So, the only way to get the private key of a public key, is simple guessing it/brute forcing it - Which can take forever to compute at some key ranges.
But What if we could reduce the key range? For example, if a public key is even, you can multiply it by 57896044618658097711785492504343953926418782139537452191302581570759080747169
And get a new public key, which is in the original range -1-bit range, which its private key is / 2 the value of the original private key.
And you can also use other methods to reduce the public key ranges even more, using only pure math.
I'd like this topic to be a home for new math tricks for making secp256k1 easier to brute force, mainly for the bitcoin puzzle transaction.
Thanks! Gilad.
In as much as the public key is formed from the private key. The
algebraic expressions used to form this cannot be reserved to make for the former. This is because the process goes through a hash before it creates public address. It is therefore not visible for any mathematical "trick" to perform such hack.