Quote from: saelea on January 02, 2025, 10:11:01 PM

I have one question regarding obtaining private key from public key knowing the range of private key from puzzle:

What makes retrieval of private key MUCH faster than bruteforcing when you know public key? No need to perform SHA256 and RIPEMD160 during bruteforce? If only those steps helps to make bruteforcing faster then elliptic curve DLP is questionable. What other hints could be retrieved with public key?

DLP is a sqrt(N) steps problem. Brute-forcing is a N steps problem.

Once you have a pubKey you can immediately compute the pubKey of the next private key, or the previous one, or the one that comes 10.000 quadrillion private keys later, and so on, all without ever needing to know what the private key is. This leads to algorithms that solve the thing in around square root number of steps, so not just "much faster" but rather "split the digits of the number of steps in two equal parts, and keep just some half" faster. With brute-force, this is totally impossible, you can never compute the address obtained from the hashing of the key that's next to the unknown key, or any other key, you have exactly zero mathematical relationships that can speed up your attack, it's just wasting power on hashing data blindly until an exact match.