topic=5218972.0.



Here's a good article for everyone interested in the details to read: https://andrea.corbellini.name/2015/06/08/elliptic-curve-cryptography-breaking-security-and-a-comparison-with-rsa.


Title: Re: What was the method? - Bitcoin puzzles
Post by: pbies on February 14, 2024, 12:32:04 PM
What are these puzzles you are refering to? I am not aware of puzzles like this, where you are given a public key and you need to derive the private key.

https://privatekeys.pw/puzzles/bitcoin-puzzle-tx


Title: Re: What was the method? - Bitcoin puzzles
Post by: SamReomo on February 14, 2024, 02:35:24 PM
@OP I think you got the best answer by BlackHatCoiner and a satisfactory answer by apogio. I suggest you to lock this thread if you're satisfied with the answers and if you want to know more than make a comment here by asking them. Because allowing this topic to be opened won't be helpful since you got your answers. I highly suggest you to lock the thread.