Quote from: PrivatePerson on Today at 08:24:15 PM

How can knowledge of an even or odd point help in hacking secp256k1?

The method i posted is just a demonstration. It will not help. Since it takes as many operations as points scalar value.
The actual method will help you recover bits of private key(private key in binary format) from public key(point) in a matter of seconds.
And it was in the curve from the start. It is inverse of double-and-add scheme. And namely it is halve-and-subtract scheme.
Halving(point division) is multiplying by multiplicative inverse.
In our case we do Q=57896044618658097711785492504343953926418782139537452191302581570759080747169*Point (division by 2)
Subtraction is adding point by additive inverse of of point you are subtracting.
All these properties come from group theory.
If you wanna dig deep into bitcoin math prepare for some hard learning.