Hey mere mortal here, How does one reply to the perceived (valid or not) risk of brute forcing private keys from signed transactions which is related to ECDSA right?
Is this FUD? Any clarity on this would be welcome.
Read this: Elliptic Curve Cryptography: a gentle introduction
It's a REALLY good 4 part series. You will enjoy it a lot.
You will read it and you will think "holy cow, that's why my corn is safe!". And "elliptic curves are so siccc". And "Goddamn Satoshi!".
If you don't have time right now, then read it tomorrow. Whatever you do, read it.
https://andrea.corbellini.name/2015/05/17/elliptic-curve-cryptography-a-gentle-introduction/?s=09
Discussion
Reply: It's not possible.
However, if you reuse your nonce, you're rekt and it's easy to derive your private key.